Uniform array ultra-wideband radar positioning imaging method based on gradient descent method

Abstract

The application discloses a kind of based on gradient descent method's uniform array ultra-wideband radar positioning imaging method, it is related to radar positioning technical field, the signal matrix model after matching filtering is constructed in the application, matrix decomposition is carried out by gradient descent method, joint direction matrix and joint electromagnetic guide vector matrix are obtained, then, two groups of two-dimensional angle estimation values with high resolution and no ambiguity are respectively obtained from the two matrices, accurate angle parameters are obtained by weighted fusion, and target three-dimensional coordinates are calculated accordingly, finally, radar image is generated by back projection algorithm, so that the number of array elements and hardware complexity are significantly reduced, the inherent angle ambiguity problem of array is overcome, the multi-target angle resolution and parameter estimation stability are improved, and the calculation efficiency and engineering realizability are also considered.

Description

Technical Field

[0001] This invention relates to the field of radar positioning technology, and in particular to a uniform array ultra-wideband radar positioning and imaging method based on gradient descent. Background Technology

[0002] Ultra-wideband (UWB) radar, with its high temporal resolution, strong penetration, and multipath resistance, has demonstrated significant value in fields such as indoor positioning, life detection, and through-wall reconnaissance. Its three-dimensional positioning relies on a multi-element transceiver system, achieving spatial positioning by acquiring the target's distance and angle information. However, high angular resolution typically necessitates a dense deployment of numerous array elements, resulting in complex hardware, high cost, and high power consumption. Furthermore, it is difficult to deploy in complex or confined environments, making it challenging to meet the application requirements of portable, low-cost radar.

[0003] To reduce hardware complexity, centralized arrays, by reducing the number of physical array elements, have become a feasible approach to maintain a larger equivalent aperture. Traditional array elements can only obtain one-dimensional angle information of the target, leading to a significant decrease in the performance of traditional subspace-based direction-finding algorithms. Meanwhile, ultra-wideband radar echoes exhibit multi-dimensional coupling characteristics of time, frequency, transmission, and reception. Traditional two-dimensional matrix models struggle to fully extract their structural information, limiting parameter estimation accuracy in multi-target environments. Although tensor decomposition methods such as PARAFAC have been introduced to handle multi-dimensional data, existing research is mostly based on regular arrays, failing to effectively address the angle ambiguity and phase jump problems unique to sparse arrays. Furthermore, existing methods typically only utilize receiver angle of arrival (AHA) information, failing to jointly estimate the transmitter departure angle (DHA) and receiver AHA. This limits the full utilization of the geometric characteristics of multistatic radars, making it difficult for existing methods to simultaneously achieve high-resolution, ambiguity-free angle estimation and robust localization under centralized array conditions in three-dimensional positioning. This makes it impossible to balance system performance and hardware cost. Summary of the Invention

[0004] In view of this, this invention proposes a uniform array ultra-wideband radar positioning and imaging method based on gradient descent. By constructing a matched-filtered signal matrix model from the echo signal of a centralized uniform array ultra-wideband radar and combining it with the geometric characteristics of the concentrated array elements of the transceiver array, and then obtaining the joint direction matrix, joint electromagnetic steering vector matrix, and spatial response matrix based on matrix decomposition using gradient descent, the multidimensional structure and multi-base geometric characteristics of the signal are fully utilized. Simultaneously, a first two-dimensional angle estimate with high resolution and no periodic ambiguity is obtained from the joint direction matrix, and a second two-dimensional angle estimate with low resolution but no ambiguity is obtained from the joint electromagnetic steering vector matrix based on spatial smoothing technology. The accuracy of the two-dimensional angles is verified, and angle weighting is performed to improve the accuracy of the angles. Based on the weighted two-dimensional angle parameters of the target and the three-dimensional coordinates of the transceiver array, the three-dimensional spatial coordinates of the target object are obtained, and back projection imaging processing of the target is performed. This method overcomes the inherent angle ambiguity problem of the array while significantly reducing the number of array elements and hardware complexity, improving the multi-target angle resolution and parameter estimation stability, while also considering computational efficiency and engineering feasibility.

[0005] The technical solution of this invention is implemented as follows: On the one hand, the present invention provides a uniform array ultra-wideband radar positioning and imaging method based on gradient descent, comprising the following steps: S1 acquires target echo signals based on centralized ultra-wideband radar, and constructs a matched-filtered signal matrix model by combining the geometric characteristics of the centralized array elements of the transceiver array. S2 performs matrix decomposition on the signal matrix model based on gradient descent to obtain the joint direction matrix, joint electromagnetic steering vector matrix, and spatial response matrix; S3 obtains a first two-dimensional angle estimate with high resolution and no periodic ambiguity based on the joint direction matrix, and obtains a second two-dimensional angle estimate with low resolution but no ambiguity from the joint electromagnetic guidance vector matrix. S4 utilizes the high-resolution characteristic of the first two-dimensional angle estimate and the unambiguous characteristic of the second two-dimensional angle estimate to perform a weighted fusion process on the two to obtain a weighted two-dimensional angle parameter. S5 obtains the three-dimensional spatial coordinates of the target object based on the weighted two-dimensional angle parameters and the three-dimensional coordinates of the transceiver array; S6 calculates the target's transmit-receive two-way travel time based on the target object's three-dimensional spatial coordinates and generates the target's radar image through a back projection algorithm.

[0006] Based on the above technical solutions, preferably, step S1 includes the following sub-steps: S11 acquires echo signals from a centralized ultra-wideband radar system to multiple incoherent far-field scattering targets. The transmitting and receiving elements of the radar system are equipped with electromagnetic vector sensors, and the transceiver arrays are arranged at half-wavelength intervals. S12 performs matched filtering on the echo signal to obtain a signal matrix model characterizing the joint response of the transmit-receive channel.

[0007] Based on the above technical solutions, preferably, in step S2, the matrix decomposition based on gradient descent is defined as the Frobenius norm error between the product of the signal matrix model and the joint direction matrix, joint electromagnetic steering vector matrix and spatial response matrix to be decomposed. The objective function is minimized by iteratively updating the three matrices. The decomposition is completed when the iterative gradient norm is less than a set threshold.

[0008] Based on the above technical solution, preferably, in step S3, obtaining a first two-dimensional angle estimate with high resolution and no periodic ambiguity based on the joint direction matrix, and obtaining a second two-dimensional angle estimate with low resolution but no ambiguity from the joint electromagnetic guidance vector matrix, includes the following sub-steps: S31 utilizes the Khatri-Rao product structure of the joint direction matrix to perform block spatial smoothing. Based on the phase information of the smoothed submatrix and combined with the three-dimensional coordinates of the transceiver array elements, the first two-dimensional angle estimate is obtained by least squares estimation. S32 utilizes the Khatri-Rao product structure of the joint electromagnetic guidance vector matrix to perform block spatial smoothing, and calculates the normalized Poynting vector based on the vector relationship of the smoothed submatrices to obtain the second two-dimensional angle estimate.

[0009] Based on the above technical solution, preferably, the weighted fusion processing in step S4 is as follows: calculate the deviation between the first two-dimensional angle estimate and the second two-dimensional angle estimate; when the deviation is less than a preset error threshold, perform a weighted average on the two according to a preset weighting coefficient, and output the result as a weighted two-dimensional angle parameter.

[0010] Based on the above technical solutions, preferably, in step S6, the transmit-receive two-way travel time of the target is calculated based on the three-dimensional spatial coordinates of the target object, and a radar image of the target is generated through a back projection algorithm, including the following sub-steps: For each target, S61 calculates the corresponding two-way travel time based on its three-dimensional spatial coordinates and the three-dimensional position of each transmit-receive array element pair; S62 extracts the signal amplitude from the corresponding received signal channel based on each two-way travel time, and superimposes the amplitudes extracted from all channels on the backward projection grid points in the time domain to form a radar image of the target.

[0011] More preferably, in step S12, the signal matrix model characterizing the joint response of the transmit-receive channel is expressed by the following equation:

[0012] in, For the first l A is a received signal vector captured in a quick snapshot. t Let A be the emission direction matrix. r For the receiving direction matrix, A r For the electromagnetic guidance matrix to be emitted, B r For electromagnetic guidance matrix, f( l ) is the first l The complex amplitude vectors of each target are captured in a quick snapshot, n( l ) represents the additive noise vector, and ⊙ represents the Khatri-Rao product. The signal matrix model is constructed by arranging the received signal vectors y(1), y(2), ..., y(L) in L time snapshots in columns.

[0013] Based on the above technical solution, preferably, in step S2, the signal matrix model is decomposed using the gradient descent method, specifically including the following iterative process: S21 initializes the joint direction matrix, joint electromagnetic guidance vector matrix, and spatial response matrix according to preset rules based on the array element position information and the assumed target angle. S22 calculates the gradient of the objective function with respect to the joint direction matrix, the joint electromagnetic steering vector matrix, and the spatial response matrix under the current matrix value; S23 updates the three matrices simultaneously along the negative gradient direction with an adaptive step size; S24 calculates the gradient norm of the objective function corresponding to the updated matrix. If it is less than the preset convergence threshold, the iteration stops and the current matrix is ​​output as the decomposition result. Otherwise, return to step S22 to continue the iteration.

[0014] On the other hand, the present invention provides a uniform array ultra-wideband radar localization and imaging system based on gradient descent, for performing the above-described uniform array ultra-wideband radar localization and imaging method based on gradient descent, comprising: The signal acquisition and modeling module is configured to acquire target echo signals based on a centralized ultra-wideband radar and, in combination with the geometric characteristics of the centralized array elements of the transceiver array, construct a matched-filtered signal matrix model. The matrix decomposition module is configured to perform matrix decomposition on the signal matrix model based on gradient descent to obtain a joint direction matrix, a joint electromagnetic steering vector matrix, and a spatial response matrix. An angle estimation module is configured to obtain a first two-dimensional angle estimate based on the joint direction matrix and a second two-dimensional angle estimate based on the joint electromagnetic guidance vector matrix. An angle fusion module is configured to perform weighted fusion processing on the first two-dimensional angle estimate and the second two-dimensional angle estimate to obtain the weighted two-dimensional angle parameters of the target; A three-dimensional positioning module is configured to calculate the three-dimensional spatial coordinates of the target object based on the weighted two-dimensional angle parameters and the known three-dimensional coordinates of the transceiver array. The radar imaging module is configured to calculate the transmit-receive two-way travel time of the target based on the three-dimensional spatial coordinates, and generate a radar image of the target through a back projection algorithm.

[0015] On the other hand, the present invention provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described uniform array ultra-wideband radar positioning and imaging method based on gradient descent.

[0016] The uniform array ultra-wideband radar positioning and imaging method based on gradient descent of the present invention has the following advantages over the prior art: 1. By combining the echo signal of a centralized uniform array ultra-wideband radar with the geometric characteristics of the centralized array elements of the transceiver array to construct a matched-filtered signal matrix model, and using matrix decomposition based on gradient descent, a joint direction matrix, a joint electromagnetic steering vector matrix, and a spatial response matrix are obtained. This fully utilizes the multidimensional structure and multi-base geometric characteristics of the signal. Simultaneously, through the joint direction matrix, a first two-dimensional angle estimate with high resolution and no periodic ambiguity is obtained. Based on spatial smoothing technology, a second two-dimensional angle estimate with low resolution but no ambiguity is obtained from the joint electromagnetic steering vector matrix. By comparing and analyzing the first and second two-dimensional angle estimates, the correctness of the two-dimensional angle is verified, and angle weighting is performed to improve the accuracy of the angle. Thus, while significantly reducing the number of array elements and hardware complexity, the inherent angle ambiguity problem of sparse arrays is overcome, and the multi-target angle resolution and parameter estimation stability are improved, while also taking into account computational efficiency and engineering feasibility. 2. By extracting low-resolution but unambiguous two-dimensional departure angle and low-resolution but unambiguous two-dimensional arrival angle from the joint electromagnetic guidance matrix using spatial smoothing technology and Poynting's theorem, and combining them with high-resolution two-dimensional angle information in the joint direction matrix, the target positioning is achieved by combining the fused high-precision two-dimensional angle with the known three-dimensional coordinates of the array and using the analytical optimization method of spatial ray intersection. The target's transmit-receive two-way travel time is calculated, and the target's back projection imaging is performed. This method can significantly reduce the system's dependence on the number of array elements while ensuring high-resolution and unambiguous angle estimation, thus achieving a balance between high-precision three-dimensional positioning and low hardware complexity. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the uniform array ultra-wideband radar positioning and imaging method based on gradient descent according to the present invention. Figure 2 This is a scatter plot of two-dimensional angle estimation results of the uniform array ultra-wideband radar positioning and imaging method based on gradient descent in the present invention under an incoherent target environment. Figure 3 This is an example of a 2D scatter plot taken from a coherent source using the uniform array ultra-wideband radar positioning and imaging method based on gradient descent, as described in this invention. Figure 4 This is a schematic diagram of a sparse uniform array ultra-wideband radar system model for the uniform array ultra-wideband radar positioning and imaging method based on gradient descent of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0020] like Figure 1-4 As shown, the uniform array ultra-wideband radar positioning and imaging method based on gradient descent of the present invention includes steps S1-S5.

[0021] Step S1: Based on the centralized ultra-wideband radar, acquire the target echo signal and construct the matched-filtered signal matrix model by combining the geometric characteristics of the centralized array elements of the transceiver array.

[0022] Step S1 first acquires the target's echo signal based on a centralized ultra-wideband radar system. This system consists of multiple transmitting and receiving array elements deployed at known spatial locations, with each element arranged at a half-wavelength interval. Each element is equipped with an electromagnetic vector sensor to acquire signals containing polarization information. By performing matched filtering on the echo signal, a signal matrix model characterizing the joint response of the transmitting and receiving channels is obtained. Then, using matrix decomposition with gradient descent, the joint direction matrix, joint electromagnetic steering vector matrix, and spatial response matrix are obtained, laying the data structure foundation for subsequent multi-dimensional parameter estimation based on the target's electromagnetic information and the spatial information of the transmitting and receiving array elements.

[0023] In actual operation, it can be further divided into sub-steps S11-S12.

[0024] Step S11: Acquire echo signals from a centralized ultra-wideband radar system for multiple incoherent far-field scattering targets, wherein both the transmitting and receiving elements of the radar system are equipped with electromagnetic vector sensors, and the transceiver arrays are arranged at half-wavelength intervals.

[0025] A centralized ultra-wideband radar system consists of several transmitting and receiving units, the number of which is denoted as follows: and The transceiver arrays are uniformly arranged with half-wavelength spacing to meet the basic requirement of unambiguous angle measurement, thereby reducing the number of physical array elements while maintaining sufficient equivalent aperture. The three-dimensional spatial coordinates of all transceiver array elements are known through pre-calibration. There are multiple independent far-field scattering targets in the system's observation scene. Each target corresponds to a unique two-dimensional angle of arrival, two-dimensional angle of departure, and polarization parameters. By cascading the matched filter outputs of all transceiver channels in a predetermined order, a structured long vector form of multi-channel signal is obtained.

[0026] Specifically, the first Launching array elements and the first The spatial coordinates of the receiving array elements are denoted as follows: and superscript Similarly, for the transmitting array... This means that, for the receiving array, This represents the transpose of a vector. The geometric spacing between the transceiver arrays satisfies the half-wavelength constraint. This centralized ultra-wideband radar system has observation scenarios where... A number of independent far-field scatterers. For the first... For each target, the two-dimensional angle of arrival (2D-DOA) obtained from the transmission array observation is denoted as... The two-dimensional departure angle (2D-DOD) corresponding to the receiving array is expressed as... Its polarization properties can be described by the auxiliary polarization angle and phase difference parameter, denoted as , respectively. and .

[0027] Step S12: Perform matched filtering on the echo signal to obtain a signal matrix model characterizing the joint response of the transmit-receive channel.

[0028] The aforementioned multi-channel signals are further constructed into a signal matrix model with clear physical meaning. The echo component of each target can be represented as a linear combination of the transmit direction vector, receive direction vector, transmit / receive electromagnetic guidance vector, and spatial response vector. Mathematically, this model can be uniformly expressed as the product of the Khatri-Rao product of the transmit direction matrix, transmit electromagnetic guidance matrix, receive direction matrix, and receive electromagnetic guidance matrix, and the target spatial response vector. This allows for the joint characterization of array geometry, polarization characteristics, and target scattering characteristics. Specifically, the signal matrix model characterizing the joint response of the transmit and receive channels can be expressed by the following equation:

[0029] in, For the first l The received signal vectors are captured in a quick snapshot, where K represents the number of incoherent far-field scattering targets in the observed scene. Describe the spatial phase relationship of the k-th target relative to the transmission array. It contains the target's emission polarization information. Describe the spatial phase relationship of the k-th target relative to the receiving array. Includes the target's received polarization information. Represents the k-th target's... l A quick snapshot of the complex amplitude. Represents the Kronecker product, A t Let B be the emission direction matrix. t For the electromagnetic guidance matrix to be emitted, A r To receive the direction matrix, B r To receive the electromagnetic guidance matrix, f( l ) is the first l The complex amplitude vectors of each target are captured in a quick snapshot, n( l ) represents the additive noise vector, and ⊙ represents the Khatri-Rao product. The signal matrix model is constructed by arranging the received signal vectors y(1), y(2), ..., y(L) in L time snapshots in columns.

[0030] Step S2: Perform matrix decomposition on the signal matrix model based on gradient descent to obtain the joint direction matrix, joint electromagnetic steering vector matrix, and spatial response matrix.

[0031] The signal matrix model is decomposed using gradient descent. The objective function is defined as the Frobenius norm error between the signal matrix model and the product of the joint direction matrix, the joint electromagnetic steering vector matrix, and the spatial response matrix to be decomposed. The objective function is minimized by iteratively updating the three matrices. The decomposition is completed when the iterative gradient norm is less than a set threshold.

[0032] Specifically, it is used to receive signals from the matrix. The direction matrices of the transmitting and receiving arrays are decomposed from the matrix. and joint electromagnetic guidance matrix and spatial response matrix .

[0033] The objective function is to minimize the following error function using gradient descent:

[0034] in, This represents the Frobenius norm of the matrix, i.e.: To apply gradient descent, it is necessary to compute each matrix. , and The gradient with respect to the objective function. Gradient calculation is based on the chain rule and uses the derivative of the matrix.

[0035] right Gradient: Calculate the error term For the matrix The gradient can be obtained using the chain rule: in, It is the reconstruction error, representing The difference between the predicted value and the actual value.

[0036] right The gradient: Similarly, calculate the gradient of the matrix. The gradient can be obtained using the chain rule: in, It is a matrix transpose, It is an error term. It is the spatial response matrix.

[0037] right The gradient: Similarly, calculate the gradient with respect to the matrix. The gradient is obtained as follows: in, yes transpose, It is an error term. It is the direction matrix of the transmitting and receiving arrays.

[0038] Based on the gradient calculation results, the matrix is ​​updated using the gradient descent method. , and The specific update rules are as follows:

[0039] Based on the principle of gradient descent, the matrix is ​​adjusted according to the following update rules. : in The learning rate (step size) determines the pace of each update.

[0040] Similarly, matrix The update rules are as follows: matrix The update rules are as follows: These update rules are used to adjust the matrix in each iteration. , and This minimizes the reconstruction error.

[0041] The convergence condition is usually defined as stopping the iteration when the norm of the gradient is less than a set threshold.

[0042] For matrix , and The gradients are: The algorithm is considered convergent if and only if the algorithm is convergent. It is a set threshold (e.g.) ).

[0043] Step S3: Based on the joint direction matrix, obtain a first two-dimensional angle estimate with high resolution and no periodic ambiguity, and obtain a second two-dimensional angle estimate with low resolution but no ambiguity from the joint electromagnetic guidance vector matrix.

[0044] Specifically, based on the joint direction matrix, and according to the Khatri-Rao product form when the joint direction matrix is ​​constructed, spatial smoothing is performed in blocks. The first two-dimensional angle estimate with high resolution and no periodic ambiguity is obtained by using the least squares method from the normalized phase information and the three-dimensional spatial information of the transmitting and receiving array elements, through the following steps.

[0045] The joint direction matrix is ​​in the form of Perform front space smoothing techniques on Some parts are normalized, specifically:

[0046] Among them, subscript Representing the joint matrix The Okay, what we get now This is the normalized emission direction matrix.

[0047] Based on the known spatial positions of each element in the uniform emission array, construct the emission direction matrix. Each column corresponds to a two-dimensional direction vector of the potential target, due to the emission direction matrix. The phase is about Linear, meaning the first two-dimensional angle of arrival estimate of the target can be obtained using the least squares technique, and the direction phase h of the k-th target. k （t） Represented as:

[0048] in, Represents phase in radians, mapped phase yes The period, its range is Within the interval, This represents the estimated directional phase of the k-th target in the Mt-th receiver element. Denotes an Mt-dimensional complex column vector, [ ] T This represents the matrix transpose, where λ is the radar signal wavelength.

[0049] At the same time:

[0050] in, It is the normalized Poynting vector of the k-th target.

[0051] Furthermore, for the above equation, we have: .

[0052] The geometric relationship of the array provides physical constraints for the least squares solution, which allows the angle estimation problem to be transformed into a linear fitting problem.

[0053] By using least squares fitting, the emission matrix is ​​matched with the direction matrix. By solving the problem of minimizing the sum of squared errors, the normalized Poynting vector of the target is obtained. Therefore, we have estimates of the first two-dimensional wave departure angle, azimuth angle, and elevation angle, which are expressed as follows:

[0054] in, The direction cosine is represented in the x-direction. The direction cosine is represented by the y-direction. This represents the pitch angle of the k-th target. Let represent the azimuth angle of the k-th target, and arcsin represents the angle corresponding to this projection length.

[0055] because and The structure is consistent, and the estimation of the first two-dimensional wave arrival angle azimuth and elevation angle is performed based on the estimation process of solving the first two-dimensional wave departure angle azimuth and elevation angle.

[0056] The spatial smoothing process specifically involves:

[0057] The estimation of the first two-dimensional angle of arrival (AOA) and elevation angle is as follows:

[0058] Step S32: Based on the Khatri-Rao product form when constructing the electromagnetic guidance vector matrix, perform spatial smoothing in blocks, and use the normalized Poynting vector to obtain a second two-dimensional angle estimate with low resolution characteristics but no periodic ambiguity.

[0059] Based on the Khatri-Rao product structure of the joint electromagnetic guidance composite matrix, the normalized transmit-receive electromagnetic guidance matrix is ​​separated from the joint matrix by spatial smoothing technique.

[0060] Normalized receiver electromagnetic steering vector obtained using spatial smoothing:

[0061]

[0062] The normalized electric and magnetic field vectors corresponding to each target are extracted from the separated receiver-transmitter electromagnetic guidance matrix components. Based on Poynting's theorem, the electric and magnetic field vectors are cross-multiplied to obtain the normalized Poynting vector, which reflects the instantaneous energy flow direction of the electromagnetic wave. This vector directly points to the signal propagation direction, and its calculation process is entirely based on the physical measurements of the electromagnetic field, independent of the array geometry. Based on the three rectangular components of the Poynting vector in the reference coordinate system, the azimuth and elevation angles of the target are calculated using inverse trigonometric functions, serving as the second two-dimensional angle estimates. The angular resolution obtained by this method is relatively low due to the inherent aperture and measurement accuracy of the electromagnetic vector sensor, but because it is based on direct physical law derivation, it does not suffer from periodic ambiguity.

[0063] The second two-dimensional wave-departure angle parameter, which has low resolution but no ambiguity, is obtained by transforming trigonometric relationships:

[0064] In the formula, ~ represents the estimate of the corresponding parameter.

[0065] The transformation yields a second two-dimensional angle of arrival parameter with low resolution but no blurring:

[0066] Step S4: Utilize the high-resolution characteristics of the first two-dimensional angle estimate and the unambiguous characteristics of the second two-dimensional angle estimate to perform weighted fusion processing on the two to obtain weighted two-dimensional angle parameters.

[0067] Calculate the deviation between the first two-dimensional angle estimate and the second two-dimensional angle estimate; when the deviation is less than a preset error threshold, perform a weighted average on the two according to a preset weighting coefficient, and output the result as a weighted two-dimensional angle parameter, which includes the third two-dimensional wave departure angle and the third two-dimensional wave arrival angle.

[0068] The third two-dimensional wave angle after fusion is:

[0069] The third two-dimensional angle of arrival is:

[0070] In the above formula, For weighted calculation, a weight of 90% is generally used to achieve two-dimensional angle weighting and obtain the third two-dimensional angle information.

[0071] Step S5: Obtain the three-dimensional spatial coordinates of the target object based on the weighted two-dimensional angle parameters and the three-dimensional coordinates of the transceiver array.

[0072] After achieving high-resolution, unambiguous estimation of the third two-dimensional angle of departure (2D-DOD) of the transmitting array and the third two-dimensional angle of arrival (2D-DOA) of the receiving array, the target can be located in three dimensions using the known spatial coordinates of the array elements. Let the coordinates of the transmitting array be... The coordinates of the receiving array are By converting two-dimensional angle information into three-dimensional unit direction vectors and Based on the coordinates of the launch array elements and Starting from the coordinates of the receiving array element, establish a ray along the direction vector:

[0073] Where λ, μ∈R are ray parameters, and r （t） With r （t） These represent incident rays and emitted rays, respectively.

[0074] Since the rays may not intersect perfectly at a single point, the intersection point of the nearest points can be found using the least squares method to obtain the three-dimensional coordinates of the target. :

[0075] Where argmin represents making Find the smallest independent variable x, and then obtain the result. This is the estimated three-dimensional position of the target in space, which is used to solve for the target's three-dimensional spatial coordinates and locate the target.

[0076] Step S6: Calculate the target's transmit-receive two-way travel time based on the target object's three-dimensional spatial coordinates, and generate the target's radar image using a back projection algorithm.

[0077] For each target, the corresponding two-way travel time is calculated based on its three-dimensional spatial coordinates and the three-dimensional position of each transmit-receive array element pair.

[0078] In obtaining the estimated three-dimensional coordinates of the target Then, the transmit-receive round-trip distance is calculated based on the position information of the transceiver array:

[0079] Then the round-trip travel time can be calculated: .

[0080] Based on the two-way travel time, the signal amplitude is extracted from the corresponding received signal channel, and the amplitudes extracted from all channels are coherently superimposed on the back-projected grid points to form a radar image of the target.

[0081] Calculation of back projection imaging of the target:

[0082] in, This represents the total number of channels of the filtered echo signal obtained by the ultra-wideband radar.

[0083] In one specific embodiment, the centralized ultra-wideband radar system consists of Arbitrarily distributed EMVS transmission arrays and It is composed of arbitrarily distributed EMVS receiver arrays, with element spacing of respectively. and , This represents the number of snapshots, assuming it exists. The targets are in the far field, and their pitch angles are as follows: , azimuth angle is , For the EMVS related parameters of the transmit array, the auxiliary polarization angle is... The polarization phase difference is In the simulation experiment, the signal-to-noise ratio (SNR) is defined as:

[0084] In the formula, , These are the signal matrix and the noise matrix, respectively.

[0085] The accuracy of angle estimation is evaluated using RMSE. Let Monte Carlo degree be denoted as:

[0086] in, and This represents the estimated values ​​of the pitch and azimuth angles of the k-th target. and This represents the true values ​​of the elevation and azimuth angles of the k-th target, assuming the number of EMVS transmission arrays... Arbitrarily distributed in three dimensions In space, the number of EMVS receiver arrays is of URA array, its , , , Figure 2The scatter plot shows the two-dimensional angle estimation results of the centralized uniform array ultra-wideband radar direction finding algorithm proposed in this invention under incoherent target environment. It can be clearly observed that the algorithm can accurately estimate the two-dimensional angle of arrival and two-dimensional angle of departure of each target, and can realize automatic parameter matching. Experimental results show that the present invention maintains excellent angle estimation performance under incoherent source conditions, and achieves high-precision and high-resolution direction parameter recovery, providing a reliable foundation for subsequent three-dimensional spatial positioning.

[0087] When it is a single fast shot At the same time, improve , Figure 3 The diagram shows a 2D scatter plot of the direction-finding algorithm of this invention under a single snapshot from a coherent source. For data from a single snapshot, the two-dimensional angle estimation method of this invention can still accurately recover the third two-dimensional angle of arrival and the two-dimensional angle of departure for each target, indicating that the proposed direction-finding algorithm has high stability and accuracy in incoherent target scenarios. This demonstrates that even under conditions of limited data or instantaneous snapshots, the method of this invention can still accurately recover the third two-dimensional angle parameters of each target, further verifying the high stability and reliability of the algorithm under limited data conditions, and ensuring excellent application performance of the system in dynamic or complex environments.

[0088] The present invention provides a uniform array ultra-wideband radar positioning and imaging system based on gradient descent, which is used to execute the above-mentioned uniform array ultra-wideband radar positioning and imaging method based on gradient descent. It includes a signal acquisition and modeling module, a matrix decomposition module, an angle estimation module, an angle fusion module, a three-dimensional positioning module, and a radar imaging module.

[0089] The signal acquisition and modeling module is configured to acquire target echo signals based on a centralized ultra-wideband radar, and to construct a matched-filtered signal matrix model by combining the geometric characteristics of the centralized array elements of the transceiver array.

[0090] The matrix decomposition module is configured to perform matrix decomposition on the signal matrix model based on gradient descent to obtain the joint direction matrix, the joint electromagnetic steering vector matrix, and the spatial response matrix.

[0091] The angle estimation module is configured to obtain a first two-dimensional angle estimate based on the joint direction matrix and a second two-dimensional angle estimate based on the joint electromagnetic guidance vector matrix.

[0092] The angle fusion module is configured to perform weighted fusion processing on the first two-dimensional angle estimate and the second two-dimensional angle estimate to obtain the weighted two-dimensional angle parameters of the target.

[0093] The three-dimensional positioning module is configured to calculate the three-dimensional spatial coordinates of the target object based on the weighted two-dimensional angle parameters and the known three-dimensional coordinates of the transceiver array.

[0094] The radar imaging module is configured to calculate the transmit-receive two-way travel time of the target based on the three-dimensional spatial coordinates, and generate a radar image of the target through a back projection algorithm.

[0095] The present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described uniform array ultra-wideband radar positioning and imaging method based on gradient descent.

[0096] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0097] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0098] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the shown or discussed mutual couplings or direct couplings or communication connections may be through some service interfaces; indirect couplings or communication connections between apparatuses or units may be electrical or other forms.

[0099] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0100] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0101] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0102] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A uniform array ultra-wideband radar positioning and imaging method based on gradient descent, characterized in that, Includes the following steps: S1 acquires target echo signals based on centralized ultra-wideband radar, and constructs a matched-filtered signal matrix model by combining the geometric characteristics of the centralized array elements of the transceiver array. S2 performs matrix decomposition on the signal matrix model based on gradient descent to obtain the joint direction matrix, joint electromagnetic steering vector matrix, and spatial response matrix; S3 obtains a first two-dimensional angle estimate with high resolution and no periodic ambiguity based on the joint direction matrix, and obtains a second two-dimensional angle estimate with low resolution but no ambiguity from the joint electromagnetic guidance vector matrix. S4 utilizes the high-resolution characteristic of the first two-dimensional angle estimate and the unambiguous characteristic of the second two-dimensional angle estimate to perform a weighted fusion process on the two to obtain a weighted two-dimensional angle parameter. S5 obtains the three-dimensional spatial coordinates of the target object based on the weighted two-dimensional angle parameters and the three-dimensional coordinates of the transceiver array; S6 calculates the target's transmit-receive two-way travel time based on the target object's three-dimensional spatial coordinates and generates the target's radar image through a back projection algorithm.

2. The uniform array ultra-wideband radar positioning and imaging method based on gradient descent as described in claim 1, characterized in that, Step S1 includes the following sub-steps: S11 acquires echo signals from a centralized ultra-wideband radar system to multiple incoherent far-field scattering targets. The transmitting and receiving elements of the radar system are equipped with electromagnetic vector sensors, and the transceiver arrays are arranged at half-wavelength intervals. S12 performs matched filtering on the echo signal to obtain a signal matrix model characterizing the joint response of the transmit-receive channel.

3. The uniform array ultra-wideband radar positioning and imaging method based on gradient descent as described in claim 1, characterized in that, In step S2, the matrix decomposition based on gradient descent is defined by the Frobenius norm error between the product of the signal matrix model and the joint direction matrix, joint electromagnetic steering vector matrix and spatial response matrix to be decomposed. The objective function is minimized by iteratively updating the three matrices. The decomposition is completed when the iterative gradient norm is less than a set threshold.

4. The uniform array ultra-wideband radar positioning and imaging method based on gradient descent as described in claim 1, characterized in that, In step S3, based on the joint direction matrix, a first two-dimensional angle estimate with high resolution and no periodic ambiguity is obtained, and a second two-dimensional angle estimate with low resolution but no ambiguity is obtained from the joint electromagnetic guidance vector matrix, including the following sub-steps: S31 utilizes the Khatri-Rao product structure of the joint direction matrix to perform block spatial smoothing. Based on the phase information of the smoothed submatrix and combined with the three-dimensional coordinates of the transceiver array elements, the first two-dimensional angle estimate is obtained by least squares estimation. S32 utilizes the Khatri-Rao product structure of the joint electromagnetic guidance vector matrix to perform block spatial smoothing, and calculates the normalized Poynting vector based on the vector relationship of the smoothed submatrices to obtain the second two-dimensional angle estimate.

5. The uniform array ultra-wideband radar positioning and imaging method based on gradient descent as described in claim 1, characterized in that, The weighted fusion process in step S4 is as follows: calculate the deviation between the first two-dimensional angle estimate and the second two-dimensional angle estimate; when the deviation is less than a preset error threshold, perform a weighted average on the two values ​​according to a preset weighting coefficient, and output the result as a weighted two-dimensional angle parameter.

6. The uniform array ultra-wideband radar positioning and imaging method based on gradient descent as described in claim 1, characterized in that, In step S6, the transmit-receive two-way travel time of the target is calculated based on the three-dimensional spatial coordinates of the target object, and a radar image of the target is generated through a back projection algorithm, including the following sub-steps: For each target, S61 calculates the corresponding two-way travel time based on its three-dimensional spatial coordinates and the three-dimensional position of each transmit-receive array element pair; S62 extracts the signal amplitude from the corresponding received signal channel based on each two-way travel time, and superimposes the amplitudes extracted from all channels on the backward projection grid points in the time domain to form a radar image of the target.

7. The uniform array ultra-wideband radar positioning and imaging method based on gradient descent as described in claim 2, characterized in that, In step S12, the signal matrix model characterizing the joint response of the transmit-receive channel is expressed by the following equation: in, For the first l A is a received signal vector captured in a quick snapshot. t Let A be the emission direction matrix. r For the receiving direction matrix, A r For the electromagnetic guidance matrix to be emitted, B r To receive the electromagnetic guidance matrix, f( l ) is the first l The complex amplitude vectors of each target are captured in a quick snapshot, n( l ) represents the additive noise vector, and ⊙ represents the Khatri-Rao product. The signal matrix model is constructed by arranging the received signal vectors y(1), y(2), ..., y(L) in L time snapshots in columns.

8. The uniform array ultra-wideband radar positioning and imaging method based on gradient descent as described in claim 1, characterized in that, In step S2, the signal matrix model is decomposed based on gradient descent, specifically including the following iterative process: S21 initializes the joint direction matrix, joint electromagnetic guidance vector matrix, and spatial response matrix according to preset rules based on the array element position information and the assumed target angle. S22 calculates the gradient of the objective function with respect to the joint direction matrix, the joint electromagnetic steering vector matrix, and the spatial response matrix under the current matrix value; S23 updates the three matrices simultaneously along the negative gradient direction with an adaptive step size; S24 calculates the gradient norm of the objective function corresponding to the updated matrix. If it is less than the preset convergence threshold, the iteration stops and the current matrix is ​​output as the decomposition result. Otherwise, return to step S22 to continue the iteration.

9. A uniform array ultra-wideband radar positioning and imaging system based on gradient descent, characterized in that, A method for performing a uniform array ultra-wideband radar localization and imaging method based on gradient descent as described in any one of claims 1 to 7, comprising: The signal acquisition and modeling module is configured to acquire target echo signals based on a centralized ultra-wideband radar and, in combination with the geometric characteristics of the centralized array elements of the transceiver array, construct a matched-filtered signal matrix model. The matrix decomposition module is configured to perform matrix decomposition on the signal matrix model based on gradient descent to obtain a joint direction matrix, a joint electromagnetic steering vector matrix, and a spatial response matrix. An angle estimation module is configured to obtain a first two-dimensional angle estimate based on the joint direction matrix and a second two-dimensional angle estimate based on the joint electromagnetic guidance vector matrix. An angle fusion module is configured to perform weighted fusion processing on the first two-dimensional angle estimate and the second two-dimensional angle estimate to obtain the weighted two-dimensional angle parameters of the target; A three-dimensional positioning module is configured to calculate the three-dimensional spatial coordinates of the target object based on the weighted two-dimensional angle parameters and the known three-dimensional coordinates of the transceiver array. The radar imaging module is configured to calculate the transmit-receive two-way travel time of the target based on the three-dimensional spatial coordinates, and generate a radar image of the target through a back projection algorithm.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the uniform array ultra-wideband radar positioning and imaging method based on gradient descent as described in any one of claims 1-8.

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