A wide-band high-precision DOA estimation method based on optimal redundant linear array

Abstract

This invention relates to the field of antenna technology and discloses a wideband high-precision DOA estimation method based on an optimal redundant linear array. The method includes: establishing a sampling model: constructing a sampling model based on uniform sampling samples at the Nyquist sampling frequency, the sampling model including a multi-set sampling model and a dual-channel coprime sampling model; processing the sampled data and then substituting the processed data into a formula for high-precision frequency estimation. This wideband high-precision DOA estimation method based on an optimal redundant linear array, using a coprime sampling model, significantly reduces the system's data processing volume and sampling hardware requirements. For coprime sampling conditions, a frequency estimation algorithm based on sparse Bayes is proposed, and the algorithm runs quickly, thus meeting the real-time requirements of the frequency measurement system. The coprime sampling model can firstly reduce the ADC's sampling rate, thus reducing the ADC's hardware cost, decreasing the amount of data in the receiving channel, and lowering the requirements for the chip's data processing capabilities.

Description

Technical Field

[0001] This invention relates to the field of antenna technology, specifically to a wideband high-precision DOA estimation method based on an optimal redundant linear array. Background Technology

[0002] With the continuous development of radar countermeasure equipment, the single-beam scanning amplitude comparison method is commonly used in the mainstream radar countermeasure reconnaissance equipment currently in service. The accuracy and angular resolution of this method depend on the beamwidth, making it difficult to achieve a high level.

[0003] To change this situation, phase interferometers have been gradually used to replace amplitude comparison method for direction finding in equipment development. This can effectively improve the estimation accuracy, but it cannot distinguish multiple signals at the same time.

[0004] In comparison, the array direction finding system, which is widely adopted in many fields such as radar, communication, and sonar, has the ability to simultaneously find directions from multiple signals, has high direction finding accuracy, and strong anti-interference capabilities.

[0005] However, for drone platforms, the uniform array antennas commonly used in radar are not well adapted to the application scenario of drone platforms and have poor performance.

[0006] Chinese Patent 2021113243853 discloses an array antenna, a sparse rectangular array, and an antenna design method. This patent discloses an optimal redundant parallel array. When using this array, a wideband DOA method is required. An important prerequisite for wideband DOA estimation is frequency estimation. Traditional wideband DOA estimation requires a high sampling frequency. Therefore, a wideband high-precision DOA estimation method based on an optimal redundant linear array is proposed to solve the above-mentioned problems. Summary of the Invention

[0007] (a) Technical problems to be solved

[0008] To address the shortcomings of existing technologies, this invention provides a wideband high-precision DOA estimation method based on an optimal redundant linear array, which has the advantages of low sampling frequency and solves the problem of high sampling frequency.

[0009] (II) Technical Solution

[0010] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0011] Establish a sampling model: Construct a sampling model based on uniformly sampled samples with Nyquist sampling frequency. The sampling model includes a multi-set sampling model and a dual-channel coprime sampling model.

[0012] The sampled data is processed and then substituted into a formula for high-precision frequency estimation.

[0013] The beneficial effects of this invention are:

[0014] This wideband high-precision DOA estimation method based on an optimal redundant linear array and a coprime sampling model significantly reduces the system's data processing volume and sampling hardware requirements. For coprime sampling conditions, a sparse Bayes-based frequency estimation algorithm is proposed, and its rapid execution is achieved, thus meeting the real-time requirements of frequency measurement systems. An optimal selection criterion for coprime parameters in coprime sampling is established, and an evaluation index for the reduction in sampling rate is proposed. The coprime sampling model firstly reduces the ADC's sampling rate, decreasing its hardware cost; secondly, it reduces the amount of data in the receiving channel, lowering the requirements for chip data processing capabilities and further reducing hardware costs. The high-precision frequency estimation algorithm based on sparse representation can achieve high-precision signal carrier frequency estimation. By designing a rapid implementation scheme, the algorithm's execution time is significantly reduced, meeting the real-time requirements of frequency measurement.

[0015] Based on the above technical solution, the present invention can be further improved as follows.

[0016] Furthermore, the multi-set sampling model refers to a sampling scheme that selects multiple channels based on uniform sampling samples based on the Nyquist sampling frequency. When using this sampling scheme, only one receiving channel and ADC module need to be added to the traditional array antenna to perform high-precision estimation of the signal carrier frequency, providing frequency support for the DOA estimation module.

[0017] Furthermore, the dual-channel coprime sampling model includes two sampling channels with sampling rates lower than the Nyquist sampling frequency and coprime to each other. After arranging the data from the two sampling channels in a strict time sequence, a periodic non-uniformly sampled sample can be obtained. A sampling and estimation system with a similar structure is designed. Compared with the sampling methods in uniform undersampling and the Chinese Remainder Theorem (CRT), the frequency estimation accuracy and resolution of coprime dual-channel sampling are higher.

[0018] Furthermore, the sampling model includes a received signal model, assuming that there are K narrowband signals in space, with carrier frequencies of respectively... The received signal model is then...

[0019] .

[0020] Furthermore, to characterize the effectiveness of the dual-channel coprime sampling scheme in reducing sampling frequency and data processing volume, this paper proposes a metric—the "compression factor". Specifically, it is divided into sampling compression factor. and data compression factor ;

[0021] The sampling compression factor refers to the degree to which the sampling rate is reduced relative to the Nyquist sampling rate, and is calculated using the following formula:

[0022] . Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the multi-set sampling structure of the present invention;

[0024] Figure 2 This is a schematic diagram of the frequency estimation system based on coprime sampling of the present invention;

[0025] Figure 3 This is a schematic diagram of the data segmentation processing of the sampling and receiving structure of the present invention. Detailed Implementation

[0026] 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.

[0027] Example 1: A wideband high-precision DOA estimation method based on optimal redundant linear array. This invention includes establishing a sampling model:

[0028] A sampling model is constructed based on uniformly sampled samples at the Nyquist sampling frequency. The sampling model includes a multi-set sampling model and a dual-channel coprime sampling model.

[0029] The sampled data is processed and then substituted into a formula for high-precision frequency estimation.

[0030] Preferably, the multi-set sampling model refers to a sampling scheme that selects multiple channels based on uniform sampling samples based on the Nyquist sampling frequency. When using this sampling scheme, it is only necessary to add a receiving channel and an ADC module to the traditional array antenna to perform high-precision estimation of the signal carrier frequency and provide frequency support for the DOA estimation module.

[0031] Preferably, the dual-channel coprime sampling model includes two sampling channels with sampling rates lower than the Nyquist sampling frequency and coprime to each other. After arranging the data from the two sampling channels in a strict time sequence, a periodic non-uniformly sampled sample can be obtained. A sampling and estimation system with a similar structure is designed. Compared with the sampling methods in uniform undersampling and Chinese Remainder Theorem (CRT), the frequency estimation accuracy and resolution of coprime dual-channel sampling are higher.

[0032] Preferably, the sampling model includes a received signal model, assuming that there are K narrowband signals in space, with carrier frequencies of respectively The received signal model is then...

[0033] ;

[0034] Preferably, in order to characterize the effect of the dual-channel coprime sampling scheme on reducing the sampling frequency and the reduction of data processing volume, this paper proposes a metric—the "compression factor". Specifically, it is divided into sampling compression factor. and data compression factor ;

[0035] The sampling compression factor refers to the degree to which the sampling rate is reduced relative to the Nyquist sampling rate, and is calculated using the following formula:

[0036]

[0037] Since the exact range of the signal carrier frequency within the monitoring frequency band is unknown, in order to ensure complete recovery of the assumed standard sampling frequency, i.e., the Nyquist frequency... As the upper limit of the target frequency band, obviously Assuming the sampling interval time is... The received data at the corresponding standard sampling frequency is

[0038] , This represents the Dirac function.

[0039] By assembling all received data within each sampling time segment into a vector according to the sampling order, the received data vector for the first sampling time segment under standard sampling can be obtained. Then the received data in the i-th sampling time segment Specifically, it can be expanded as follows

[0040] in

[0041]

[0042] Further derivation yields:

[0043]

[0044] The following is a receiving data model for dual-channel coprime undersampling.

[0045] Because the standard sampling frequency is Therefore, it can be assumed that the sampling rates of the two coprime sampling receiving channels are respectively and ,in and They are a pair of coprime numbers. Assume... The time period is a sampling segment, in which Then the corresponding sampling time series within a sampling segment is

[0046]

[0047] The received samples of one sampling period are obtained by arranging the received data from two coprime sampling channels in chronological order.

[0048] ,

[0049] in, The number of coprime sampling points, and the coprime sampling matrix. Similar to sparse choice matrices The position of its non-zero terms depends on ;

[0050] Figure 3 Two methods for segmenting and processing received data.

[0051] Assuming a sampling period ,Right now ,like Figure 3 As shown, the non-overlapping segmentation scheme includes A length of In addition to the sampling segments, a semi-overlapping segmentation scheme can also be used, which includes... A length of Sampling fragments;

[0052] Autocorrelation function within the sampling segment The corresponding covariance matrix is

[0053] The topological property of the covariance matrix can be verified based on the relationship between the covariance matrix and the autocorrelation function.

[0054]

[0055] The corresponding covariance matrix and its estimated value are respectively

[0056] .

[0057] In this embodiment: High-precision frequency estimation based on TCMR:

[0058] Traditional methods of spectrum sensing directly estimate the power spectral density of the signal and then perform signal energy detection to estimate the signal frequency. A common method for super-resolution spectrum estimation based on coprime sampling is spectral extension based on coprime parameters. The number of samples constituting the sparse signal determines the upper limit of the number of different signal carrier frequencies that can be identified simultaneously.

[0059] Toplitz matrix reconstruction:

[0060] The theoretical value of the covariance matrix of coprime sampling is assumed. Compared with the actual estimated value estimation error satisfy

[0061] It can then be deduced that the estimation error It follows these rules:

[0062]

[0063] Therefore, it can be deduced that...

[0064]

[0065] in This represents the degree of freedom to obey. The chi-square distribution, from the properties of the chi-square distribution, can be obtained

[0066]

[0067] In summary, solving for the denoised initial covariance matrix Tx can be transformed into the following optimization problem:

[0068]

[0069] To achieve efficient computation, after converting to the L1 norm, we can obtain...

[0070] parameter The value of w can be obtained using the command function "chi2inv(1-w,|S|2)" in MATLAB mathematical software. In this paper, the parameter w is the commonly used empirical value of 0.0001.

[0071] Fast calculation method:

[0072] Considering that the initial covariance matrix for denoising is a square matrix, the corresponding trace norm and kernel norm are equivalent, therefore the optimization model can be optimized. Transform into

[0073]

[0074] The trace norm minimization model is then transformed into a LASSO model using the Lagrange form.

[0075]

[0076] Based on the definition of the 2-norm, the above LASSO model can be expanded as follows:

[0077]

[0078] Based on the definition of the trace norm, the equation can be... Further simplified to

[0079]

[0080] in .

[0081] Based on the KKT (Karuch-Kuhn-Tucker) conditions in convex optimization theory, it is assumed that the estimated error parameter... Then an optimization model can be derived. The approximate optimal solution satisfies

[0082]

[0083] in, It is a matrix structure based on the Toeplitz matrix. Compressed into vector The operation.

[0084] The above equation In essence, it contains A system of linear equations with M variables, where M is the number of elements in the initial uniform linear array. To solve this system of equations, we first need to... The right side transforms into

[0085]

[0086]

[0087] in, Representation matrix The OK, Represented by matrix The 1st to A new matrix composed of columns, Represented by matrix The arrive A new matrix composed of rows.

[0088] To simplify the system of linear equations The calculation inserts a zero vector into the matrix. After the Mth column, the formula Transform it into a block matrix equation, and thus obtain

[0089]

[0090] in , Representing vectors Flip it up and down.

[0091] Obviously, the above formula Given a system of complex linear equations, to simplify calculations, we transform it into a system of real linear equations. Assume... According to the above formula After simplification, we get

[0092]

[0093] in, Represents a complex vector The real part, Represents a complex vector The imaginary part.

[0094] It is a non-singular matrix, based on the formula The vector can be obtained by finding the pseudo-inverse. Then, the corresponding vector can be obtained. Based on the symmetric Toeplitz property of the initial denoised covariance matrix, the denoised covariance matrix can be obtained. for

[0095] .

[0096] Eigenvalue decomposition:

[0097] Using the SORTE signal count estimation algorithm

[0098]

[0099] The number of frequencies contained in a signal can be estimated using the minimum information criterion (AIC).

[0100] Frequency estimation:

[0101]

[0102] ;

[0103] The optimal selection criterion for coprime parameters in coprime sampling was established, and an evaluation index for the reduction of sampling rate was proposed. Coprime sampling has the following two significant advantages in reducing hardware requirements: ① First, it can reduce the sampling rate of the ADC, thereby reducing the hardware cost of the ADC; ② It can reduce the amount of data in the receiving channel, thereby reducing the requirements for chip data processing capabilities and also reducing hardware costs.

[0104] Example 2: A wideband high-precision DOA estimation method based on an optimal redundant linear array. This invention includes establishing a sampling model:

[0105] A sampling model is constructed based on uniformly sampled samples at the Nyquist sampling frequency. The sampling model includes a multi-set sampling model and a dual-channel coprime sampling model.

[0106] The sampled data is processed and then substituted into a formula for high-precision frequency estimation.

[0107] Preferably, the multi-set sampling model refers to a sampling scheme that selects multiple channels based on uniform sampling samples based on the Nyquist sampling frequency. When using this sampling scheme, it is only necessary to add a receiving channel and an ADC module to the traditional array antenna to perform high-precision estimation of the signal carrier frequency and provide frequency support for the DOA estimation module.

[0108] Preferably, the dual-channel coprime sampling model includes two sampling channels with sampling rates lower than the Nyquist sampling frequency and coprime to each other. After arranging the data from the two sampling channels in a strict time sequence, a periodic non-uniformly sampled sample can be obtained. A sampling and estimation system with a similar structure is designed. Compared with the sampling methods in uniform undersampling and Chinese Remainder Theorem (CRT), the frequency estimation accuracy and resolution of coprime dual-channel sampling are higher.

[0109] Preferably, the sampling model includes a received signal model, assuming that there are K narrowband signals in space, with carrier frequencies of respectively The received signal model is then...

[0110] ;

[0111] Preferably, in order to characterize the effect of the dual-channel coprime sampling scheme on reducing the sampling frequency and the reduction of data processing volume, this paper proposes a metric—the "compression factor". Specifically, it is divided into sampling compression factor. and data compression factor ;

[0112] The sampling compression factor refers to the degree to which the sampling rate is reduced relative to the Nyquist sampling rate, and is calculated using the following formula:

[0113]

[0114] Since the exact range of the signal carrier frequency within the monitoring frequency band is unknown, in order to ensure complete recovery of the assumed standard sampling frequency, i.e., the Nyquist frequency... As the upper limit of the target frequency band, obviously Assuming the sampling interval time is... The received data at the corresponding standard sampling frequency is

[0115] , This represents the Dirac function.

[0116] By assembling all received data within each sampling time segment into a vector according to the sampling order, the received data vector for the first sampling time segment under standard sampling can be obtained. Then the received data in the i-th sampling time segment Specifically, it can be expanded as follows

[0117]

[0118] in

[0119]

[0120] Further derivation yields:

[0121]

[0122] The following is a receiving data model for dual-channel coprime undersampling.

[0123] Because the standard sampling frequency is Therefore, it can be assumed that the sampling rates of the two coprime sampling receiving channels are respectively and ,in and They are a pair of coprime numbers. Assume... The time period is a sampling segment, in which Then the corresponding sampling time series within a sampling segment is

[0124]

[0125] The received samples of one sampling period are obtained by arranging the received data from two coprime sampling channels in chronological order.

[0126] ,

[0127] in, The number of coprime sampling points, and the coprime sampling matrix. Similar to sparse choice matrices The position of its non-zero terms depends on ;

[0128] Figure 3 Two methods for segmenting and processing received data.

[0129] Assuming a sampling period ,Right now ,like Figure 3 As shown, the non-overlapping segmentation scheme includes A length of In addition to the sampling segments, a semi-overlapping segmentation scheme can also be used, which includes... A length of Sampling fragments;

[0130] Autocorrelation function within the sampling segment The corresponding covariance matrix is

[0131] The topological property of the covariance matrix can be verified based on the relationship between the covariance matrix and the autocorrelation function.

[0132]

[0133] The corresponding covariance matrix and its estimated value are respectively

[0134] .

[0135] In this embodiment, the high-precision frequency estimation method based on sparse representation is as follows:

[0136] To address the problem of sparse signal representation, a covariance vector sparse representation (CVSR) model is constructed by utilizing the sparsity of signal carrier frequencies in the continuous frequency domain.

[0137] Frequency estimation algorithm based on CVSR:

[0138] Where the initial covariance vector As the first column element of the initial covariance matrix, it can be represented as

[0139]

[0140] Assuming an initial covariance vector Therefore, we can deduce that

[0141]

[0142] Based on the spatially sparse nature of the direction of arrival (DOA), a sparse representation of the initial covariance vector can be used to obtain an estimate of the initial covariance vector that satisfies the following conditions:

[0143]

[0144] Where the estimation error vector The emergence of overcomplete dictionaries stems from the finite number of signal samples. From vector The composition, without considering mesh mismatch, satisfies...

[0145] ;

[0146] Based on sparse Bayesian learning theory, a fast Bessel frequency estimation algorithm is proposed. This algorithm can ① achieve high-precision signal carrier frequency estimation, and ② by designing a fast implementation scheme, the algorithm's time consumption is greatly reduced, which can meet the real-time requirements of frequency measurement.

[0147] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0148] 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 method for wideband high-precision DOA estimation based on optimal redundant linear array, comprising the following steps: Establish a sampling model: Construct a sampling model based on uniformly sampled samples with Nyquist sampling frequency. The sampling model includes a multi-set sampling model and a dual-channel coprime sampling model. The sampled data is processed and then substituted into a formula for high-precision frequency estimation. The multi-set sampling model refers to a sampling scheme that selects multiple channels based on uniform sampling samples based on the Nyquist sampling frequency. When using this sampling scheme, it is only necessary to add a receiving channel and an ADC module to the traditional array antenna to perform high-precision estimation of the signal carrier frequency and provide frequency support for the DOA estimation module. The dual-channel coprime sampling model includes two sampling channels with sampling rates lower than the Nyquist sampling frequency and coprime to each other. The data from the two sampling channels are arranged in strict time order to obtain a periodic non-uniformly sampled sample. Compared with uniform undersampling and the sampling method in the Chinese remainder theorem, the frequency estimation accuracy and resolution of coprime dual-channel sampling are higher.

2. The wide-band high-precision DOA estimation method based on optimal redundant linear array according to claim 1, characterized in that: The sampling model, which includes a multi-set sampling model and a dual-channel coprime sampling model, also includes a received signal model, assuming that there are K narrowband signals in space, with carrier frequencies of respectively... The received signal model is then... 。 3. The wide-band high-precision DOA estimation method based on optimal redundant linear array according to claim 1, characterized in that: To characterize the effectiveness of the dual-channel coprime sampling scheme in reducing sampling frequency and data processing volume, a metric—compression factor—is proposed. Specifically, it is divided into sampling compression factor. and data compression factor ; The sampling compression factor refers to the degree to which the sampling rate is reduced relative to the Nyquist sampling rate, and is calculated using the following formula: ， wherein and are a pair of coprime numbers.

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