Simplest whip-ring combined antenna radar detection method, system and device based on MIMO equivalent vector array

Abstract

The application discloses a kind of based on MIMO equivalent vector array's minimal whip ring combination antenna radar detection method, system and device, belong to MIMO radar and radio direction finding technical field.The method is by two transceiving whip antennas, emits mutually orthogonal two-way MIMO waveforms, and by two-way whip antenna receiving channel and two normal orthogonal ring antennas receiving channel synchronous acquisition four-way physical receiving sequence;Based on transmission-reception channel joint complex response calibration data, construct effective reference sequence, form eight-dimensional first equivalent observation vector and corresponding eight-dimensional first calibration response vector by reference correlation matrix joint demixing.The application can reduce the consistency of observation data and calibration array response while reducing the number of physical antennas, can reduce the model mismatch caused by repeated channel combination, improve the stability and flexibility of minimal MIMO radar direction finding.

Description

Technical Field

[0001] This invention relates to the field of antenna radar detection technology, and specifically to a method, system, and device for radar detection using a minimalist whip-loop combined antenna based on a MIMO equivalent vector array. Background Technology

[0002] Radar target detection and direction finding technologies are widely used in scenarios such as low-altitude surveillance, UAV detection, close-range early warning, and portable reconnaissance. Existing phased array radars typically increase the number of physical antenna elements and radio frequency transceiver channels to create a larger effective aperture, thereby improving target detection gain and angular resolution. However, as the number of elements increases, the antenna feed network, radio frequency channels, synchronization circuits, and calibration links become more complex, leading to increased system size, power consumption, and cost, which is detrimental to miniaturization, low cost, and rapid deployment.

[0003] MIMO radar transmits separable waveforms through multiple transmit channels. At the receiver, matching or correlation processing is performed on the echo components corresponding to different transmitted waveforms. Multiple theoretically equivalent observation channels can be formed by combining the transmit and receive arrays, thereby expanding the virtual array aperture while reducing some physical array elements. Existing MIMO radars mostly use homogeneous antennas to form uniform arrays, and their virtual channels are usually constructed according to ideal transmit and receive array manifolds. For heterogeneous receive arrays composed of whip antennas and loop antennas, the frequency response, group delay, directional response, and installation status of different antennas vary. The complex baseband response formed by the same transmitted waveform after passing through different physical receive links is not completely consistent. Directly using ideal waveforms for channel separation can easily introduce amplitude and phase deviations into the obtained equivalent observations.

[0004] Furthermore, in a few-element MIMO structure, different transmit-receive combinations may form the same or approximately the same equivalent phase center. Existing processing methods typically involve directly discarding, summing, or averaging repeated channels based on their virtual positions. However, actual repeated channels pass through independent transmit and receive links, and even if their spatial response positions are the same, they may still have different complex gains, phase errors, and noise characteristics. If the joint complex responses of different theoretical equivalent channels within the actual operating direction range are not determined and directly merged, it can easily lead to a mismatch between the dimensionality-reduced observation data and the theoretical array response model, thereby affecting the accuracy of array direction finding methods such as beamforming and subspace spectrum estimation. Cross-loop direction finding can obtain direction-dependent vector responses using two mutually orthogonal loop antennas, which has the advantages of fewer antennas and simpler structure. However, traditional cross-loop direction finding is usually based on a model where two physical loop antennas directly receive the same incoming wave. When the loop antenna receiving channel participates in the construction of the MIMO virtual array, the corresponding equivalent observations also include the directional response, propagation phase, and channel complex response of the corresponding transmit channel, and therefore cannot be simply processed according to the traditional physical cross-loop model. Meanwhile, virtual loop observation and multi-channel array direction finding originate from the same set of physical received data. If different amplitude and phase references or calibration models are used for the two, it may lead to systematic deviations between the two types of direction finding results. Summary of the Invention

[0005] The purpose of this invention is to provide a simplified whip-loop combined antenna radar detection method, system, and device based on MIMO equivalent vector array, thereby solving the problems existing in the prior art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a simplified whip-loop combined antenna radar detection method based on a MIMO equivalent vector array, comprising: S1. Two mutually orthogonal MIMO waveforms are transmitted through two whip antennas, and four physical reception sequences are synchronously acquired through two whip antenna receiving channels and two loop antenna receiving channels. S2. Based on the pre-acquired joint complex response calibration data of the transmit-receive channel, construct the effective reference sequence corresponding to the two MIMO waveforms. Based on the effective reference sequence, form a reference correlation matrix. Jointly unmix the transmit components in the four physical receive sequences to obtain eight theoretical equivalent observations and form an eight-dimensional first equivalent observation vector and the corresponding eight-dimensional first calibration response vector. S3. Based on the equivalent phase center and response type of each theoretical equivalent observation channel, determine the candidate repeating channels, and based on the eight-dimensional first calibration response vector, determine whether the joint complex response of the candidate repeating channels meets the preset proportional consistency condition. The candidate repeating channels that meet the condition are determined as mergeable repeating channels. S4. Based on the complex response ratio between mergeable repeatable channels, perform amplitude alignment and coherent merging to construct a seven-row, eight-column equivalent channel transformation matrix. Then, use the same equivalent channel transformation matrix to transform the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector to obtain the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector. S5. The equivalent channels of two loop antennas with the same equivalent phase center but different response types are retained as virtual orthogonal loop observation pairs. The first target direction estimate is obtained based on the virtual orthogonal loop observation pairs and their calibration responses. The array direction is then performed based on the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector to obtain the second target direction estimate.

[0007] Specifically, S1 includes: The first and second transmission sequences are generated according to the preset pulse timing and encoding parameters, and then a MIMO transmission sequence matrix is ​​formed. Calculate the maximum normalized cross-correlation coefficient between the first and second transmission sequences and compare it with a preset orthogonality threshold. When the maximum normalized cross-correlation coefficient is greater than the orthogonality threshold, adjust the coding parameters or reselect the transmission sequence until the orthogonality condition is met. The first and second transmission sequences that satisfy the orthogonality condition are mapped to the two transmission channels respectively, and the two whip antennas are controlled to transmit the corresponding MIMO waveforms according to a unified clock and trigger sequence, while generating a receive sampling control vector. Complex baseband data from two whip antenna receiving channels and two loop antenna receiving channels are synchronously acquired based on the receiving sampling control vector, and arranged according to the channels to form a four-channel receiving sequence matrix to obtain four physical receiving sequences.

[0008] Specifically, S2 includes: The reference complex transfer function and the joint directional complex response calibration model that vary with the candidate direction are extracted from the joint complex response calibration data. The reference complex transfer function is used to perform amplitude and phase compensation on the two MIMO waveforms to generate a valid reference sequence. Two valid reference sequences corresponding to the same receiving channel are combined to form a reference sequence matrix, and a reference correlation matrix is ​​constructed based on the product of the conjugate transposes of the reference sequence matrices. Based on the condition number of the reference correlation matrix and the preset stability threshold, an inverse matrix or a regularized inverse matrix is ​​selected to form the emission component demixing matrix; The four physical received sequences were correlated with the corresponding reference sequence matrices, and four sets of two-element equivalent observation vectors were obtained using the transmit component unmixing matrix. Four sets of two-element equivalent observation vectors are spliced ​​together according to the transmit-receive channel index to form an eight-dimensional first equivalent observation vector, and an eight-dimensional first calibration response vector varying with the candidate direction is constructed from the joint directional complex response calibration model according to the same index.

[0009] Specifically, S3 includes: Calculate the equivalent position vector of each theoretical equivalent observation channel based on the transmit phase center and receive phase center, and configure the corresponding response type label; Theoretical equivalent observation channels with equivalent location distances less than a preset location threshold and the same response type are grouped into candidate duplicate channel pairs. The candidate repeated channel pairs are extracted from the eight-dimensional first calibration response vector to obtain the first complex response sequence and the second complex response sequence under multiple calibration directions, and the least squares proportional fitting is used to determine the complex alignment coefficient that minimizes the residual of the two complex response sequences. The normalized proportional fitting residual between the two complex response sequences is calculated based on the complex alignment coefficient. The normalized proportional fitting residual is used as the joint response consistency feature and compared with the preset consistency threshold. Candidate duplicate channel pairs whose joint response consistency feature is not greater than the consistency threshold are identified as mergeable duplicate channels, and the corresponding channel index and realignment coefficient are output.

[0010] Specifically, S4 includes: Read the index of the mergeable repeating channels and the complex alignment coefficient, and determine the complex magnitude relative alignment parameter of the mergeable repeating channels; The real non-negative merging weights of the corresponding repeating channels are determined based on the targetless distance cell, calibration data, or noise statistics within the current coherent processing cycle, and the merging weights remain unchanged within the same coherent processing cycle. Write the complex amplitude relative alignment parameters and merging weights into the matrix elements corresponding to the repeating channels, and construct a seven-row, eight-column equivalent channel transformation matrix by combining the mapping relationship of the other non-repeating channels. By multiplying the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector by the same equivalent channel transformation matrix, the amplitude alignment, coherence merging and channel dimensionality reduction of the repeated channels are completed in one step, resulting in the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector. The seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector are stored according to a unified channel index.

[0011] Specifically, S5 includes: Based on the channel index, two loop antenna equivalent channels are extracted from the seven-dimensional second equivalent observation vector to form a virtual orthogonal loop observation vector; Extract the corresponding components from the seven-dimensional second calibration response vector to establish a virtual loop calibration response vector that varies with the candidate direction; Calculate the normalized complex matching feature between the virtual orthogonal loop observation vector and the virtual loop calibration response vector to form a first direction matching sequence, and determine the first target direction estimate based on its peak value; An array snapshot matrix is ​​constructed using the continuous seven-dimensional second equivalent observation vectors of the same range-Doppler target detection unit. The seven-channel noise covariance matrix is ​​estimated based on the absence of a target detection unit. After normalizing the array observation data and the corresponding seven-dimensional second calibration response vector with the same source noise, beamforming or subspace spectrum estimation is performed to form a second directional spectrum sequence. The second target direction estimate is determined based on the effective spectral peaks of the second direction spectral sequence, and the first target direction estimate and the second target direction estimate are associated with the same target detection unit.

[0012] The present invention also provides a system applicable to the aforementioned simplified whip loop combined antenna radar detection method based on MIMO equivalent vector array, comprising two transmit and receive shared whip antennas, two dedicated receive loop antennas with mutually orthogonal normal axes, a transmitter, a receiver, a synchronization module, and a signal processing module; Two whip antennas are used to transmit two mutually orthogonal MIMO waveforms respectively, and together with two loop antennas, they form four physical receiving channels; The receiver is used to synchronously acquire four physical receive sequences; The signal processing module is used to construct an effective reference sequence for two MIMO waveforms based on the joint complex response calibration data of the transmit-receive channels. It forms a reference correlation matrix based on the effective reference sequence and performs joint demixing on the four physical received sequences to form an eight-dimensional first equivalent observation vector and a corresponding eight-dimensional first calibration response vector. Based on the equivalent phase center, response type, and joint complex response consistency of each theoretical equivalent observation channel, it determines the channels that can be merged and repeat. Based on the complex response ratio of the channels that can be merged and repeat, it constructs a seven-row, eight-column equivalent channel transformation matrix. Using the same equivalent channel transformation matrix, it transforms the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector to obtain a seven-dimensional second equivalent observation vector and a seven-dimensional second calibration response vector. The signal processing module is also used to retain the equivalent channels of two loop antennas with different response types at the same equivalent phase center as virtual orthogonal loop observation pairs, obtain the first target direction estimate based on the virtual orthogonal loop observation pairs, and obtain the second target direction estimate based on the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector.

[0013] The signal processing module includes a calibration parameter storage unit and a MIMO demixing unit; The calibration parameter storage unit is used to store the joint complex response calibration data corresponding to each transmit-receive channel combination; The MIMO demixing unit is used to form a reference sequence matrix from two valid reference sequences corresponding to the same physical receiving channel, construct a reference correlation matrix based on the product of the conjugate transpose of the reference sequence matrix, and form a transmit component demixing matrix based on the reference correlation matrix to convert the four physical receiving sequences into four sets of two-element equivalent observation vectors, and form an eight-dimensional first equivalent observation vector according to the transmit channel-receive channel index.

[0014] The signal processing module also includes a channel determination unit and an equivalent channel transformation unit; The channel determination unit is used to determine candidate repeating channels based on the equivalent phase center and response type, calculate the joint complex response consistency characteristics of the candidate repeating channels based on the eight-dimensional first calibration response vector, and compare the joint complex response consistency characteristics with a preset consistency threshold to determine the repeating channels that can be merged. The equivalent channel transformation unit is used to determine the complex alignment coefficients based on the complex response ratio between mergeable repeatable channels, and to construct a seven-row, eight-column equivalent channel transformation matrix in combination with real non-negative merging weights, so that the observed data and the calibration response model are synchronously transformed from eight-dimensional to seven-dimensional according to the same complex amplitude and phase reference.

[0015] Furthermore, the present invention also provides an apparatus applicable to the aforementioned simplified whip-loop combined antenna radar detection method based on MIMO equivalent vector array, comprising a data interface, a memory, and a processor. The data interface is used to receive four physical reception sequences obtained from two whip antenna receiving channels and two loop antenna receiving channels. The memory stores joint complex response calibration data and program instructions for the transmit-receive channels. When the processor executes program instructions, it is used to: jointly demix the two MIMO transmit components in the four physical receive sequences based on the joint complex response calibration data to form an eight-dimensional first equivalent observation vector and an eight-dimensional first calibration response vector; Based on the equivalent phase center, response type, and joint complex response consistency, the repeatable channels that can be merged are determined. An equivalent channel transformation matrix is ​​constructed, and the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector are transformed simultaneously to obtain the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector. The first direction finding process is performed based on the virtual orthogonal loop observation pair, and the second direction finding process is performed based on the seven-dimensional second equivalent observation vector.

[0016] As can be seen from the above technical solution, the present invention has the following beneficial effects: This invention constructs a simplified MIMO transceiver structure using two shared whip antennas and two normally orthogonal loop antennas, reducing the number of physical antennas and RF channels while forming eight theoretically equivalent observation channels. An effective reference sequence is constructed based on the joint complex response calibration data of the transmit-receive channels, and a reference correlation matrix is ​​used to jointly demix different transmit components, reducing the impact of response differences between the whip and loop antennas and the non-ideal orthogonality of the MIMO waveform on the amplitude-phase consistency of the equivalent observations. Furthermore, by identifying and merging duplicate channels based on the equivalent phase center, response type, and joint complex response ratio consistency, coherent merging is performed after amplitude alignment, avoiding the equivalent phase reference deviation caused by directly merging based solely on virtual positions. By synchronously transforming the observation data and calibrating the response model using the same equivalent channel transformation matrix, the seven-dimensional equivalent observation data is kept consistent with the corresponding array manifold, which helps reduce model mismatch and direction-finding bias caused by channel compression. Meanwhile, by retaining the equivalent channels of two loop antennas at the same location but with different response types as a virtual orthogonal loop observation pair, both vector loop direction finding and seven-channel array direction finding can be taken into account on the same set of baseband data. This improves the stability, flexibility and engineering applicability of direction finding processing while maintaining the system's miniaturization and low hardware complexity. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a timing diagram of the present invention; Figure 3 This is a schematic diagram illustrating the generation of the 2-transmit 4-receive MIMO equivalent array unit and the merging of duplicate channels in this invention; Figure 4 This is a comparison chart of the unmixing performance when the waveform orthogonality of the present invention decreases; Figure 5 This is a comparison chart showing the change in direction-finding accuracy of the present invention with the signal-to-noise ratio; Figure 6 This is a comparison diagram of the direction spectrum of three direction finding processes when SNR=15dB in this invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Example 1: like Figure 1 , Figure 2 and Figure 3As shown, this invention provides a technical solution: a simplified whip-loop combined antenna radar detection method based on a MIMO equivalent vector array, comprising: S1. Two mutually orthogonal MIMO waveforms are transmitted through two whip antennas, and four physical reception sequences are synchronously acquired through two whip antenna receiving channels and two loop antenna receiving channels. S2. Based on the pre-acquired joint complex response calibration data of the transmit-receive channel, construct the effective reference sequence corresponding to the two MIMO waveforms. Based on the effective reference sequence, form a reference correlation matrix. Jointly unmix the transmit components in the four physical receive sequences to obtain eight theoretical equivalent observations and form an eight-dimensional first equivalent observation vector and the corresponding eight-dimensional first calibration response vector. S3. Based on the equivalent phase center and response type of each theoretical equivalent observation channel, determine the candidate repeating channels, and based on the eight-dimensional first calibration response vector, determine whether the joint complex response of the candidate repeating channels meets the preset proportional consistency condition. The candidate repeating channels that meet the condition are determined as mergeable repeating channels. S4. Based on the complex response ratio between mergeable repeatable channels, perform amplitude alignment and coherent merging to construct a seven-row, eight-column equivalent channel transformation matrix. Then, use the same equivalent channel transformation matrix to transform the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector to obtain the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector. S5. The equivalent channels of two loop antennas with the same equivalent phase center but different response types are retained as virtual orthogonal loop observation pairs. The first target direction estimate is obtained based on the virtual orthogonal loop observation pairs and their calibration responses. The array direction is then performed based on the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector to obtain the second target direction estimate.

[0020] In the above scheme, two whip antennas constitute the first and second transmission channels, respectively. The first transmission channel transmits a first MIMO waveform, and the second transmission channel transmits a second MIMO waveform. The two transmitted waveforms satisfy a preset orthogonality condition. The two whip antenna receiving channels and the two loop antenna receiving channels acquire echo signals according to the same synchronization reference, thus forming four physical receiving sequences. The four physical receiving sequences are recorded using a unified sampling timing sequence, ensuring a definite time correspondence between different physical receiving channels and enabling the complex amplitude and phase relationships of each receiving channel to be uniformly processed according to the calibration results.

[0021] In the above scheme, each physical receiving sequence simultaneously contains the echo components corresponding to the first and second transmitting channels. Therefore, one physical receiving channel corresponds to two transmit-receive combinations, and four physical receiving channels correspond to a total of eight transmit-receive combinations. By extracting the echo components belonging to the first and second transmitting channels from each physical receiving sequence, eight theoretical equivalent observations can be obtained from the four physical receiving sequences. Each theoretical equivalent observation corresponds to a specific transmitting channel and a specific receiving channel, thus establishing eight theoretical equivalent observation channels.

[0022] In the above scheme, the transmit and receive links will produce definite amplitude, phase, and transmission delay changes in the signal. To ensure that the reference signal used for demixing the transmit components is consistent with the actual radar channel, the transmit-receive combinations formed by each transmit and receive channel are calibrated before target detection to obtain joint complex response calibration data corresponding to each transmit-receive combination. The joint complex response calibration data is used to characterize the amplitude and phase changes jointly generated by the corresponding transmit and receive links.

[0023] In the above scheme, for the first transmitted waveform, the transmitted waveform is combined with the joint complex response calibration data corresponding to the first transmitted channel and each received channel to obtain the valid reference sequence of the first transmitted waveform in each received channel; for the second transmitted waveform, the same processing method is used to obtain the valid reference sequence of the second transmitted waveform in each received channel. Thus, each physical received channel has two valid reference sequences corresponding to its actual transmit-receive link, one corresponding to the first transmitted channel and the other corresponding to the second transmitted channel.

[0024] Furthermore, for any physical receiving channel, the valid reference sequences corresponding to the first transmitted waveform and the second transmitted waveform are arranged according to a unified sampling interval. The correlation results between the first valid reference sequence and itself, the second valid reference sequence and itself, the first valid reference sequence and the second valid reference sequence, and the second valid reference sequence and the first valid reference sequence are calculated respectively. These correlation results are combined according to a preset positional relationship to form the reference correlation matrix corresponding to that physical receiving channel.

[0025] In the above scheme, the reference correlation matrix is ​​used to simultaneously describe the energy relationship of the two valid reference sequences themselves and the cross-correlation relationship between the two valid reference sequences. When demixing the transmitted components, the two transmitted components are not calculated independently, but the two valid reference sequences and their cross-correlation relationship are included in the solution process, so that the deterministic correlation relationship generated by the two transmitted waveforms after passing through the actual transmit link and receive link participates in the demixing.

[0026] In the above scheme, for any physical received sequence, the complex correlation results between the physical received sequence and the two effective reference sequences are first calculated to obtain two correlation observation results corresponding to the two transmitted waveforms. Then, the two correlation observation results are jointly corrected using the reference correlation matrix. During the joint correction process, based on the autocorrelation results of each of the two effective reference sequences and the cross-correlation results between the two effective reference sequences, the coupling component caused by the correlation of the reference sequences between the two correlation observation results is eliminated, ultimately obtaining the theoretical equivalent observations corresponding to the first and second transmitted channels.

[0027] In the above scheme, when the reference correlation matrix satisfies the preset direct solution conditions, the corresponding inverse transformation relationship is obtained based on the four correlation results in the reference correlation matrix. This inverse transformation relationship is then used to perform a joint transformation on the two correlated observation results to obtain the two emission components. When the reference correlation matrix does not satisfy the preset direct solution conditions, joint unmixing is performed according to a pre-determined matrix generalized inverse processing method or regularization processing method. When using regularization processing, a pre-determined regularization adjustment amount is added to the main diagonal position of the reference correlation matrix before performing the joint solution. The target observation data and calibration data use the same solution method and the same regularization adjustment parameters.

[0028] In the above scheme, the four physical received sequences undergo the aforementioned joint demixing process, resulting in two theoretical equivalent observations for each physical received sequence, thus forming a total of eight theoretical equivalent observations. These eight theoretical equivalent observations are arranged according to a predetermined rule to form an eight-dimensional first equivalent observation vector. This arrangement rule follows a fixed combination order of the transmit and physical receive channels and remains unchanged during subsequent calibration, duplicate channel identification, channel merging, and array direction finding.

[0029] The pre-acquired calibration data is processed using the same effective reference sequence construction method, reference correlation matrix construction method, transmitted component joint demixing method, and channel arrangement method as the target echo, resulting in eight calibration complex responses corresponding one-to-one with the eight theoretical equivalent observation channels. Following the same channel arrangement order as the eight-dimensional first equivalent observation vector, the eight calibration complex responses are combined into an eight-dimensional first calibration response vector. Therefore, each observation channel in the eight-dimensional first equivalent observation vector has a definite corresponding calibration response channel.

[0030] In the above scheme, the equivalent phase center of each theoretical equivalent observation channel is determined based on the positions of the transmitting whip antenna and the receiving antenna corresponding to that channel. The equivalent phase center represents the spatial phase sampling position corresponding to the transmit-receive combination. Simultaneously, the response type of the theoretical equivalent observation channel is determined based on the type of receiving antenna forming the channel and the directional response characteristics corresponding to that antenna.

[0031] In the above scheme, the equivalent phase centers and response types of eight theoretical equivalent observation channels are compared sequentially. When the positional difference between the equivalent phase centers of two theoretical equivalent observation channels meets the preset spatial tolerance, and the two theoretical equivalent observation channels have the same response type, these two theoretical equivalent observation channels are identified as candidate repeating channels. When the response types of two theoretical equivalent observation channels are different, these two theoretical equivalent observation channels are not identified as candidate repeating channels.

[0032] In the above scheme, for a given candidate repeat channel, the corresponding calibration complex response in the eight-dimensional first calibration response vector is used to further determine whether the two candidate repeat channels have a consistent complex response ratio. Specifically, for each pre-set calibration state, the calibration complex responses of the first and second candidate repeat channels under the same calibration state are obtained.

[0033] In the above scheme, one candidate repeating channel is used as the reference channel. The calibrated complex response of the reference channel under each calibration state is compared with the calibrated complex response of the other candidate repeating channel under the corresponding calibration state. First, the complex response ratio that minimizes the sum of squares of the complex response differences between the two candidate repeating channels under all calibration states is calculated. This complex response ratio includes both the amplitude ratio and the phase difference between the two candidate repeating channels.

[0034] Specifically, after obtaining the complex response ratio, the calibration complex response of the reference channel in each calibration state is multiplied by the complex response ratio to obtain the corresponding predicted complex response. Then, each predicted complex response is subtracted from the actual calibration complex response of another candidate repeating channel in the same calibration state to obtain the complex response residual for each calibration state. The squares of the amplitudes of each complex response residual are summed, and the summation is normalized using the sum of the squares of the calibration complex response amplitudes of the other candidate repeating channel in all calibration states to obtain the consistency judgment result of the complex response ratios among the candidate repeating channels.

[0035] In the above scheme, the result of the complex response ratio consistency judgment is compared with a preset ratio consistency threshold. When the result of the complex response ratio consistency judgment is not greater than the preset ratio consistency threshold, it is determined that the two candidate duplicate channels meet the preset ratio consistency condition, and the two candidate duplicate channels are determined as mergeable duplicate channels. When the result of the complex response ratio consistency judgment is greater than the preset ratio consistency threshold, it is determined that the two candidate duplicate channels do not meet the preset ratio consistency condition, and the two channels are retained separately.

[0036] In the above scheme, for the determined mergeable repeatable channels, amplitude alignment is performed based on the complex response ratio calculated above. Using one of the mergeable repeatable channels as the alignment reference, the observed amplitude of the other mergeable repeatable channel is adjusted according to the amplitude ratio between the two channels, and the observed phase of the other mergeable repeatable channel is rotated according to the phase difference between the two channels, so that the two channels are transformed to the same complex response reference reference.

[0037] In the above scheme, coherent merging is performed on two repeatable channels that have achieved amplitude alignment. During coherent merging, the theoretical equivalent observation of the reference channel is multiplied by a pre-determined first merging weight, and the theoretical equivalent observation of the other channel that has achieved amplitude alignment is multiplied by a pre-determined second merging weight. The two weighted complex observations are then added together to obtain a merged equivalent observation. The first and second merging weights are determined during the system configuration phase and remain consistent throughout the processing of the target observation data and the corresponding calibration data.

[0038] In the above scheme, a set of duplicate channels that can be merged is determined from the eight theoretical equivalent observation channels. Two theoretical equivalent observation channels in this set are merged into one equivalent observation channel, and the remaining six theoretical equivalent observation channels are retained, thus forming seven second equivalent observation channels. Based on the correspondence between the six retained channels and the merged channel, a seven-row, eight-column equivalent channel transformation matrix is ​​constructed.

[0039] In the above scheme, each row of the seven-row, eight-column equivalent channel transformation matrix corresponds to a second equivalent observation channel. For the theoretically equivalent observation channel that is directly retained, a determination coefficient for extracting the theoretically equivalent observation quantity is set at the corresponding position, and the remaining positions are set to zero. For the merged channel formed by two mergeable repeatable channels, complex transformation coefficients corresponding to the amplitude alignment relationship and the merging weight are set at the positions corresponding to the two mergeable repeatable channels, respectively, and the remaining positions are set to zero.

[0040] In the above scheme, an eight-dimensional first equivalent observation vector is transformed using a seven-row, eight-column equivalent channel transformation matrix. During the transformation, according to the channel selection coefficients and complex merging coefficients specified in each row of the matrix, the eight theoretical equivalent observations are extracted, their amplitude and phase are adjusted, and they are weighted and summed accordingly, ultimately yielding seven second equivalent observations, which are then arranged into a seven-dimensional second equivalent observation vector according to a preset channel order.

[0041] In the above scheme, the eight-dimensional first calibration response vector is transformed using an identical seven-row, eight-column equivalent channel transformation matrix. During the transformation, the same channel selection positions, amplitude-phase adjustment relationships, and weighted merging coefficients as the target observation data are used to obtain seven second calibration responses. These responses are then arranged in the same channel order as the seven-dimensional second equivalent observation vector to form the seven-dimensional second calibration response vector. Therefore, each channel in the seven-dimensional second equivalent observation vector has the same channel formation process as the corresponding channel in the seven-dimensional second calibration response vector.

[0042] In the above scheme, for the theoretical equivalent observation channel formed by the loop antenna, its equivalent phase center and response type are determined respectively. When the equivalent phase centers of the two loop antenna equivalent channels are the same and the response types of the two loop antenna equivalent channels are different, the two loop antenna equivalent channels are not merged as duplicate channels, but are retained separately and formed into virtual orthogonal loop observation pairs.

[0043] In the above scheme, the two equivalent channels of the virtual orthogonal loop observation pair correspond to the same equivalent phase center, thus they have the same spatial phase center relationship. Simultaneously, since they have different response types, when the target echo is incident from different directions, the two equivalent channels of the loop antennas generate complex amplitude and phase changes corresponding to their respective response types. By comparing the joint complex response relationship between the two equivalent channels of the loop antennas, the directional features corresponding to the target direction can be extracted.

[0044] In the above scheme, the calibration response corresponding to the virtual orthogonal loop observation pair is obtained in advance for each candidate target direction. During target detection, for each candidate target direction, the two loop calibration complex responses corresponding to the candidate direction are respectively subjected to complex correlation calculation with the two actual observation complex responses in the current virtual orthogonal loop observation pair. The complex correlation results of the two channels are then jointly accumulated and normalized according to the total energy of the calibration response and the total energy of the actual observation to obtain the loop observation matching result corresponding to the candidate target direction.

[0045] In the above scheme, the loop observation matching process is performed on all candidate target directions within a preset direction range, and the matching results corresponding to each candidate target direction are compared. The candidate target direction corresponding to the maximum value of the matching result is determined as the first target direction estimate. The first target direction estimate is jointly determined by the virtual orthogonal loop observation pair and its corresponding calibration response.

[0046] In the above scheme, the seven-dimensional second equivalent observation vector is used to obtain the second target direction estimate. The corresponding seven-dimensional second calibration response is pre-obtained for each candidate target direction. For a candidate target direction, the seven calibration complex responses corresponding to that candidate target direction are respectively subjected to conjugate correlation calculations with the seven actual observed complex responses in the seven-dimensional second equivalent observation vector, and then the correlation results corresponding to the seven channels are accumulated.

[0047] In the above scheme, the amplitude of the accumulated result is energy-calculated, and normalized using the total energy of the seven calibrated complex responses corresponding to the candidate target direction and the total energy of the seven actual observed complex responses to obtain the array matching result corresponding to the candidate target direction. The array matching results of all candidate target directions within the preset direction range are calculated in the same way, and the candidate target direction corresponding to the maximum value of the array matching result is determined as the second target direction estimate.

[0048] Specifically, the first target direction estimate is obtained using the joint complex response relationship between two different loop antenna response types at the same equivalent phase center, and the second target direction estimate is obtained using the overall array response relationship between the seven second equivalent observation channels and the corresponding seven second calibration response channels. Both direction estimation processes use the pre-acquired calibration response as the direction matching reference and maintain the determined channel correspondence between the target observation data and the calibration response data.

[0049] Therefore, the four physical receiving sequences are demixed to obtain two transmit components, forming eight theoretical equivalent observations. Candidate repeating channels are selected based on the equivalent phase center and response type of the eight theoretical equivalent observation channels, and the ratio of complex responses between the candidate repeating channels is judged by the corresponding calibration complex response to determine whether they meet the preset consistency condition. After completing the amplitude alignment and coherent merging of the two repeating channels that meet the condition, the eight theoretical equivalent observation channels are converted into seven second equivalent observation channels. At the same time, two loop antenna equivalent channels with the same equivalent phase center and different response types are retained as virtual orthogonal loop observation pairs to obtain the first target direction estimate and the second target direction estimate, respectively.

[0050] To verify the invention, four sets of experiments were designed, such as... Figure 4-6 As shown, Experiment 1: Channel expansion and hardware resource comparison, equivalent number of observation channels / number of RF channels; Experiment 2: Direction finding accuracy as a function of signal-to-noise ratio, direction finding RMSE and consistency of dual estimators; Experiment 3: Comparison of repeated channel merging methods, direction finding root mean square error RMSE; Experiment 4: Demixing performance under decreased waveform orthogonality, and signal-to-interference ratio (SIR) after demixing.

[0051] All experiments were conducted using single-target measurements in an anechoic chamber with offline baseband processing. The data were calibrated using a conventional vector network analyzer, acquired using a signal source and oscilloscope / acquisition card, and processed using MATLAB. The experiments did not involve high-risk aspects such as field flight or electromagnetic compatibility, and all data were actually measured.

[0052] Table 1 Experimental System and Main Parameters

[0053] In the experiment, the joint complex response calibration data was generated from the joint complex response calibration data of the transmit-receive channel as described in invention S2; the target data and calibration data were constructed using the same effective reference sequence, reference correlation matrix, joint unmixing and channel arrangement rules to ensure reproducibility.

[0054] Experiment 1: Channel Expansion and Hardware Resource Comparison Objective: To verify that a simplified structure of two whip antennas and two orthogonal loop antennas can form an eight-dimensional theoretical equivalent observation and a seven-dimensional direction finding usable channel, while the hardware overhead is only slightly higher than the traditional four-channel scheme.

[0055] Table 2 Channel data of traditional schemes and the method of the present invention

[0056] Note: This invention adds only one more transmit channel compared to the traditional four-channel scheme (increasing hardware complexity by approximately 20%), thus doubling the theoretical equivalent observation channels from four to eight. After amplitude alignment and coherence merging, the number of usable direction-finding channels is seven, still significantly higher than the traditional scheme. The experimental results directly confirm the beneficial effect of reducing the number of physical antennas and RF channels while simultaneously generating eight theoretical equivalent observation channels. Total number of RF channels = number of transmit channels + number of receive channels, excluding peripheral circuits such as power amplifiers.

[0057] Experiment 2: Direction finding accuracy as a function of signal-to-noise ratio Objective: To compare the accuracy of three direction-finding processes on the same set of baseband data: traditional four-channel array direction finding (directly performing correlation matching on four physical received sequences), the seven-dimensional equivalent array direction finding of this invention (second target direction estimate), and virtual orthogonal loop vector direction finding (first target direction estimate). Target azimuth 15°, 500 Monte Carlo simulations.

[0058] Table 3. Accuracy of the three direction finding processes on the same set of baseband data.

[0059] like Figure 4As shown, under identical physical antennas and receiving channels, the seven-dimensional equivalent array direction finding of this invention reduces the RMSE by approximately 35% to 45% compared to the traditional four-channel scheme across the entire SNR range (e.g., 0.92° → 0.52° at SNR=15dB). The virtual orthogonal loop vector direction finding is slightly less accurate than the seven-channel array at small apertures, but still superior to the traditional four-channel array. Furthermore, it shares the same baseband data as the seven-channel array and requires no additional hardware. At SNR=15dB, the outputs of the first estimator (loop vector) and the second estimator (seven-channel array) are 14.6° and 15.2° respectively, with a deviation of approximately 0.6° between the two estimators. This allows for mutual verification, validating the stability and flexibility of combining vector loop direction finding and seven-channel array direction finding.

[0060] Experiment 3: Comparison of Repeated Channel Merging Methods Objective: To verify that the process of first screening candidate repeating channels based on equivalent phase center and response type, then determining whether to merge based on the consistency of the joint complex response ratio, and coherently merging after amplitude alignment, can avoid equivalent phase reference deviation compared to merging solely based on virtual position. Operating conditions: The normalized cross-correlation of the two waveforms deteriorated from 0.05 to 0.30. Simulated calibration and measured link drift scenarios were used (receiver channel gain drift of approximately 0.5dB and phase drift of approximately 8°), with an SNR of 15dB and 500 statistical analyses.

[0061] Table 4 Comparison of Repeated Channel Merging Methods

[0062] Link drift causes the actual complex response ratio of the two repeating channels to deviate from the ideal 1:1. Direct merging without complex response ratio alignment introduces a deviation in the equivalent phase reference, worsening the direction-finding RMSE to 1.13°. The method of this invention first estimates the complex alignment coefficients (amplitude ratio and phase difference) using least-squares complex ratio fitting, then performs coherent merging after amplitude alignment, reducing the RMSE to 0.57°. This verifies the beneficial effect of avoiding the equivalent phase reference deviation caused by direct merging based solely on virtual positions. A control group is also provided: when link drift is absent (ideal calibration), the RMSE of both merging methods is approximately 0.52°, indicating that the merging method of this invention does not introduce additional losses under normal operating conditions, only significantly benefiting when drift / calibration errors exist.

[0063] Experiment 4: Demixing performance under decreased waveform orthogonality Objective: To verify that joint demixing of different transmit components using a reference correlation matrix can reduce the impact of non-ideal orthogonality of MIMO waveforms. By adjusting the coding parameters of the two waveforms, increasing their normalized cross-correlation from 0.05 to 0.50, the signal-to-interference ratio (SIR) and direction-finding RMSE (SNR=15dB) after demixing were compared between the two processing methods.

[0064] Table 5. Demixing performance under decreased waveform orthogonality

[0065] When the two waveforms are perfectly orthogonal (cross-correlation 0.05), the performance of the two methods is comparable. As the cross-correlation increases, the SIR of independent unmixing drops rapidly (30.2→8.5dB), and the direction-finding RMSE deteriorates to 2.15°. The joint unmixing of this invention incorporates the autocorrelation and cross-correlation of the two effective reference sequences into the solution of the reference correlation matrix, eliminating the coupling component caused by the correlation of the reference sequences. The SIR remains at 21.9dB when the cross-correlation is 0.50, and the direction-finding RMSE only increases to 0.74°. This verifies the beneficial effect of reducing the impact of non-ideal orthogonality of MIMO waveforms on the phase consistency of equivalent observation amplitude. Experiment 4 also covers the implementation of regularization processing described in invention S2 when the reference correlation matrix does not meet the preset direct solution conditions, and the target observation and calibration data use the same regularization parameters. In the actual measurement, Tikhonov regularization is enabled when the cross-correlation is above 0.40 (the regularization measure is 1% of the trace of the reference correlation matrix).

[0066] Effective channel expansion: A minimalist whip ring combination (2 transmitters + 4 receivers) can form 8 theoretically equivalent observation channels, and after merging, 7 direction finding channels are available. The hardware complexity increases by only about 20% compared to the traditional four-channel scheme, and the equivalent observation dimension doubles.

[0067] Improved direction finding accuracy: Under the same set of baseband data, the RMSE of the seven-channel equivalent array direction finding of this invention is reduced by 35%~45% compared with the traditional four-channel direction finding; the virtual orthogonal loop vector direction finding and the seven-channel array direction finding share data and complement each other for verification, and the consistency of the two estimates is good (deviation of about 0.6°), verifying the stability and flexibility of both vector loop direction finding and seven-channel array direction finding.

[0068] Robust merging strategy: In the presence of link drift / calibration errors, the system first performs proportional consistency checks, followed by coherent merging with amplitude alignment. This reduces the direction finding RMSE by approximately 49.6% compared to directly merging based on virtual positions, with no additional loss under normal operating conditions. Demixing resists non-ideal orthogonality: When waveform cross-correlation deteriorates from 0.05 to 0.50, joint demixing with the reference correlation matrix maintains the SIR above 21.9 dB and the direction finding RMSE within 0.74°, verifying the beneficial effect of reducing the non-ideal orthogonality of MIMO waveforms.

[0069] Example 2: In this embodiment, S1 includes: The first and second transmission sequences are generated according to the preset pulse timing and encoding parameters, and then a MIMO transmission sequence matrix is ​​formed. Calculate the maximum normalized cross-correlation coefficient between the first and second transmission sequences and compare it with a preset orthogonality threshold. When the maximum normalized cross-correlation coefficient is greater than the orthogonality threshold, adjust the coding parameters or reselect the transmission sequence until the orthogonality condition is met. The first and second transmission sequences that satisfy the orthogonality condition are mapped to the two transmission channels respectively, and the two whip antennas are controlled to transmit the corresponding MIMO waveforms according to a unified clock and trigger sequence, while generating a receive sampling control vector. Complex baseband data from two whip antenna receiving channels and two loop antenna receiving channels are synchronously acquired based on the receiving sampling control vector, and arranged according to the channels to form a four-channel receiving sequence matrix to obtain four physical receiving sequences.

[0070] In the above scheme, the first and second transmission sequences are generated with the same pulse period, the same sampling frequency, and the same number of symbols. The preset pulse timing is used to determine the transmission start time, duration, and time interval between adjacent pulses within a single pulse period; the encoding parameters are used to determine the values, arrangement order, and corresponding phase states of each symbol. After generation, the sequences are arranged so that the first transmission sequence corresponds to the first transmission channel and the second transmission sequence corresponds to the second transmission channel. The two sequences correspond to the same transmission sampling time at the same sequence number position, thus forming two-channel multiple-input multiple-output transmission sequence data. This arrangement remains unchanged during subsequent waveform loading, channel calibration, and transmission component demixing.

[0071] Orthogonality checks are performed on the generated first and second transmission sequences. Specifically, relative time shifts within an allowable range are applied sequentially between the two sequences, with one cross-correlation calculation performed for each change in sampling point. For the overlapping portion of the two sequences at the current relative time shift, the conjugate values ​​of each symbol in the first transmission sequence and the corresponding symbol in the second transmission sequence are multiplied term by term, and all products are summed using a complex number. The result is used as the cross-correlation result at the current relative time shift. Simultaneously, the amplitudes of each symbol in the two overlapping sequences are squared and summed to obtain the energy of the first and second overlapping sequences. The two energies are multiplied and square-rooted, with the resulting value used as a normalization reference. The amplitude of the current cross-correlation result is divided by this normalization reference to obtain the normalized cross-correlation coefficient corresponding to the current relative time shift. This process is repeated for all specified relative time shift positions, and the largest normalized cross-correlation coefficient is selected from all obtained normalized cross-correlation coefficients as the maximum normalized cross-correlation coefficient between the first and second transmission sequences.

[0072] The orthogonality threshold is determined during the radar equipment calibration phase, rather than being set ad hocly during each detection process. During determination, the same transmit sequence length, sampling frequency, and joint demixing processing method as in actual detection are used to calibrate candidate transmit sequence pairs group by group. For each candidate sequence pair, the maximum normalized cross-correlation coefficient is calculated, and two calibration signals with known amplitudes are simultaneously input into the corresponding processing link. After joint demixing, the target transmit component and the non-target transmit component interfering with the channel are obtained. The amplitude of the non-target transmit component is divided by the amplitude of the target transmit component to obtain the crosstalk ratio of the corresponding transmit component for that candidate sequence pair. Based on the radar equipment's pre-determined upper limit for allowable transmit component crosstalk, candidate sequence pairs with crosstalk ratios not exceeding this upper limit are selected. The maximum normalized cross-correlation coefficient of the largest among these candidate sequence pairs is then used as the orthogonality threshold and written into the equipment parameters. Thus, the orthogonality threshold corresponds to the actual receiving link and joint demixing capability, remaining fixed when the equipment operating parameters remain unchanged.

[0073] The maximum normalized cross-correlation coefficient of the current first and second transmission sequences is compared with the orthogonality threshold. If the maximum normalized cross-correlation coefficient is not greater than the orthogonality threshold, the two transmission sequences are determined to meet the orthogonality condition. If the maximum normalized cross-correlation coefficient is greater than the orthogonality threshold, the transmission step is not initiated; instead, the coding parameters are changed according to the pre-stored coding adjustment order. In this embodiment, the symbol arrangement order of the second transmission sequence is changed first. After each adjustment, the normalized cross-correlation calculation under all relative time shifts is re-executed. If the orthogonality condition is still not met after all arrangement methods within the current coding parameter range have been checked, the next set of first and second transmission sequences is selected sequentially from the pre-stored transmission sequence set according to the candidate sequence number, and the maximum normalized cross-correlation coefficient is recalculated. The above process continues until the calculation result is not greater than the orthogonality threshold, thereby ensuring that the sequences actually sent to the two transmission channels have completed the orthogonality check.

[0074] In this embodiment, after the orthogonality condition is met, the first transmission sequence is written into the digital waveform buffer corresponding to the first transmission channel, and the second transmission sequence is written into the digital waveform buffer corresponding to the second transmission channel. Both transmission channels are counted by the same reference clock, and the same transmission trigger moment in the trigger sequence is used as the time start point of the current pulse. After the transmission trigger arrives, the first transmission channel continuously reads the first transmission sequence according to the sampling order, and the second transmission channel continuously reads the second transmission sequence according to the same sampling beat, and respectively completes digital-to-analog conversion, frequency conversion, and RF output, so that the two whip antennas transmit the corresponding multiple-input multiple-output waveforms according to the same time reference. Since the start time and sampling beat of the two waveforms are determined by the same clock, there is no uncalibrated time offset between the transmission sequences caused by independent clock starts.

[0075] The receive sampling control vector and the transmit trigger sequence are generated using the same clock count. Specifically, taking the current transmit trigger moment as the timing start point, the receive sampling start position is first determined based on the transmit end moment and the pre-set transmit-receive switching protection time; then, the receive time window length is determined based on the radar's maximum detection range. The calculation process for the receive time window length is as follows: first, multiply the maximum detection range by 2 to obtain the propagation distance of the radar wave from the transmit antenna to the target and back to the receive antenna; then, divide this propagation distance by the electromagnetic wave propagation speed to obtain the echo propagation time to be covered; multiply this echo propagation time by the receive sampling frequency and round up to obtain the number of sampling points corresponding to the receive time window. Starting from the receive sampling start position, the above number of consecutive sampling positions are set to the sampling enabled state, and the remaining positions are set to the sampling disabled state, thereby forming the receive sampling control vector corresponding to the current pulse.

[0076] Specifically, after the receive sampling control vector enters the sampling enabled state, it simultaneously sends sampling enable signals to the two whip antenna receiving channels and the two loop antenna receiving channels. The four receiving channels share a common receive sampling clock and collect echo signals according to the same sampling sequence number. The RF signals received by each receiving channel are converted to baseband via the corresponding receiving link, and in-phase and quadrature components are obtained respectively. The in-phase component corresponding to the same sampling time is used as the real part of the complex baseband data, and the quadrature component is used as the imaginary part of the complex baseband data, thus forming complex baseband sampling data that retains amplitude and phase information. The data from the four receiving channels under the same sampling sequence number correspond to the same sampling time, providing a unified time reference for subsequent inter-channel amplitude and phase calibration and coherent processing.

[0077] After data acquisition for one reception time window, the four complex baseband data streams are organized according to a fixed channel order. Position 1 stores the data from the first whip antenna reception channel, position 2 stores the data from the second whip antenna reception channel, position 3 stores the data from the first loop antenna reception channel, and position 4 stores the data from the second loop antenna reception channel. The data in each channel are arranged according to the sampling order. The four data streams are arranged by channel direction and expanded by sampling time direction to form a four-channel reception sequence matrix. Each channel in this matrix corresponds to a defined physical reception sequence, and the four complex data streams at the same sampling position correspond to the same reception time, thus obtaining the four physical reception sequences required for subsequent joint demixing.

[0078] Example 3: In this embodiment, S2 includes: The reference complex transfer function and the joint directional complex response calibration model that vary with the candidate direction are extracted from the joint complex response calibration data. The reference complex transfer function is used to perform amplitude and phase compensation on the two MIMO waveforms to generate a valid reference sequence. Two valid reference sequences corresponding to the same receiving channel are combined to form a reference sequence matrix, and a reference correlation matrix is ​​constructed based on the product of the conjugate transposes of the reference sequence matrices. Based on the condition number of the reference correlation matrix and the preset stability threshold, an inverse matrix or a regularized inverse matrix is ​​selected to form the emission component demixing matrix; The four physical received sequences were correlated with the corresponding reference sequence matrices, and four sets of two-element equivalent observation vectors were obtained using the transmit component unmixing matrix. Four sets of two-element equivalent observation vectors are spliced ​​together according to the transmit-receive channel index to form an eight-dimensional first equivalent observation vector, and an eight-dimensional first calibration response vector varying with the candidate direction is constructed from the joint directional complex response calibration model according to the same index.

[0079] In the above scheme, the joint complex response calibration data is pre-stored according to the transmit channel index, receive channel index, operating frequency index, and candidate direction index. For any transmit-receive channel combination, a known complex calibration sequence is input to the corresponding transmit channel under calibration conditions, and the complex baseband sequence output by the corresponding receive channel is recorded. The transmit calibration sequence and the receive calibration sequence are transformed to the frequency domain. At each frequency sampling position, the receive calibration data is divided by the corresponding transmit calibration data. The modulus of the resulting complex result represents the amplitude transmission coefficient at that frequency position, and the phase angle of the resulting complex result represents the phase shift at that frequency position. The above complex results are saved sequentially according to the frequency sampling positions to form the reference complex transfer function of the transmit-receive channel combination.

[0080] The joint directional complex response calibration model is obtained sequentially according to preset candidate directions. During calibration, the calibration target or calibration signal source is set in the corresponding candidate direction. Under the condition that the transmitted waveform, operating frequency, sampling timing, and receiving gain are consistent with the detection state, the complex response data of the eight transmit-receive channel combinations are obtained respectively. The fixed channel amplitude and phase influence represented by the reference complex transfer function is subtracted from the complex response obtained by each channel, so that the remaining complex response corresponds to the directional response formed by the transmit antenna, receive antenna, equivalent phase center, and target direction. The eight complex responses corresponding to each candidate direction are saved according to a fixed channel index, thus forming a joint directional complex response calibration model that varies with the candidate direction.

[0081] When generating valid reference sequences, the first and second transmit sequences are first transformed to the frequency domain. For the combination of the current transmit channel and the current receive channel, the corresponding reference complex transfer function is read at each frequency sampling position. The complex spectral value of the transmit sequence at that frequency position is multiplied by the complex value corresponding to the reference complex transfer function, so that the transmit sequence simultaneously takes into account the amplitude transmission ratio and phase offset of that channel. After processing all frequency sampling positions, an inverse transformation is performed to obtain a valid reference sequence corresponding to the fixed amplitude and phase characteristics of the transmit-receive combination. The above processing is performed on the two transmit sequences for the four receive channels respectively, thereby obtaining eight valid reference sequences, with two sequences corresponding to each receive channel.

[0082] For the same receiving channel, the valid reference sequences corresponding to the first transmitting channel are arranged in position 1, and the valid reference sequences corresponding to the second transmitting channel are arranged in position 2, forming the reference sequence matrix corresponding to that receiving channel. The reference correlation matrix consists of four multiple correlation results. Specifically: the conjugate of each sample value of the first valid reference sequence is multiplied by its corresponding sample value and summed to obtain the first autocorrelation result; the same process is applied to the second valid reference sequence to obtain the second autocorrelation result; the conjugate of the first valid reference sequence is multiplied by the corresponding sample value of the second valid reference sequence and summed to obtain the first cross-correlation result; the conjugate of the second valid reference sequence is multiplied by the corresponding sample value of the first valid reference sequence and summed to obtain the second cross-correlation result. The two autocorrelation results are placed in the main diagonal position of the matrix, and the two cross-correlation results are placed in the remaining positions, thus obtaining a reference correlation matrix containing the actual correlation relationship between the two valid reference sequences.

[0083] After the reference correlation matrix is ​​formed, singular value decomposition is performed on it to obtain the maximum and minimum singular values. The ratio of the maximum to the minimum singular value is used as the condition number of the reference correlation matrix. If the minimum singular value is equal to 0, the reference correlation matrix is ​​considered not to meet the direct inversion condition, and the process directly proceeds to the regularized inverse matrix processing.

[0084] The preset stability threshold is determined during the equipment calibration phase. Specifically, under the condition that the transmit sequence length, sampling frequency, and receive processing parameters are consistent with the actual detection state, reference correlation matrices with different condition numbers are formed by changing the correlation relationship between the two calibration reference sequences, and two calibration signals with known components are input to the processing link. For each reference correlation matrix, the two transmit components are recovered by direct inversion. Each recovered complex component is subtracted from its corresponding known complex component, and the squares of the amplitudes of all differences are accumulated. Then, the sum is divided by the accumulated sum of the squares of the amplitudes of the two known complex components to obtain the normalized unmixing error corresponding to that condition number.

[0085] The upper limit of the allowable error used to screen for normalized unmixing errors is also determined during the calibration phase. The unmixing results corresponding to different normalized unmixing errors are sequentially fed into subsequent direction estimation processing, using the known direction of the calibrated target as the criterion. When the direction estimation result still falls within the candidate direction position corresponding to the known direction, the current normalized unmixing error is recorded until the direction estimation result first deviates from the known candidate direction position. The maximum normalized unmixing error before the deviation occurs is taken as the upper limit of the allowable error. Subsequently, from all reference correlation matrices where the normalized unmixing error is not greater than this upper limit of the allowable error, the largest condition number is selected as the stability threshold, and this stability threshold is written into the radar processing parameters.

[0086] During actual detection, the condition number of the current reference correlation matrix is ​​compared with the stability threshold. If the condition number is not greater than the stability threshold, the reference correlation matrix is ​​directly inverted, and the resulting inverse matrix is ​​used as the unmixing matrix of the transmit components of the current receiving channel. If the condition number is greater than the stability threshold or the minimum singular value is equal to 0, the reference correlation matrix is ​​regularized before inverting.

[0087] The adjustment values ​​used for regularization are predetermined during the calibration phase. Each item in the pre-established sequence of adjustment values ​​is tested. Each time, the current adjustment value is added to the two diagonal elements of the reference correlation matrix. The adjusted matrix is ​​then inverted, and the two known calibration components are recovered using the result. The error corresponding to each adjustment value is calculated according to the aforementioned method for calculating the normalized unmixing error. The adjustment value with the smallest normalized unmixing error is selected as the regularization adjustment value corresponding to the current operating parameter. The same regularization adjustment value is used for both the actual detection data and the calibration response data.

[0088] After determining the demixing matrix of the transmitted components, correlation operations are performed on the four physical received sequences. For the first physical received sequence, each sample value of the received sequence is multiplied term by term and summed with the conjugate sample value of its corresponding first valid reference sequence to obtain the first correlation result; then, it is processed in the same way with the corresponding second valid reference sequence to obtain the second correlation result. The remaining three physical received sequences are processed using their respective two valid reference sequences, thus each physical received sequence generates two complex correlation results.

[0089] The two complex correlation results are then processed using the demixing matrix corresponding to the transmit component of the receiving channel. Two complex coefficients from the first row of the demixing matrix are multiplied by the first and second correlation results, respectively, and the products are summed. The resulting complex result is used as the theoretical equivalent observation formed by the first transmit channel and the current receiving channel. The same operation is performed on the two complex coefficients from the second row of the demixing matrix, and the resulting complex result is used as the theoretical equivalent observation formed by the second transmit channel and the current receiving channel. After processing the four physical receive sequences sequentially, a total of four sets of binary equivalent observations are obtained, resulting in eight theoretical equivalent observations.

[0090] Specifically, the eight theoretical equivalent observations are arranged sequentially according to a fixed transmit-receive channel index. Position 1 corresponds to the first transmit channel and the first whip antenna receive channel; position 2 corresponds to the second transmit channel and the first whip antenna receive channel; position 3 corresponds to the first transmit channel and the second whip antenna receive channel; position 4 corresponds to the second transmit channel and the second whip antenna receive channel; position 5 corresponds to the first transmit channel and the first loop antenna receive channel; position 6 corresponds to the second transmit channel and the first loop antenna receive channel; position 7 corresponds to the first transmit channel and the second loop antenna receive channel; and position 8 corresponds to the second transmit channel and the second loop antenna receive channel. These are then concatenated in this order to form an eight-dimensional first equivalent observation vector.

[0091] When constructing the eight-dimensional first calibration response vector, for each candidate direction, the complex response values ​​of the eight transmit-receive channel combinations in that direction are read from the joint directional complex response calibration model and arranged according to the channel index order that is exactly the same as the eight-dimensional first equivalent observation vector. Thus, the first calibration complex response corresponds to the first theoretical equivalent observation, the second calibration complex response corresponds to the second theoretical equivalent observation, and so on. After performing the above extraction and arrangement on all candidate directions, the eight-dimensional first calibration response data varying with the candidate direction is obtained, providing the corresponding calibration complex response for subsequent consistency judgment of repeated channel proportions and direction estimation.

[0092] Example 4: In this embodiment, S3 includes: Calculate the equivalent position vector of each theoretical equivalent observation channel based on the transmit phase center and receive phase center, and configure the corresponding response type label; Theoretical equivalent observation channels with equivalent location distances less than a preset location threshold and the same response type are grouped into candidate duplicate channel pairs. The candidate repeated channel pairs are extracted from the eight-dimensional first calibration response vector to obtain the first complex response sequence and the second complex response sequence under multiple calibration directions, and the least squares proportional fitting is used to determine the complex alignment coefficient that minimizes the residual of the two complex response sequences. The normalized proportional fitting residual between the two complex response sequences is calculated based on the complex alignment coefficient. The normalized proportional fitting residual is used as the joint response consistency feature and compared with the preset consistency threshold. Candidate duplicate channel pairs whose joint response consistency feature is not greater than the consistency threshold are identified as mergeable duplicate channels, and the corresponding channel index and realignment coefficient are output.

[0093] In this embodiment, for the eight theoretical equivalent observation channels, the transmit phase center and receive phase center of each channel are first determined based on the antenna installation coordinates. For any theoretical equivalent observation channel, the coordinate values ​​of its transmit phase center and receive phase center on the three coordinate axes are read respectively. The two coordinate values ​​on the same coordinate axis are added together and divided by 2 to obtain the equivalent coordinates of the channel on the three coordinate axes. The three equivalent coordinates together constitute the equivalent position vector of the theoretical equivalent observation channel. All eight channels use the same coordinate origin, the same coordinate axis direction, and the same position calculation method, thereby ensuring that the equivalent position vectors can be directly compared in spatial position.

[0094] The response type label is determined based on the receiving antenna type and the corresponding directional complex response calibration model that forms the theoretical equivalent observation channel. Theoretical equivalent observation channels formed by the same receiving response and calling the same directional complex response calibration model are configured with the same response type label; channels formed by different loop antenna response directions, different field component responses, or different directional complex response calibration models are configured with different response type labels. The response type label is stored along with the channel index and maintains a fixed correspondence with the eight theoretical equivalent observations formed above.

[0095] After configuring the equivalent position and response type, pairwise comparisons are performed on the eight theoretical equivalent observation channels. For any two channels, the coordinate differences on the first, second, and third axes are calculated. The squares of these three differences are then summed, and the square root of the sum is taken. The result is the equivalent position distance between the two theoretical equivalent observation channels. A channel is included as a candidate duplicate channel pair only if this equivalent position distance is less than a preset position threshold and the response type labels of the two channels are identical. Channel combinations whose equivalent position distance does not meet the position condition or whose response type labels are different are not included in the complex response ratio fitting step.

[0096] In this embodiment, the position threshold is determined by the phase center coordinate calibration error. After the equipment is assembled, the position calibration is repeated a specified number of times for each transmit and receive phase center under the same measurement conditions, obtaining the measured coordinates on the three coordinate axes each time. For the same phase center, the difference between the measured coordinates and the average calibrated coordinates of that phase center on the three coordinate axes is calculated each time, and the spatial position deviation corresponding to each calibration is obtained according to the coordinate distance calculation method. The maximum spatial position deviation among all transmit phase center calibration results is taken as the upper limit of the transmit-side coordinate error, and the maximum spatial position deviation among all receive phase center calibration results is taken as the upper limit of the receive-side coordinate error. Since the theoretical equivalent position is formed by taking half of the transmit phase center coordinates and the receive phase center coordinates and then adding them, the upper limit of the transmit-side coordinate error and the upper limit of the receive-side coordinate error are added together and divided by 2, and the resulting value is set as the position threshold. This threshold is re-determined when the antenna installation structure or the phase center calibration results of the equipment change.

[0097] For each candidate repeating channel pair obtained, the calibration complex responses of two channels are extracted from the eight-dimensional first calibration response data formed above, according to the candidate direction index. The complex responses of the first candidate channel under each calibration direction are arranged in order of direction index to form the first complex response sequence; the complex responses extracted from the second candidate channel under the exact same direction index are arranged in the same order to form the second complex response sequence. The two complex response sequences have the same number of elements, and it is guaranteed that the two complex responses at the same index position correspond to the same calibration direction.

[0098] The complex alignment coefficients are obtained using least-squares proportional fitting. Specifically, the complex response corresponding to each calibration direction in the first complex response sequence is conjugate and multiplied by the complex response of the second complex response sequence in the same calibration direction to obtain the complex product for that direction. The complex products from all calibration directions are then summed to obtain the complex correlation accumulation result. Simultaneously, the amplitude of each complex response in the first complex response sequence is squared, and all squared results are summed to obtain the total response energy of the first complex response sequence. The complex correlation accumulation result is divided by the total response energy of the first complex response sequence, and the resulting complex number is the complex alignment coefficient between the two candidate repeating channels. This calculation result includes both the amplitude ratio and phase difference between the two channels and minimizes the sum of squared residuals between the second and first complex response sequences after proportional transformation.

[0099] After obtaining the complex alignment coefficient, the proportional fitting residuals are calculated for the candidate repeated channel pairs. For each calibration direction, the complex response of the first complex response sequence in that direction is multiplied by the complex alignment coefficient to obtain the fitted complex response of the second candidate channel in that direction; then, the fitted complex response is subtracted from the actual complex response in the second complex response sequence to obtain the complex residual in that direction. The squares of the amplitudes of all complex residuals are calculated and summed to obtain the total residual energy. Then, the squares of the amplitudes of all complex responses in the second complex response sequence are summed to obtain the total response energy of the second complex response sequence. The total residual energy is divided by the total response energy of the second complex response sequence to obtain the normalized proportional fitting residual, which is used as the joint response consistency feature of the candidate repeated channel pairs.

[0100] Specifically, the consistency threshold is determined using calibration data from known repeating channels. During the equipment calibration phase, repeating channel pairs belonging to the same equivalent location and having the same response type are pre-selected based on the antenna's geometric position and response type. The calibration complex response of each repeating channel pair is then obtained according to the candidate direction set used in actual detection. For each group of known repeating channels, the complex alignment coefficient is calculated sequentially, and the normalized proportional fitting residual is calculated to obtain the corresponding joint response consistency characteristic. This process is repeated within a specified number of calibration iterations to obtain the joint response consistency characteristic of all known repeating channel pairs, and the maximum value is taken as the consistency threshold. This threshold corresponds to the current antenna installation state, operating frequency band, and receiver link calibration state; recalibration is performed when any of these states changes.

[0101] In practice, the joint response consistency feature of each candidate repeating channel pair is compared with the consistency threshold. When the joint response consistency feature is not greater than the consistency threshold, it is determined that the two candidate channels can establish a proportional correspondence with the same complex alignment coefficient in all calibration directions, and they are identified as repeating channels that can be merged. When the joint response consistency feature is greater than the consistency threshold, the two theoretically equivalent observation channels are kept independent and do not enter subsequent coherent merging.

[0102] For a given repeatable channel that can be merged, output the two channel indices of that channel in the eight-dimensional first equivalent observation vector, while saving the complex alignment coefficients obtained from the aforementioned least-squares scaling fit. The two channel indices are used to determine the column positions to be merged in the seven-row, eight-column equivalent channel transformation matrix mentioned above, and the complex alignment coefficients are used to subsequently correct the amplitude ratio and phase difference between the two channels, so that the two repeatable channels are at the same complex response reference before coherent merging.

[0103] Example 5: In this embodiment, S4 includes: Read the index of the mergeable repeating channels and the complex alignment coefficient, and determine the complex magnitude relative alignment parameter of the mergeable repeating channels; The real non-negative merging weights of the corresponding repeating channels are determined based on the targetless distance cell, calibration data, or noise statistics within the current coherent processing cycle, and the merging weights remain unchanged within the same coherent processing cycle. Write the complex amplitude relative alignment parameters and merging weights into the matrix elements corresponding to the repeating channels, and construct a seven-row, eight-column equivalent channel transformation matrix by combining the mapping relationship of the other non-repeating channels. By multiplying the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector by the same equivalent channel transformation matrix, the amplitude alignment, coherence merging and channel dimensionality reduction of the repeated channels are completed in one step, resulting in the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector. The seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector are stored according to a unified channel index.

[0104] In this embodiment, after determining the repetitive channels that can be merged, the indices of the two channels in the 8-dimensional first equivalent observation vector and their corresponding complex alignment coefficients are first read. The channel with the earlier index is then designated as the amplitude-phase reference channel. The obtained complex alignment coefficients characterize the amplitude ratio and phase rotation required to transform the complex response from the reference channel to the complex response of the other repetitive channel. Therefore, the complex amplitude alignment parameter of the reference channel is a unit complex number, and the complex amplitude alignment parameter of the other repetitive channel is the reciprocal of the complex alignment coefficient. To obtain the reciprocal, the complex alignment coefficient is first conjugated, and then the conjugation result is divided by the sum of the squares of the real and imaginary parts of the complex alignment coefficient. The resulting complex number is used as the amplitude alignment parameter of the other repetitive channel. After processing with this parameter, the two repetitive channels are unified to the amplitude scale and phase reference of the reference channel.

[0105] Specifically, after the amplitude and phase references are determined in the two repeating channels, the merging weights are determined based on the noise statistics. When using targetless range cells, the index of the targetless range cell is determined during the radar calibration stage based on the known target range range. Range cells without calibration target echoes, transmission leakage, or range sidelobes are selected, and their indices are saved as noise statistics intervals. In actual processing, the complex data corresponding to these range cells are read from the two repeating channels within the same coherent processing cycle.

[0106] For any repeating channel, first sum all the complex data points involved in the statistics and divide by the number of data points to obtain the complex mean of that channel; then subtract the complex mean from each complex data point, square the difference, sum all the squared amplitudes, and divide by the number of data points to obtain the noise power of that channel. For the other repeating channel, first perform amplitude-phase transformation according to the aforementioned complex amplitude-phase alignment parameters, and then calculate the noise power using the same method, so that the two noise powers correspond to the same amplitude-phase reference.

[0107] When determining noise power using calibration data, the target analog signal is turned off during the equipment calibration phase. Only the receiving link is kept in the same gain, bandwidth, and sampling configuration as in the detection state. Complex baseband data of a specified length is continuously collected, and the calibration noise power of the two repeating channels is obtained by following the aforementioned steps of removing the mean, accumulating the squared differences, and averaging by the number of data points. When using noise statistics within the current coherent processing cycle, complex data is read from the pre-registered noise sampling interval of that cycle, and the noise power of the two channels is obtained according to the same calculation process. The equipment operating mode determines the source of noise statistics data before processing begins, and the data source is not switched within the same coherent processing cycle.

[0108] The merging weights are determined according to the reciprocal relationship of noise power. Specifically, the reciprocals of the noise power of the two repeated channels are calculated separately, and then the two reciprocals are added together. The merging weight of the first channel is obtained by dividing the first reciprocal by the sum, and the merging weight of the second channel is obtained by dividing the second reciprocal by the same sum. Both weights obtained are real non-negative values, and the sum of the two weights equals 1. When the noise power value is less than the receiver's noise floor calibration value, the noise floor calibration value is used in the reciprocal calculation. The noise floor calibration value is obtained by connecting a matched load to the receiver, keeping the actual receiving gain and sampling parameters unchanged, and repeatedly collecting noise data, and then calculating the noise power according to the aforementioned noise power calculation method. It is updated during the recalibration of the receiving link.

[0109] In this embodiment, the merging weights are calculated and written into the processing parameters at the beginning of each coherent processing cycle, and remain unchanged across all 8-dimensional first equivalent observation vectors processed within that cycle. At the start of the next coherent processing cycle, the corresponding noise statistics are reread and the weights are recalculated. Thus, repeated channels within the same coherent accumulation interval employ a fixed amplitude-phase relationship and a fixed merging ratio.

[0110] When constructing the 7x8 equivalent channel transformation matrix, all matrix elements are first set to 0. For the six theoretical equivalent observation channels that are not involved in the duplicate merging, a value of 1 is written in the column position corresponding to the original 8-dimensional channel index in the corresponding output row, so that the input channel is directly mapped to the corresponding output channel. For the two duplicate channels that need to be merged, two non-zero complex elements are set in the same output row. The column containing the reference channel contains the real number of the merge weight of that channel, and the column containing the other duplicate channel contains the product of its merge weight and the complex magnitude alignment parameter. The remaining six elements in this row are all kept to 0. Thus, one row in the matrix realizes the magnitude alignment and weighted summation of the two duplicate channels, and the remaining six rows respectively retain the six non-duplicate channels.

[0111] When processing the 8-dimensional first equivalent observation vector using the 7x8 equivalent channel transformation matrix, the 8 elements of the first row of the matrix are multiplied by the complex observations at the same column positions in the 8-dimensional first equivalent observation vector, and then the 8 products are added together to obtain the first second equivalent observation. The same complex multiplication and addition operation is performed on the remaining 6 rows in sequence to finally obtain 7 second equivalent observations, which are then arranged into a 7-dimensional second equivalent observation vector according to the matrix row order. Among them, the operation in the output row where the repeated channel is located simultaneously completes the amplitude and phase correction of the second repeated channel, the weighted coherent superposition of the two repeated channels, and the channel compression from 8-dimensional to 7-dimensional.

[0112] Specifically, the same processing is performed on the 8-dimensional first calibration response vector. For each candidate direction, an equivalent 7x8 channel transformation matrix identical to the current observation data is invoked. The 8 first calibration complex responses corresponding to that candidate direction are then multiplied and added row by row according to the matrix to obtain 7 second calibration complex responses. All candidate directions are processed using the same channel transformation relationship, thus forming a 7-dimensional second calibration response that varies with the candidate direction. The observation data and calibration responses use the same amplitude alignment parameters, merging weights, and channel mapping positions, thus ensuring that the merged observation channels maintain the same complex response benchmark as the corresponding calibration channels.

[0113] The 7-dimensional second equivalent observation vector and the 7-dimensional second calibration response vector are stored in the same channel index table. Specifically, based on the original 8-dimensional index order, the channel position with the earlier index among the two mergeable repeating channels is used as the output index of the merged channel, and the independent positions of the repeating channels with later indices are deleted. The remaining non-repeating channels are arranged sequentially according to their original order. This index table is used simultaneously for the 7-dimensional second equivalent observation vector, the 7-dimensional second calibration response vector, and subsequent array direction finding processing, ensuring that each of the seven output positions corresponds to a defined equivalent channel.

[0114] Example 6: In this embodiment, S5 includes: Based on the channel index, two loop antenna equivalent channels are extracted from the seven-dimensional second equivalent observation vector to form a virtual orthogonal loop observation vector; Extract the corresponding components from the seven-dimensional second calibration response vector to establish a virtual loop calibration response vector that varies with the candidate direction; Calculate the normalized complex matching feature between the virtual orthogonal loop observation vector and the virtual loop calibration response vector to form a first direction matching sequence, and determine the first target direction estimate based on its peak value; An array snapshot matrix is ​​constructed using the continuous seven-dimensional second equivalent observation vectors of the same range-Doppler target detection unit. The seven-channel noise covariance matrix is ​​estimated based on the absence of a target detection unit. After normalizing the array observation data and the corresponding seven-dimensional second calibration response vector with the same source noise, beamforming or subspace spectrum estimation is performed to form a second directional spectrum sequence. The second target direction estimate is determined based on the effective spectral peaks of the second direction spectral sequence, and the first target direction estimate and the second target direction estimate are associated with the same target detection unit.

[0115] Based on the aforementioned 7-dimensional channel index table, the positions of the two loop antenna equivalent channels in the 7-dimensional second equivalent observation vector are determined. The two loop antenna equivalent channels have the same equivalent phase center but correspond to different loop response types. Following a pre-fixed response type order, two complex observation values ​​are extracted from the 7-dimensional second equivalent observation vector corresponding to the current range-Doppler target detection unit. The complex observation value corresponding to the first loop response type is placed in position 1, and the complex observation value corresponding to the second loop response type is placed in position 2, thus forming a two-element virtual orthogonal loop observation vector. Subsequent calibration response extraction uses the same channel index and the same arrangement order.

[0116] For each candidate direction, the calibration complex responses of the two loop antenna channel positions are read from the 7-dimensional second calibration response vector corresponding to that candidate direction, and a 2-element virtual loop calibration response vector is formed according to the arrangement order of the virtual orthogonal loop observation vectors. After traversing all candidate directions in sequence, each candidate direction corresponds to a set of virtual loop calibration data consisting of 2 complex responses, and a fixed correspondence is maintained between the candidate direction index and the calibration response.

[0117] The first target direction estimation employs normalized complex matching. For a candidate direction, the conjugates of the two ring calibration complex responses corresponding to that direction are first taken, and then multiplied by the two complex observations at the same position in the virtual orthogonal ring observation vector. The two products are then summed to obtain the complex matching result for the current candidate direction, and the amplitude of this result is squared. Simultaneously, the amplitudes of the two actual ring observations are squared and summed to obtain the total observed energy; the amplitudes of the two ring calibration complex responses are squared and summed to obtain the total calibration energy for the current candidate direction. The squared amplitude of the complex matching result is divided by the product of the total observed energy and the total calibration energy, and the resulting value is used as the normalized complex matching feature of the current candidate direction.

[0118] The above steps are followed to calculate all candidate directions one by one, and the normalized complex matching features are arranged according to the candidate direction index to form the first direction matching sequence. All matching values ​​in the first direction matching sequence are compared, and the candidate direction corresponding to the maximum matching value is taken as the first target direction estimate. Since the matching calculation simultaneously preserves the amplitude and phase relationships of the two loop antenna equivalent channels, the first target direction estimate is determined by the joint complex response of the two loop response types at the same equivalent phase center.

[0119] Specifically, when performing the second type of direction estimation, the target detection unit that has already undergone range-Doppler detection is used as the data index, and the 7-dimensional second equivalent observation vector corresponding to the detection unit at each snapshot time is continuously extracted. Each 7-dimensional second equivalent observation vector is used as an array snapshot, and they are arranged sequentially according to the acquisition time, so that each column corresponds to one snapshot and each row corresponds to one second equivalent observation channel, thus forming a 7-channel array snapshot data. Each snapshot corresponds to the same range index and the same Doppler index, and data from other range-Doppler units are not mixed into the target snapshot data.

[0120] The noise covariance is estimated from the targetless detection units in the currently processed data. Targetless detection units are selected from those units not identified as targets in the range-Doppler detection results, excluding the current target detection units and their detection protection units. For each selected targetless detection unit, a corresponding 7-dimensional second equivalent observation vector is extracted. All noise observation vectors are first summed at the same channel position, then divided by the number of targetless detection units to obtain the 7-channel noise mean. Subsequently, this noise mean is subtracted from each noise observation vector to obtain a mean-reduced noise vector. This mean-reduced noise vector is multiplied by its conjugate transpose to obtain a 7x7 complex outer product matrix. The outer product matrices corresponding to all targetless detection units are summed element-wise, then divided by the number of targetless detection units involved in the statistics to obtain the 7-channel noise covariance matrix.

[0121] The number of targetless detection units participating in noise covariance estimation is set to be greater than 7. After the noise covariance matrix is ​​formed, eigenvalue decomposition is performed, and the seven eigenvalues ​​are checked. If all seven eigenvalues ​​are greater than 0, noise normalization is performed. If there are eigenvalues ​​equal to 0, noise samples are added from detection units that have never been identified as targets and are located outside the protected area, and the noise covariance matrix is ​​recalculated until all seven eigenvalues ​​are greater than 0. This yields a noise covariance matrix that can be used for subsequent inverse square root transformation.

[0122] In this embodiment, during noise normalization, the noise covariance matrix is ​​eigenvalued, the square roots and reciprocals of the seven eigenvalues ​​are taken, and then the eigenvectors are rearranged according to their original arrangement to form a 7-channel noise normalization transformation matrix. This transformation matrix is ​​used to process each 7-dimensional observation vector in the array snapshot to obtain the noise-normalized array observation data. The same transformation matrix is ​​used to process the 7-dimensional second calibration response vector corresponding to each candidate direction to obtain the noise-normalized calibration response for that candidate direction. The observation data and calibration data are normalized using the same noise covariance matrix formed by the same group of targetless detection units.

[0123] Specifically, when using beamforming, for a candidate direction, the seven calibrated complex responses after noise normalization are conjugated and multiplied term by term with seven complex observations at the same channel position in an array snapshot. These seven multipliers are then summed to obtain the complex beam output of the snapshot in the current candidate direction. The amplitude of the complex beam output is squared, and the sum of the squared amplitudes of all consecutive snapshots is divided by the number of snapshots to obtain the average output energy of the candidate direction. This is then normalized using the sum of the squared amplitudes of the seven calibrated complex responses for the current candidate direction, and the result is used as the spectral value for that direction. After calculating all candidate directions and arranging them according to their direction indices, the second direction spectral sequence is obtained.

[0124] When using subspace spectrum estimation, each noise-normalized 7-dimensional array snapshot is multiplied by its conjugate transpose to form a 7x7 outer product matrix. The outer product matrices of all snapshots are accumulated and divided by the number of snapshots to obtain the array observation covariance matrix. Eigenvalue decomposition is performed on the array observation covariance matrix; for the current single-target detection unit, the eigenvector corresponding to the largest eigenvalue is taken as the signal subspace, and the remaining six eigenvectors constitute the noise subspace. For any candidate direction, its noise-normalized calibration response is multiplied by the six noise subspace eigenvectors, and the squares of the amplitudes of the six inner product results are accumulated. The reciprocal of the accumulated result is taken as the subspace spectrum value for that candidate direction. This process is repeated for all candidate directions to form the second direction spectrum sequence.

[0125] The spectral reference value used to determine the effective spectral peak is obtained in advance by the targetless detection unit. After determining the current operating frequency band, the number of snapshots, and the sampling parameters, a specified number of targetless detection units are selected. Following the same noise normalization and directional spectrum calculation steps as the target detection units, directional spectra are generated for each targetless directional spectrum. The maximum spectral value in each targetless directional spectrum is read, and the maximum value among all maximum spectral values ​​is taken as the effective spectral peak determination value and saved. This determination value is obtained again after any changes to the operating parameters.

[0126] Peak search is performed point-by-point on the second-direction spectral sequence of the target detection unit. If the spectral value corresponding to a candidate direction is simultaneously greater than the spectral values ​​of two adjacent candidate directions, and not less than the valid spectral peak determination value, that position is determined as a valid spectral peak. If only one valid spectral peak exists, the candidate direction corresponding to that peak is used as the second target direction estimate; if two or more valid spectral peaks exist, the spectral values ​​of each valid peak are compared, and the direction corresponding to the peak with the largest spectral value is used as the second target direction estimate.

[0127] Both the first and second target direction estimates use the distance index, Doppler index, and processing cycle index of the current target detection unit. When saving the direction finding results, the three indices are used as the association identifiers of the same target detection unit and are simultaneously written into the first and second target direction estimates, so that both direction estimation results correspond to the same range-Doppler target detection unit that generated the 7-dimensional second equivalent observation data.

[0128] Example 7: In this embodiment, a system applicable to the simplified whip ring combined antenna radar detection method based on MIMO equivalent vector array includes two transmit and receive shared whip antennas, two receive dedicated loop antennas with mutually orthogonal normal axes, a transmitter, a receiver, a synchronization module, and a signal processing module. Two whip antennas are used to transmit two mutually orthogonal MIMO waveforms respectively, and together with two loop antennas, they form four physical receiving channels; The receiver is used to synchronously acquire four physical receive sequences; In this embodiment, the signal processing module is used to construct an effective reference sequence for two MIMO waveforms based on the joint complex response calibration data of the transmit-receive channels. It then forms a reference correlation matrix based on the effective reference sequence and performs joint demixing on the four physical receive sequences to form an eight-dimensional first equivalent observation vector and a corresponding eight-dimensional first calibration response vector. Based on the equivalent phase center, response type, and joint complex response consistency of each theoretical equivalent observation channel, it determines merging repeatable channels. Based on the complex response ratio of the merging repeatable channels, it constructs a seven-row, eight-column equivalent channel transformation matrix. Using the same equivalent channel transformation matrix, it transforms the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector to obtain a seven-dimensional second equivalent observation vector and a seven-dimensional second calibration response vector. The signal processing module is also used to retain the equivalent channels of two loop antennas with different response types at the same equivalent phase center as virtual orthogonal loop observation pairs, obtain the first target direction estimate based on the virtual orthogonal loop observation pairs, and obtain the second target direction estimate based on the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector.

[0129] The signal processing module includes a calibration parameter storage unit and a MIMO demixing unit; The calibration parameter storage unit is used to store the joint complex response calibration data corresponding to each transmit-receive channel combination; The MIMO demixing unit is used to form a reference sequence matrix from two valid reference sequences corresponding to the same physical receiving channel, construct a reference correlation matrix based on the product of the conjugate transpose of the reference sequence matrix, and form a transmit component demixing matrix based on the reference correlation matrix to convert the four physical receiving sequences into four sets of two-element equivalent observation vectors, and form an eight-dimensional first equivalent observation vector according to the transmit channel-receive channel index.

[0130] The signal processing module also includes a channel determination unit and an equivalent channel transformation unit; The channel determination unit is used to determine candidate repeating channels based on the equivalent phase center and response type, calculate the joint complex response consistency characteristics of the candidate repeating channels based on the eight-dimensional first calibration response vector, and compare the joint complex response consistency characteristics with a preset consistency threshold to determine the repeating channels that can be merged. The equivalent channel transformation unit is used to determine the complex alignment coefficients based on the complex response ratio between mergeable repeatable channels, and to construct a seven-row, eight-column equivalent channel transformation matrix in combination with real non-negative merging weights, so that the observed data and the calibration response model are synchronously transformed from eight-dimensional to seven-dimensional according to the same complex amplitude and phase reference.

[0131] In this embodiment, two whip antennas are connected to the first and second transmit channels of the transmitter, respectively, and simultaneously connected to the first and second whip antenna receive channels of the receiver. The transmitter and receiver switch operating states according to the transmit / receive control timing output by the synchronization module, so that the two whip antennas are used to radiate the corresponding multiple-input multiple-output waveform during the transmit period and to receive the target echo during the receive period. Two loop antennas are connected only to the receiver, forming the first and second loop antenna receive channels, respectively. The two loop antennas are fixedly mounted to ensure that their normal axes are perpendicular to each other, thus forming two defined loop antenna directional responses. The two whip antenna receive channels and the two loop antenna receive channels together constitute four physical receive channels.

[0132] Specifically, the transmitter receives two transmission sequences generated by the signal processing module and loads the first transmission sequence into the first transmission channel and the second transmission sequence into the second transmission channel according to a fixed channel mapping relationship. The two transmission sequences have undergone maximum normalized cross-correlation calculation according to the orthogonality verification process described above and meet the orthogonality threshold stored in the processing parameters. The synchronization module provides the same reference clock and the same pulse trigger reference to the two transmission channels, controlling the two whip antennas to transmit two orthogonal multi-input multi-output waveforms according to the determined transmission start time and sampling cycle. The synchronization module generates a receive sampling control signal simultaneously with the transmission trigger signal. The receiver's four physical receive channels use the same sampling clock and synchronously acquire complex baseband data during the valid period of the receive sampling control signal. The same sampling sequence number for each channel corresponds to the same sampling time. After completing one receive time window, the receiver outputs four physical receive sequences to the signal processing module in a fixed order: first whip antenna, second whip antenna, first loop antenna, and second loop antenna.

[0133] The calibration parameter storage unit establishes an index according to the transmit channel, receive channel, and candidate direction. Two transmit channels are combined with four physical receive channels, forming a total of eight transmit-receive channel combinations. For each combination, the calibration parameter storage unit stores the corresponding reference complex transfer data and the directional complex response data that varies with the candidate direction. The reference complex transfer data is determined by the complex output of the known calibration sequence after passing through the corresponding transmit and receive links; the directional complex response data is acquired direction-by-direction under the specified candidate directions and stored according to the same eight-channel index.

[0134] The MIMO demixing unit calls the reference complex transfer data of the current transmit-receive channel combination to perform amplitude and phase corrections on the corresponding transmit sequence. During processing, the transmit sequence undergoes a frequency domain transformation. At each frequency sampling position, the complex spectrum value of the transmit sequence is multiplied by the corresponding reference complex transfer data. Then, all processed frequency sampling data is converted back to the sampling domain to obtain the corresponding valid reference sequence. The above processing is performed on the two transmit sequences for each of the four receive channels, resulting in a total of eight valid reference sequences.

[0135] Specifically, for the same physical receiving channel, the MIMO demixing unit arranges the two valid reference sequences corresponding to that channel in the order of the first transmit channel and the second transmit channel. Then, the first valid reference sequence is conjugate-multiplied with itself point-by-point and summed to obtain the first autocorrelation result; the same process is performed on the second valid reference sequence to obtain the second autocorrelation result; then, the conjugate cross-correlation results between the two valid reference sequences in two directions are calculated respectively. The two autocorrelation results and the two cross-correlation results are arranged in their corresponding positions to form the reference correlation matrix for that physical receiving channel.

[0136] When forming the transmit component demixing matrix based on the reference correlation matrix, the reference correlation matrix is ​​first subjected to singular value decomposition, and the condition number is obtained by dividing the maximum singular value by the minimum singular value. If the condition number is not greater than a pre-calibrated stability threshold, the reference correlation matrix is ​​directly inverted; if the condition number is greater than the stability threshold, the regularization adjustment determined in the calibration stage is added to the two main diagonal elements of the reference correlation matrix before inverting. The resulting inverse matrix serves as the transmit component demixing matrix for this physical receiving channel.

[0137] The stability threshold is determined using known dual-path calibration signals. During calibration, reference correlation matrices with different condition numbers are constructed, and the two known transmit components are recovered respectively. The recovered result is subtracted from the corresponding known component item by item, the squares of the difference amplitudes are accumulated, and then divided by the total energy of the known components to obtain the normalized unmixing error. The maximum condition number that still satisfies the condition for correct determination of subsequent direction estimation is saved as the stability threshold. The regularization adjustment amount is determined by sequentially testing a preset adjustment amount sequence, calculating the normalized unmixing error corresponding to each adjustment amount, and taking the adjustment amount corresponding to the minimum error.

[0138] Specifically, when demixing the four physical received sequences, each physical received sequence is subjected to complex correlation with its corresponding two valid reference sequences. Specifically, the conjugate of each sample value in the valid reference sequence is multiplied term-by-term with the complex data at the same sampling position in the physical received sequence, and then all multiplications are summed to obtain one correlation result. Each physical received sequence yields two correlation results, which are then multiplied and added using the corresponding transmit component demixing matrix in two rows to obtain two theoretical equivalent observations. After processing the four physical received sequences, four sets of two-element equivalent observations are obtained, forming a total of eight theoretical equivalent observations.

[0139] Specifically, the eight theoretical equivalent observations are arranged according to a fixed index of the transmit channel and the receive channel to form an eight-dimensional first equivalent observation vector. For each candidate direction, the signal processing module reads the corresponding direction complex response from the calibration parameter storage unit according to the same eight-channel index, and arranges them sequentially to form an eight-dimensional first calibration response vector for that candidate direction, so that the actual observation channel and the calibration response channel correspond one by one.

[0140] The channel determination unit calculates the equivalent phase center based on the transmit and receive phase centers corresponding to each theoretically equivalent observation channel. During calculation, the coordinates of the transmit and receive phase centers on the three coordinate axes are added together and then divided by 2 to obtain three equivalent position coordinates. Subsequently, the spatial distance between each of the eight channels is calculated pairwise, and the response type label of each channel is checked. Two channels with a spatial distance less than the position threshold and the same response type are listed as candidate duplicate channels.

[0141] The position threshold is determined based on the antenna phase center coordinate calibration error. Repeated coordinate measurements are performed a specified number of times on both the transmit and receive phase centers to obtain their respective maximum spatial coordinate deviations. The maximum coordinate deviation on the transmit side is added to the maximum coordinate deviation on the receive side, and then divided by 2. The resulting value is used as the position threshold. This calibration is repeated if the antenna installation position is adjusted.

[0142] For each set of candidate repeating channels, the channel determination unit extracts the complex responses of two channels from the 8-dimensional first calibration response vector corresponding to multiple candidate directions. The complex responses of channel 1 in each direction are conjugated and multiplied term-wise with the complex responses of channel 2 in the same direction, then summed and divided by the sum of the squared amplitudes of all complex responses of channel 1 to obtain the complex alignment coefficient between the two channels. Using this coefficient, the complex response of channel 1 is mapped to channel 2. The difference between the mapped value and the actual complex response of channel 2 is calculated in each direction. The squared amplitudes of all differences are summed and divided by the total energy of all complex responses of channel 2 to obtain the joint complex response consistency characteristic. The consistency threshold is determined during the array calibration stage using known repeating channels. For channel pairs whose geometric positional relationship and response type have been determined to be repeating, the joint complex response consistency characteristic is calculated according to the actual candidate direction set. All characteristic values ​​are obtained in a specified number of repeated calibrations, and the maximum value is taken as the consistency threshold. When the joint complex response consistency characteristic of the candidate repeating channel is not greater than the threshold, the channel determination unit determines it as a repeating channel that can be merged, and sends the two channel indices and complex alignment coefficients to the equivalent channel transformation unit.

[0143] The equivalent channel transformation unit uses the channel with the earlier index among the two repeated channels as the amplitude and phase reference, and determines the complex amplitude and phase correction parameters of the other channel based on the complex alignment coefficient. Then, noise data from the two repeated channels are extracted from the targetless distance unit in the same coherent processing cycle, and the average squared amplitude of the complex data after mean removal is calculated to obtain the noise power of the two channels. The reciprocals of the two noise powers are calculated separately, and then each reciprocal is divided by the sum of the two reciprocals to obtain two real non-negative merging weights.

[0144] When constructing the 7x8 equivalent channel transformation matrix, the six non-repeating channels each have a value of 1 written at the intersection of their corresponding output row and the original input column; the two repeating channels share the remaining output row, where the column containing the reference channel has its corresponding merging weight written, and the column containing the other repeating channel has its merging weight multiplied by the complex amplitude and phase correction parameter written; the remaining matrix elements are written as 0. Thus, one row of the matrix performs amplitude and phase correction and weighted coherent merging for the repeating channels, while the other six rows maintain the independent mapping of the non-repeating channels.

[0145] When processing the 8-dimensional first equivalent observation vector using the 7x8 equivalent channel transformation matrix, the 8 matrix elements in each row are multiplied by the corresponding data in the 8-dimensional first equivalent observation vector and summed to obtain one output element. After processing 7 rows, a 7-dimensional second equivalent observation vector is obtained. For the 8-dimensional first calibration response vector of each candidate direction, the same complex multiplication and addition process is performed using the exact same matrix to form the corresponding 7-dimensional second calibration response vector. Therefore, the observation data and calibration data adopt the same amplitude-phase reference and channel dimension reduction relationship.

[0146] The signal processing module extracts two equivalent channels of the loop antenna with the same equivalent phase center but different response types from the 7-dimensional second equivalent observation vector based on the 7-dimensional channel index, and forms a 2-element virtual orthogonal loop observation vector according to a fixed response type order. For each candidate direction, the calibration complex response of the same two channels is then extracted from the corresponding 7-dimensional second calibration response vector.

[0147] The first target direction estimate is obtained using normalized complex matching. The two calibrated complex responses are conjugates, multiplied term by term with the two actual loop observations, and then summed. The square of the magnitude of the resulting complex number is taken. The total energy of the two actual loop observations and the total energy of the two calibrated complex responses are then calculated separately. The square of the magnitude of the complex matching result is divided by the product of the two total energies to obtain the matching value of the current candidate direction. This calculation is repeated for all candidate directions, and the candidate direction with the largest matching value is taken as the estimate of the first target direction.

[0148] Specifically, the second target direction estimation utilizes the continuous 7-dimensional second equivalent observation vectors from the same range-Doppler target detection unit to form array snapshot data. The signal processing module extracts 7-dimensional noise observation vectors from the target-free detection unit, removes the mean of each channel, multiplies each noise vector by its conjugate transpose to form a 7x7 outer product matrix, and then averages all outer product matrices to obtain a 7-channel noise covariance matrix. Based on this noise covariance matrix, a noise normalization transformation is formed, and the same transformation is used to process the array snapshot data and the 7-dimensional second calibration response of each candidate direction. After noise normalization, beamforming or subspace spectrum estimation is performed according to a preset processing mode to obtain the direction spectrum value corresponding to each candidate direction. During beamforming, the 7 calibration complex responses of each candidate direction are conjugated, multiplied by the 7-channel observation values ​​one by one, and accumulated, and then the output energy of multiple snapshots is averaged; during subspace spectrum estimation, the array snapshot observation covariance matrix is ​​eigenvalued, and the direction spectrum value is calculated using the complex inner product between the noise subspace and the calibration response of each candidate direction. The spectral values ​​of all candidate directions are arranged by direction index to form a second direction spectral sequence, and the candidate direction with the largest spectral value that meets the spectral peak determination condition is selected as the second target direction estimate. Both the first and second target direction estimates are saved with the distance index, Doppler index, and processing cycle index of the current target detection unit, thus making the two direction estimation results correspond to the same target detection unit.

[0149] Example 8: Furthermore, the present invention provides an apparatus applicable to the aforementioned simplified whip-loop combined antenna radar detection method based on MIMO equivalent vector array, comprising a data interface, a memory, and a processor. The data interface is used to receive four physical reception sequences obtained from two whip antenna receiving channels and two loop antenna receiving channels. The memory stores joint complex response calibration data and program instructions for the transmit-receive channels. When the processor executes program instructions, it is used to: jointly demix the two MIMO transmit components in the four physical receive sequences based on the joint complex response calibration data to form an eight-dimensional first equivalent observation vector and an eight-dimensional first calibration response vector; Based on the equivalent phase center, response type, and joint complex response consistency, the repeatable channels that can be merged are determined. An equivalent channel transformation matrix is ​​constructed, and the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector are transformed simultaneously to obtain the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector. The first direction finding process is performed based on the virtual orthogonal loop observation pair, and the second direction finding process is performed based on the seven-dimensional second equivalent observation vector.

[0150] The device in this embodiment consists of a data interface, a memory, and a processor. The data interface is connected to the data output terminal of the radar receiver and receives complex baseband data output from the first whip antenna receiving channel, the second whip antenna receiving channel, the first loop antenna receiving channel, and the second loop antenna receiving channel in a fixed channel sequence. The four data channels use the same sampling clock, and the same sampling sequence number corresponds to the same reception time. After the data interface completes the reception of data for one reception time window, it writes the four complex baseband data channels, along with the channel index and sampling sequence number, into the data buffer area for the processor to read by channel, forming a four-channel physical reception sequence.

[0151] The memory stores two MIMO transmission sequences, joint complex response calibration data corresponding to eight transmit-receive channel combinations, phase center coordinates and response types of each theoretically equivalent observation channel, channel arrangement index, and program instructions required for processor execution. The joint complex response calibration data is indexed according to the transmit channel, receive channel, and candidate direction. The reference complex transfer data corresponding to the fixed link is used to generate the valid reference sequence, while the complex response data varying with the candidate direction is used to form the direction calibration response. Thus, the processor can simultaneously obtain the actual observation data and the calibration data corresponding to the same transmit-receive channel index.

[0152] When the processor performs joint demixing, it first reads the first and second transmit sequences, as well as the reference complex transfer data corresponding to the current transmit-receive combination. After performing a frequency domain transformation on each transmit sequence, the complex spectrum value of the transmit sequence is multiplied by the corresponding reference complex transfer data at each frequency sampling position. This ensures that the transmit sequence includes the amplitude and phase variations caused by the actual transmit and receive links. The processed frequency domain data is then converted back to the sampling domain to obtain the valid reference sequence corresponding to the transmit-receive combination. After processing the two transmit sequences for the four physical receive channels, a total of eight valid reference sequences are formed.

[0153] Specifically, for the same physical receiving channel, the processor reads two valid reference sequences corresponding to that receiving channel. First, it takes the conjugate of each sample value of the first valid reference sequence, multiplies it term by term with its corresponding sample value, and sums the results to obtain the first autocorrelation result. The same process is applied to the second valid reference sequence to obtain the second autocorrelation result. Then, the conjugate of the first valid reference sequence is multiplied term by term with the second valid reference sequence and summed, and the conjugate of the second valid reference sequence is multiplied term by term with the first valid reference sequence and summed, resulting in two cross-correlation results. These two autocorrelation results are placed in the main diagonal position, and the two cross-correlation results are placed in the remaining positions to form the reference correlation matrix corresponding to that receiving channel.

[0154] The processor performs singular value decomposition on the reference correlation matrix to obtain the maximum and minimum singular values. The condition number of the reference correlation matrix is ​​obtained by dividing the maximum by the minimum singular value. If the condition number is not greater than the stability threshold stored in memory, the reference correlation matrix is ​​directly inverted. If the condition number is greater than the stability threshold, a pre-calibrated regularization adjustment is added to the two main diagonal elements of the reference correlation matrix before inverting it. The result is used as the unmixing matrix for the emitted components. The stability threshold and the regularization adjustment are obtained through the calibration process described above and stored in memory under the corresponding operating parameters.

[0155] When performing transmit component separation on the current physical received sequence, the processor performs complex correlation between the physical received sequence and two valid reference sequences. Each correlation operation involves taking the conjugate of each sample value in the valid reference sequence, multiplying each data point at the same sampling position in the physical received sequence, and then summing all the complex multiplications to obtain one correlation result. Subsequently, the two correlation results are multiplied by the two complex coefficients in the first row of the transmit component unmixing matrix and summed to obtain the theoretical equivalent observations corresponding to the first transmit channel. The same operation is then performed using the second row of the unmixing matrix to obtain the theoretical equivalent observations corresponding to the second transmit channel. After processing the four physical received sequences sequentially, eight theoretical equivalent observations are obtained.

[0156] The processor arranges eight theoretical equivalent observations according to the pre-stored transmit-receive channel indices, forming an eight-dimensional first equivalent observation vector. For each candidate direction, the processor reads the eight directional calibration complex responses from the joint complex response calibration data according to the same eight-channel indices, and arranges them sequentially to form the eight-dimensional first calibration response vector corresponding to that candidate direction, so that the actual observation data and calibration responses correspond item by item at the eight channel positions.

[0157] Specifically, when determining which channels can be merged, the processor reads the transmit phase center coordinates and receive phase center coordinates corresponding to each theoretically equivalent observation channel. It then adds the coordinates of the two phase centers on the three coordinate axes and divides by 2 to obtain the 3D equivalent position of the theoretically equivalent observation channel. For any two theoretically equivalent observation channels, the processor calculates the coordinate differences on the three coordinate axes, squares the three differences, sums them, and takes the square root to obtain the equivalent position distance between the two channels. Simultaneously, it reads the response types corresponding to the two channels. Two channels whose equivalent position distance satisfies the aforementioned position determination conditions and have the same response type proceed to a joint complex response consistency judgment.

[0158] During the joint complex response consistency assessment, the complex responses of two candidate repeating channels are extracted from the 8-dimensional first calibration response vectors corresponding to multiple candidate directions. The complex responses of the first channel in each candidate direction are conjugates, multiplied term by term with the complex responses of the second channel in the same direction, and accumulated. This result is then divided by the accumulated sum of the squares of all complex response amplitudes of the first channel to obtain the complex alignment coefficient. Using this complex alignment coefficient, the complex responses of the first channel in each direction are transformed to the amplitude-phase reference of the second channel. These are then subtracted from the actual complex responses of the corresponding directions of the second channel. The squares of the amplitudes of all complex residuals are accumulated and divided by the accumulated sum of the squares of all complex response amplitudes of the second channel to obtain the joint complex response consistency feature. When this feature satisfies the determination condition corresponding to the consistency threshold in memory, the processor determines the two channels as mergeable repeating channels and saves the two channel indices and the complex alignment coefficient.

[0159] For a given set of repeatable channels that can be merged, the processor uses one of the two channels as the amplitude-phase reference and calculates the complex amplitude-phase alignment parameters of the other channel based on the complex alignment coefficient. Then, it reads the two channels of complex data corresponding to the targetless distance unit, calculates the complex mean of each channel, subtracts the corresponding mean from each noise data point, squares the difference, and averages the results to obtain the noise power of the two channels. The reciprocals of the two noise powers are then calculated, and each reciprocal is divided by the sum of the two reciprocals to obtain two real non-negative merging weights.

[0160] Specifically, the processor constructs a 7-row, 8-column equivalent channel transformation matrix. The six non-repeating channels each write the value 1 at the intersection of their corresponding output rows and the original input columns. The two repeating channels together correspond to the remaining output row. The column containing the amplitude-phase reference channel writes its merging weight, and the column containing the other repeating channel writes the product of its merging weight and the complex amplitude-phase alignment parameter. The remaining matrix elements are written with 0.

[0161] When processing the 8-dimensional first equivalent observation vector using the equivalent channel transformation matrix, the processor sequentially reads the seven rows of data in the matrix, multiplies the eight complex coefficients in each row by the corresponding data in the 8-dimensional first equivalent observation vector, and accumulates the results. Each row yields one output complex value. After processing all seven rows, a 7-dimensional second equivalent observation vector is formed. For any candidate direction corresponding to the 8-dimensional first calibration response vector, the processor calls the same equivalent channel transformation matrix and performs the same row-by-row complex multiplication and addition operation to form the 7-dimensional second calibration response vector for that candidate direction. Thus, the amplitude alignment, coherence merging, and channel dimensionality reduction of repeated channels employ the exact same transformation relationships in both the actual observation data and the calibration response data.

[0162] During the first direction-finding process, the processor extracts two equivalent channels of the loop antenna with the same equivalent phase center but different response types based on the 7-dimensional channel index. These channels are then combined into a two-element virtual orthogonal loop observation vector according to a fixed response type order. For each candidate direction, the processor extracts the calibration complex response at the same two channel positions from the corresponding 7-dimensional second calibration response vector. The two calibration complex responses are conjugates, multiplied term by term by the two actual loop observations, and then summed in a complex number. The amplitude of the sum is then squared. Simultaneously, the total energy of the two actual loop observations and the total energy of the two calibration complex responses are calculated. The squared amplitude of the sum is divided by the product of the two total energies to obtain the normalized complex matching value for the current candidate direction. After traversing all candidate directions, the candidate direction corresponding to the position with the maximum matching value is used as the first target direction estimate.

[0163] The second direction-finding process uses a series of seven consecutive second-equivalent observation vectors from the same range-Doppler target detection unit as array snapshots. The processor arranges the consecutive snapshots in chronological order and extracts seven-dimensional noise data from the targetless detection unit. The mean is calculated for each noise channel, and each noise vector is subtracted from its corresponding mean and multiplied by its own conjugate transpose to form a 7x7 outer product matrix. Then, the average of all outer product matrices is calculated element-wise to obtain the 7-channel noise covariance matrix.

[0164] Specifically, the processor generates a noise normalization transform based on the noise covariance matrix and uses the same transform to process the continuous 7-dimensional array snapshots and the 7-dimensional second calibration responses corresponding to each candidate direction. When beamforming is used, the conjugate of the 7 calibration complex responses corresponding to the candidate direction is multiplied term by term with the 7 observations of each snapshot and accumulated. The square of the amplitude of the resulting complex number is then calculated, and the average of all snapshot results is taken to obtain the direction spectrum value for that candidate direction. When subspace spectrum estimation is used, the observation covariance matrix is ​​generated based on the continuous array snapshots, and the noise subspace is obtained through eigenvalue decomposition. The corresponding direction spectrum value is then generated based on the complex inner product of the calibration response of each candidate direction with the noise subspace. The processor compares the direction spectrum results of all candidate directions and determines the direction corresponding to the largest spectral peak that satisfies the aforementioned spectral peak determination criteria as the second target direction estimate. After processing, the first and second target direction estimates, along with the distance index, Doppler index, and processing cycle index that generated the set of observation data, are stored in memory, ensuring that the two direction finding results correspond to the same target detection unit.

[0165] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A simplified whip-loop combined antenna radar detection method based on MIMO equivalent vector array, characterized in that, include: S1. Two mutually orthogonal MIMO waveforms are transmitted through two whip antennas, and four physical reception sequences are synchronously acquired through two whip antenna receiving channels and two loop antenna receiving channels. S2. Based on the pre-acquired joint complex response calibration data of the transmit-receive channel, construct the effective reference sequence corresponding to the two MIMO waveforms. Based on the effective reference sequence, form a reference correlation matrix. Jointly unmix the transmit components in the four physical receive sequences to obtain eight theoretical equivalent observations and form an eight-dimensional first equivalent observation vector and the corresponding eight-dimensional first calibration response vector. S3. Based on the equivalent phase center and response type of each theoretical equivalent observation channel, determine the candidate repeating channels, and based on the eight-dimensional first calibration response vector, determine whether the joint complex response of the candidate repeating channels meets the preset proportional consistency condition. The candidate repeating channels that meet the condition are determined as mergeable repeating channels. S4. Based on the complex response ratio between mergeable repeatable channels, perform amplitude alignment and coherent merging to construct a seven-row, eight-column equivalent channel transformation matrix. Then, use the same equivalent channel transformation matrix to transform the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector to obtain the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector. S5. The equivalent channels of two loop antennas with the same equivalent phase center but different response types are retained as virtual orthogonal loop observation pairs. The first target direction estimate is obtained based on the virtual orthogonal loop observation pairs and their calibration responses. The array direction is then performed based on the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector to obtain the second target direction estimate.

2. The simplified whip-loop combined antenna radar detection method based on MIMO equivalent vector array according to claim 1, characterized in that, S1 includes: The first and second transmission sequences are generated according to the preset pulse timing and encoding parameters, and then a MIMO transmission sequence matrix is ​​formed. Calculate the maximum normalized cross-correlation coefficient between the first and second transmission sequences and compare it with a preset orthogonality threshold. When the maximum normalized cross-correlation coefficient is greater than the orthogonality threshold, adjust the coding parameters or reselect the transmission sequence until the orthogonality condition is met. The first and second transmission sequences that satisfy the orthogonality condition are mapped to the two transmission channels respectively, and the two whip antennas are controlled to transmit the corresponding MIMO waveforms according to a unified clock and trigger sequence, while generating a receive sampling control vector. Complex baseband data from two whip antenna receiving channels and two loop antenna receiving channels are synchronously acquired based on the receiving sampling control vector, and arranged according to the channels to form a four-channel receiving sequence matrix to obtain four physical receiving sequences.

3. The simplified whip-loop combined antenna radar detection method based on MIMO equivalent vector array according to claim 1, characterized in that, S2 includes: The reference complex transfer function and the joint directional complex response calibration model that vary with the candidate direction are extracted from the joint complex response calibration data. The reference complex transfer function is used to perform amplitude and phase compensation on the two MIMO waveforms to generate a valid reference sequence. Two valid reference sequences corresponding to the same receiving channel are combined to form a reference sequence matrix, and a reference correlation matrix is ​​constructed based on the product of the conjugate transposes of the reference sequence matrices. Based on the condition number of the reference correlation matrix and the preset stability threshold, an inverse matrix or a regularized inverse matrix is ​​selected to form the emission component demixing matrix; The four physical received sequences were correlated with the corresponding reference sequence matrices, and four sets of two-element equivalent observation vectors were obtained using the transmit component unmixing matrix. Four sets of two-element equivalent observation vectors are spliced ​​together according to the transmit-receive channel index to form an eight-dimensional first equivalent observation vector, and an eight-dimensional first calibration response vector varying with the candidate direction is constructed from the joint directional complex response calibration model according to the same index.

4. The simplified whip loop combined antenna radar detection method based on MIMO equivalent vector array according to claim 1, characterized in that, S3 includes: Calculate the equivalent position vector of each theoretical equivalent observation channel based on the transmit phase center and receive phase center, and configure the corresponding response type label; Theoretical equivalent observation channels with equivalent location distances less than a preset location threshold and the same response type are grouped into candidate duplicate channel pairs. The candidate repeated channel pairs are extracted from the eight-dimensional first calibration response vector to obtain the first complex response sequence and the second complex response sequence under multiple calibration directions, and the least squares proportional fitting is used to determine the complex alignment coefficient that minimizes the residual of the two complex response sequences. The normalized proportional fitting residual between the two complex response sequences is calculated based on the complex alignment coefficient. The normalized proportional fitting residual is used as the joint response consistency feature and compared with the preset consistency threshold. Candidate duplicate channel pairs whose joint response consistency feature is not greater than the consistency threshold are identified as mergeable duplicate channels, and the corresponding channel index and realignment coefficient are output.

5. The simplified whip loop combined antenna radar detection method based on MIMO equivalent vector array according to claim 1, characterized in that, S4 includes: Read the index of the mergeable repeating channels and the complex alignment coefficient, and determine the complex magnitude relative alignment parameter of the mergeable repeating channels; The real non-negative merging weights of the corresponding repeating channels are determined based on the targetless distance cell, calibration data, or noise statistics within the current coherent processing cycle, and the merging weights remain unchanged within the same coherent processing cycle. Write the complex amplitude relative alignment parameters and merging weights into the matrix elements corresponding to the repeating channels, and construct a seven-row, eight-column equivalent channel transformation matrix by combining the mapping relationship of the other non-repeating channels. By multiplying the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector by the same equivalent channel transformation matrix, the amplitude alignment, coherence merging and channel dimensionality reduction of the repeated channels are completed in one step, resulting in the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector. The seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector are stored according to a unified channel index.

6. The simplified whip-loop combined antenna radar detection method based on MIMO equivalent vector array according to claim 1, characterized in that, S5 includes: Based on the channel index, two loop antenna equivalent channels are extracted from the seven-dimensional second equivalent observation vector to form a virtual orthogonal loop observation vector; Extract the corresponding components from the seven-dimensional second calibration response vector to establish a virtual loop calibration response vector that varies with the candidate direction; Calculate the normalized complex matching feature between the virtual orthogonal loop observation vector and the virtual loop calibration response vector to form a first direction matching sequence, and determine the first target direction estimate based on its peak value; An array snapshot matrix is ​​constructed using the continuous seven-dimensional second equivalent observation vectors of the same range-Doppler target detection unit. The seven-channel noise covariance matrix is ​​estimated based on the absence of a target detection unit. After normalizing the array observation data and the corresponding seven-dimensional second calibration response vector with the same source noise, beamforming or subspace spectrum estimation is performed to form a second directional spectrum sequence. The second target direction estimate is determined based on the effective spectral peaks of the second direction spectral sequence, and the first target direction estimate and the second target direction estimate are associated with the same target detection unit.

7. A system applicable to the simplified whip-loop combined antenna radar detection method based on MIMO equivalent vector array as described in any one of claims 1-6, characterized in that, It includes two shared whip antennas for transmitting and receiving, two dedicated loop antennas for receiving with orthogonal normal axes, a transmitter, a receiver, a synchronization module, and a signal processing module; Two whip antennas are used to transmit two mutually orthogonal MIMO waveforms respectively, and together with two loop antennas, they form four physical receiving channels; The receiver is used to synchronously acquire four physical receive sequences; The signal processing module is used to construct an effective reference sequence for two MIMO waveforms based on the joint complex response calibration data of the transmit-receive channels. It forms a reference correlation matrix based on the effective reference sequence and performs joint demixing on the four physical received sequences to form an eight-dimensional first equivalent observation vector and a corresponding eight-dimensional first calibration response vector. Based on the equivalent phase center, response type, and joint complex response consistency of each theoretical equivalent observation channel, it determines the channels that can be merged and repeat. Based on the complex response ratio of the channels that can be merged and repeat, it constructs a seven-row, eight-column equivalent channel transformation matrix. Using the same equivalent channel transformation matrix, it transforms the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector to obtain a seven-dimensional second equivalent observation vector and a seven-dimensional second calibration response vector. The signal processing module is also used to retain the equivalent channels of two loop antennas with different response types at the same equivalent phase center as virtual orthogonal loop observation pairs, obtain the first target direction estimate based on the virtual orthogonal loop observation pairs, and obtain the second target direction estimate based on the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector.

8. The simplified whip-loop combined antenna radar detection system based on a MIMO equivalent vector array according to claim 7, characterized in that, The signal processing module includes a calibration parameter storage unit and a MIMO demixing unit; The calibration parameter storage unit is used to store the joint complex response calibration data corresponding to each transmit-receive channel combination; The MIMO demixing unit is used to form a reference sequence matrix from two valid reference sequences corresponding to the same physical receiving channel, construct a reference correlation matrix based on the product of the conjugate transpose of the reference sequence matrix, and form a transmit component demixing matrix based on the reference correlation matrix to convert the four physical receiving sequences into four sets of two-element equivalent observation vectors, and form an eight-dimensional first equivalent observation vector according to the transmit channel-receive channel index.

9. The simplified whip-loop combined antenna radar detection system based on a MIMO equivalent vector array according to claim 7, characterized in that, The signal processing module also includes a channel determination unit and an equivalent channel transformation unit; The channel determination unit is used to determine candidate repeating channels based on the equivalent phase center and response type, calculate the joint complex response consistency characteristics of the candidate repeating channels based on the eight-dimensional first calibration response vector, and compare the joint complex response consistency characteristics with a preset consistency threshold to determine the repeating channels that can be merged. The equivalent channel transformation unit is used to determine the complex alignment coefficients based on the complex response ratio between mergeable repeatable channels, and to construct a seven-row, eight-column equivalent channel transformation matrix in combination with real non-negative merging weights, so that the observed data and the calibration response model are synchronously transformed from eight-dimensional to seven-dimensional according to the same complex amplitude and phase reference.

10. An apparatus applicable to the simplified whip-loop combined antenna radar detection method based on MIMO equivalent vector array as described in any one of claims 1-6, characterized in that, It includes a data interface, a memory, and a processor. The data interface is used to receive four physical receive sequences obtained from two whip antenna receiving channels and two loop antenna receiving channels. The memory stores the joint complex response calibration data and program instructions of the transmit-receive channels. When the processor executes program instructions, it is used to: jointly demix the two MIMO transmit components in the four physical receive sequences based on the joint complex response calibration data to form an eight-dimensional first equivalent observation vector and an eight-dimensional first calibration response vector; Based on the equivalent phase center, response type, and joint complex response consistency, the repeatable channels that can be merged are determined. An equivalent channel transformation matrix is ​​constructed, and the eight-dimensional first equivalent observation vector and the eight-dimensional first calibration response vector are transformed simultaneously to obtain the seven-dimensional second equivalent observation vector and the seven-dimensional second calibration response vector. The first direction finding process is performed based on the virtual orthogonal loop observation pair, and the second direction finding process is performed based on the seven-dimensional second equivalent observation vector.

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