A uniform rectangular matrix target direction estimation method based on array manifold matrix learning
The target azimuth estimation method based on uniform rectangular array learning through array manifold matrix learning solves the problem of high computational complexity in two-dimensional target azimuth estimation and achieves efficient and accurate target azimuth estimation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2023-12-21
- Publication Date
- 2026-07-03
AI Technical Summary
In existing technologies, two-dimensional target orientation estimation methods have high computational complexity and their accuracy is affected by angle mismatch errors, making them difficult to effectively solve in practical applications.
A uniform rectangular array target orientation estimation method based on array manifold matrix learning is adopted. By iteratively calculating the two-dimensional direction angle set and accuracy vector of the candidate target signal, the array manifold matrix is constructed, which reduces computational complexity and improves estimation accuracy.
It reduces the complexity of parameter iteration calculation, improves computational efficiency, and is unaffected by the discretization of the observation angle domain, maintaining high target orientation estimation accuracy.
Smart Images
Figure CN117540138B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to signal processing methods, specifically a method for estimating the azimuth of a target in a uniform rectangular array based on array manifold matrix learning. Background Technology
[0002] Target azimuth estimation is a powerful tool for target detection and is widely used in radar, sonar, and wireless communication. Developing efficient and high-precision target azimuth estimation methods is crucial for improving the performance of target detection systems. Among existing target azimuth estimation methods, sparse methods offer high estimation accuracy and maintain good performance even under adverse conditions such as low signal-to-noise ratio and limited snapshot data, thus attracting widespread attention and research. Currently, most sparse target azimuth estimation methods process linear array time-domain snapshot data, targeting one-dimensional target azimuth estimation problems. Generally, sparse target azimuth estimation methods discretize the observation angle space, construct an array manifold matrix using the obtained discrete angle points for sparse parameter estimation, and obtain the target azimuth estimate based on the sparse parameter estimates. We typically refer to this type of sparse target azimuth estimation method involving angle discretization as a grid-based method. For grid-based sparse target azimuth estimation methods, the density of discrete angle points affects both the accuracy and computational complexity of the target azimuth estimation; using denser discrete angle points can achieve higher estimation accuracy to some extent, but the computational complexity will increase significantly.
[0003] For the two-dimensional target orientation estimation problem, directly extending the one-dimensional grid-based sparse target orientation estimation method to a two-dimensional form significantly increases the number of discrete angle points involved and the dimension of the array manifold matrix, thus significantly increasing the computational complexity of sparse parameters and hindering practical applications. Furthermore, if the target orientation deviates from the preset discrete angle points, i.e., an angle mismatch error exists, the angle estimation accuracy of the grid-based sparse target orientation estimation method will decrease. Angle refinement processing is needed to compensate for the angle mismatch error and ensure the accuracy of angle estimation. This additional angle refinement processing further increases the computational complexity of the grid-based sparse target orientation estimation method. For another type of gridless sparse target orientation estimation method, although it does not require angle discretization and has high computational efficiency, it often requires prior knowledge of the number of targets, which is impractical in reality, thus limiting the practical application of this type of method.
[0004] Therefore, there is an urgent need to propose a solution to the problem of high computational complexity in the two-dimensional direct extension of the one-dimensional grid-based sparse target orientation estimation method. Summary of the Invention
[0005] This invention aims to at least solve one of the technical problems existing in the prior art. To this end, this invention proposes a target orientation estimation method for a uniform rectangular matrix based on array manifold matrix learning. Through the array manifold matrix learning strategy, a two-dimensional direction angle set with elements added sequentially from zero is obtained, and an array manifold matrix with fewer column vectors is constructed for parameter iterative calculation, thereby reducing computational complexity and improving computational efficiency.
[0006] To achieve the above objectives, this invention proposes a method for estimating the azimuth of a uniform rectangular array target based on array manifold matrix learning, comprising:
[0007] S1 obtains the expression for the array manifold matrix based on the array layout information of the uniform rectangular array;
[0008] S2 iteratively calculates the two-dimensional direction angle set, accuracy vector, and Gaussian white noise accuracy parameter of the candidate target signal according to the array manifold matrix learning strategy. In each iteration, the array manifold matrix is updated using the two-dimensional direction angle set. Then, the posterior estimate (i.e., posterior mean and posterior covariance matrix) of the candidate target signal is calculated using the accuracy vector, Gaussian white noise accuracy parameter, and updated array manifold matrix. The posterior mean is used as the estimated value of the candidate target signal.
[0009] S3 uses the estimated values of the obtained candidate target signals to calculate the normalized spatial spectrum value. The two-dimensional direction angles corresponding to the first K maximum values in the normalized spatial spectrum value are the target azimuth estimates, where K is the number of real target signals.
[0010] Furthermore, the expression for the array manifold matrix is:
[0011]
[0012] In the formula, This is the set of two-dimensional directional angles of the candidate target signal. θ represents the number of candidate target signals. i and The first The pitch and azimuth angles in two-dimensional directions. Angle in two dimensions The guide vector on is expressed as:
[0013]
[0014] In the formula, For Kronecker product, in,(·)T It is the transpose operator. λ is the wavelength of the target signal, M z and M y d represents the number of elements along the z-axis and y-axis of the uniform rectangular array, respectively. z and d y These represent the element spacing along the z-axis and y-axis, respectively.
[0015] Furthermore, the parameter iterative calculation based on the array manifold matrix learning strategy includes the following steps:
[0016] S201 initializes the two-dimensional direction angle set, precision vector, and Gaussian white noise precision parameters of the candidate target signal, and sets the maximum number of iterations and the iteration convergence condition;
[0017] S202 updates the two-dimensional direction angle set Θ and precision vector. Update value Θ using a set of two-dimensional direction angles new The new array manifold matrix A(Θ) is obtained. new );
[0018] The S203 update Gaussian white noise accuracy parameter β is calculated using the following formula:
[0019]
[0020] In the formula, tr(·) is the trace operation of a matrix. To perform operations on the Moore-Penrose pseudo-inverse matrix, I M For M=M y ×M z 3D identity matrix Let Y = [y(1), ..., y(T)] be the sampling covariance matrix, Y = [y(1), ..., y(T)] be the time-domain snapshot data matrix of the uniform rectangular matrix, T be the number of time-domain snapshots, and y(t), t = 1, ..., T be the t-th time-domain snapshot data vector. H This is the conjugate transpose operation;
[0021] S204 updates the posterior mean μ = [μ(1),…,μ(T)] and the posterior covariance matrix ∑ of the candidate target signal, and uses the posterior mean as the estimate of the candidate target signal, i.e. Where, the formulas for calculating μ(t), t=1,…,T and ∑ are respectively:
[0022] μ(t)=β∑A(Θ new ) H y(t),
[0023] ∑=[diag(α new )+βA(Θ new ) HA(Θ new )] -1 ,
[0024] In the formula, diag(α) new ) represents the updated value α of the precision vector. new A diagonal matrix with elements on the main diagonal, (·) -1 Invert a matrix;
[0025] S205 repeats S202, S203, and S204, and performs iteration counting; if the iteration count reaches the maximum number of iterations, or the iteration convergence condition is met, the iteration calculation ends, and the two-dimensional direction angle set Θ is output. new and the estimated value of the candidate target signal The iterative convergence condition is as follows:
[0026]
[0027] In the formula, Let ||·|| be the estimated value of the candidate target signal obtained in the previous iteration, τ be the iteration convergence decision threshold, size(·) represent the matrix dimension, and "&&" represent the logical "AND" operation. F Let f be the Frobenius norm of the matrix.
[0028] Furthermore, the two-dimensional direction angle set Θ and the precision vector The update calculation includes:
[0029] First, the update process of Θ and α involves two update operations: adding a new angle and updating an existing angle.
[0030] In the new angle addition operation, a new two-dimensional direction angle is calculated. Add to Θ, calculate Precision parameters of candidate target signals in the direction To add to α, calculate the logarithmic marginal likelihood increment Δl0 of the new angle addition operation;
[0031] In the existing angle update operation, for each existing two-dimensional direction angle in Θ Calculate auxiliary parameters and like Then proceed to the existing angle deletion operation, that is, remove from Θ. Remove the precision parameter α from α. i Calculate the logarithmic marginal likelihood increment of the existing angle deletion operation. like Then proceed to the existing angle re-estimation operation, that is, calculate the updated value. Used for replacement Calculation accuracy parameter update value Used to replace α i Calculate the logarithmic marginal likelihood increment of the existing angle re-estimation operation.
[0032] Among them, the three logarithmic marginal likelihood increments Δl0, and The calculation formulas are as follows:
[0033]
[0034]
[0035]
[0036] In the formula, For parameter pairs The logarithmic marginal likelihood contribution. The auxiliary parameters and The calculation formulas are as follows:
[0037]
[0038]
[0039] In the formula,
[0040] Secondly, during the update process of Θ and α, a total of The logarithmic marginal likelihood increments, namely Δl0 and Compare this The maximum log-marginal likelihood increment is obtained by performing a log-marginal likelihood increment operation. If Δl0 is the maximum, then the new angle addition operation is performed, and the updated values of Θ and α are obtained respectively. and And update the number of candidate target signals. like If the value is the maximum, then the existing angle deletion operation is performed, and the updated values of Θ and α are obtained as follows: Θ new =(Θ) -i and α new =(α) -i And update the number of candidate target signals. in(·) -i This indicates removing the i-th element; if If the value is maximum, then the existing angle re-estimation operation is performed to obtain updated values for Θ and α, respectively. and And make It remains unchanged.
[0041] Furthermore, in the new angle addition operation and the existing angle re-estimation operation, efficient two-dimensional direction angle calculation and accuracy parameter calculation of candidate target signals are performed sequentially:
[0042] S501 was calculated using a two-dimensional zoom-FFT:
[0043]
[0044] In the formula, Z -k (:,q) is a matrix Z -k The q-th column vector; zoomFFT2D(·) represents the two-dimensional zoom-FFT operation; S[·] represents the vector matrix transformation operation, that is, the vector in parentheses is transformed into an M-column vector. z ×M y 3D matrix, such as vector Z -k (:,q)=vec(S[Z -k (:,q)]), vec(·) is a matrix vectorization operation; A -i Remove the angle between A(Θ) and the two-dimensional direction. The relevant matrix after the part, μ -k (t) is μ(t) removed from the context. The vector following the relevant part, ∑ -k Remove Σ and The relevant part of the matrix For ∑ -k The Hermitian square root;
[0045] S502 obtains the two-dimensional frequency estimate corresponding to the maximum value in G. use The estimated two-dimensional directional angle values are calculated. The calculation formula is:
[0046]
[0047] S503 Calculation Precision parameters of candidate target signals in the direction The calculation formula is:
[0048]
[0049] In the formula, and Two-dimensional directional angle estimate The corresponding auxiliary parameters.
[0050] Furthermore, in calculating the normalized spatial spectrum value... At that time, in P, the first P k The calculation formula is:
[0051]
[0052] In the formula, μ k (t) is the k-th element of the posterior mean μ(t); max(·) means taking the maximum value.
[0053] Compared with the prior art, the beneficial effects of the present invention are:
[0054] The array manifold matrix used in the parameter iteration calculation of this invention is obtained by iterative learning from an empty matrix. That is, the number of column vectors of the array manifold matrix gradually increases and always remains at a small value (slightly larger than the number of real target signals). This reduces the matrix dimension of the array manifold matrix, thereby reducing the complexity of parameter iteration calculation and improving computational efficiency.
[0055] On the other hand, in this invention, efficient two-dimensional orientation angle calculation does not require discretization of the observation angle domain. Therefore, the estimation accuracy of the two-dimensional orientation angle calculation is not affected by angle mismatch, which makes this invention have high target orientation estimation accuracy. Attached Figure Description
[0056] 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.
[0057] Figure 1 This is a schematic diagram of the flowchart of the present invention;
[0058] Figure 2 This is a schematic diagram of a uniform rectangular array in a specific embodiment;
[0059] Figure 3 The root mean square error curves of target orientation estimation results of different methods under different signal-to-noise ratios in specific embodiments are shown.
[0060] Figure 4 The average running time of different methods under different signal-to-noise ratio conditions in specific embodiments. Detailed Implementation
[0061] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments. 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.
[0062] According to an embodiment of the present invention, the present invention proposes a method for estimating the azimuth of a uniform rectangular array target based on array manifold matrix learning. The technical solution adopted includes the following steps:
[0063] Step 1: Use an M-shaped object placed vertically on the yoz plane y ×M z A uniform rectangular matrix of element M is used for target azimuth estimation, where M... y M is the number of matrix elements along the y-axis. z Let be the number of array elements along the z-axis, and d be the distances between array elements along the y-axis and z-axis, respectively. y and d z Assume that during the target orientation estimation process, the set of two-dimensional direction angles of the candidate target signals is as follows: in, θ represents the number of candidate target signals. i and The first Based on the array information of the uniform rectangular array, the pitch and azimuth angles in each two-dimensional direction are expressed as follows:
[0064]
[0065] In the formula, the first Column guide vector For Kronecker product, λ is the signal wavelength, (·) T This is the transpose operator.
[0066] Step 2: Using an array manifold matrix learning strategy, iteratively calculate the two-dimensional direction angle set Θ and the accuracy vector of the candidate target signal. And the Gaussian white noise accuracy parameter β. The implementation steps are as follows.
[0067] 1) Step 21: Set the maximum number of iterations MaxIter and the iteration convergence decision threshold τ; initialize Θ and α, including:
[0068] Step 211, set the Gaussian white noise accuracy parameter β = 103 Θ is an empty set, i.e., Θ = [].
[0069] Step 212: Using the time-domain snapshot data matrix Y = [y(1), ..., y(T)] of the uniform rectangular matrix, the first two-dimensional direction angle is calculated according to the efficient two-dimensional angle calculation formula. Calculate based on the accuracy parameter calculation formula of the candidate target signal. Precision parameters of candidate target signals in the direction
[0070] Step 213, let Number of candidate target signals Calculate the posterior mean μ(t) of the candidate target signal: μ = β∑A(Θ) H y(t) and the posterior covariance matrix ∑=[diag(α)+βA(Θ) H A(Θ)] -1 , where t=1,…,T, T is the number of time-domain snapshots, (·) -1 Invert a matrix.
[0071] 2) Step 22, update Θ and α to obtain the updated value Θ new and α new ,include:
[0072] Step 221: Calculate the relevant parameters for the new angle addition operation. Based on the efficient two-dimensional angle calculation formula, a new angle is calculated. Based on the formula for calculating the accuracy parameters of the candidate target signal, the following is obtained: corresponding Calculate the logarithmic marginal likelihood increment of the new angle addition operation.
[0073] Step 222: Calculate the relevant parameters for the existing angle deletion operation and the existing angle re-estimation operation, namely:
[0074] For each of Θ Calculate the corresponding auxiliary parameters and
[0075] like Then calculate the logarithmic marginal likelihood increment of the existing angle deletion operation.
[0076] like Then calculate the relevant parameters for re-estimating the existing angles. Based on the efficient two-dimensional angle calculation formula, calculate... Update value α is calculated based on the formula for calculating the accuracy parameters of the candidate target signal. i Update value Calculate the log marginal likelihood increment of the existing angle re-estimation operation.
[0077] Step 223, the results of the comparison The logarithmic marginal likelihood increments, namely Δl0 and Once the largest log-likelihood increment is obtained, the angle update operation corresponding to that largest log-likelihood increment is performed, i.e.:
[0078] If △l0 is the largest, then the new angle will be... Add to Θ, Add to α to get the updated value and And update the number of candidate target signals.
[0079] like The maximum will be the existing angle. Remove from Θ, and α i Remove from α to obtain the updated value Θ. new =(Θ) -i and α new =(α) -i And update in(·) -i This indicates that the i-th element is removed;
[0080] like The maximum will be the existing angle. Replace with α i Replace with Get updated value and And make It remains unchanged.
[0081] This concludes step 22. In this step, when calculating the logarithmic marginal likelihood increment, Corresponding contribution in,
[0082] 3) Step 23, update the Gaussian white noise accuracy parameter β, the calculation formula is:
[0083]
[0084] In the formula, tr(·) is the trace operation of a matrix. To perform operations on the Moore-Penrose pseudo-inverse matrix, I M For M=M y ×M z 3D identity matrix
[0085] 4) Step 24: Update the posterior mean μ=[μ(1),…,μ(T)] and posterior covariance matrix ∑=[diag(α)] of the candidate target signal. new )+βA(Θ new ) H A(Θ new )] -1 And the posterior mean is used as the estimated value of the candidate target signal, that is... Where the μ(t) of the t=1,…,T column is β∑A(Θ) new ) H y(t).
[0086] 5) Step 25: Repeat steps 22, 23, and 24, and perform iteration counting; if the iteration count reaches MaxIter, or simultaneously satisfies... and End iteration, output Θ new and in, The value is the estimated value of the candidate target signal obtained in the previous iteration, where size(·) represents the matrix dimension, ||·|| F Let f be the Frobenius norm of the matrix.
[0087] This concludes step 2. In this step, the estimated two-dimensional directional angle values... The efficient calculation formula is:
[0088]
[0089] In the formula, It is the two-dimensional frequency estimate corresponding to the maximum value in the two-dimensional zoom-FFT output G. in Z -k (:,q) is a matrix Z -k The q-th column vector, zoomFFT2D(·) represents the two-dimensional zoom-FFT operation, and S[·] represents the vector matrix transformation operation, that is, the vector in parentheses is transformed into an M-column vector. z ×M y 3D matrix, such as vector Z -k (:,q)=vec(S[Z -k (:,q)]), vec(·) is a matrix vectorization operation, A-i Remove the sine wave from A(Θ). The relevant matrix after the part, μ -k (t) is μ(t) removed from the context. The vector following the relevant part, ∑ -k Remove Σ and The relevant part of the matrix For M -k The Hermitian square root.
[0090] In step 2, Precision parameters of candidate target signals in the direction The calculation formula is:
[0091]
[0092] Step 3: Utilize the estimated value of the candidate target signal Calculate the normalized spatial spectral value The two-dimensional directional angles corresponding to the first K maximum values in P are the estimated target azimuth angles, where K is the number of actual target signals. Specifically, the Kth maximum value in P represents the estimated target azimuth angle. element P k The calculation formula is:
[0093]
[0094] In the formula, μ k (t) is the k-th element of the posterior mean μ(t). max(·) means taking the maximum value.
[0095] Simulation Experiment Cases
[0096] This simulation experiment uses a 6×4 element uniform rectangular matrix placed vertically on the yoz plane for target orientation estimation, where the number of matrix elements along the y-axis is M. y =6, the number of elements in the z-axis matrix is M z =4, element spacing d y and d z All are half-wavelengths. A schematic diagram of this uniform rectangular array is shown below. Figure 2 As shown. The simulation assumes that K = 2 far-field narrowband signals are incident on this uniform rectangular array, and the two-dimensional angles of the incident signals are respectively... and The number of snapshots in the time-domain snapshot data of the uniform rectangular array was set to 50, and the signal-to-noise ratio (SNR) was increased from -10dB to 20dB. Target azimuth estimation was performed using the method of this invention and two reference methods, with 200 independent experiments conducted for each method. The root mean square error (RMSE) and average running time of the target azimuth estimation results under different SNR conditions were calculated, and performance curves were plotted as follows: Figure 3 and Figure 4 As shown.
[0097] from Figure 3 As can be seen, when the signal-to-noise ratio (SNR) is less than 0 dB, the root mean square (RMS) error of the target orientation estimation result of this invention is the smallest; when the SNR is greater than or equal to 0 dB, the RMS error of the target orientation estimation result of this invention is similar to that of the SAMV-RELAX method, both approaching the lower bound of Cramer-Rao. Therefore, it can be concluded that the target orientation estimation accuracy of this invention is superior to the other two methods.
[0098] from Figure 4 As can be seen, under different signal-to-noise ratio conditions, the average running time of the present invention is slightly longer than that of the FGML method, but shorter than that of the SAMV-RELAX method, and is always less than 1 second. Therefore, the present invention has high operating efficiency.
[0099] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.
Claims
1. A method for estimating the azimuth of a uniform rectangular array target based on array manifold matrix learning, characterized in that, Includes the following steps: S1 obtains the expression for the array manifold matrix based on the array layout information of the uniform rectangular array; S2 iteratively calculates the two-dimensional direction angle set, precision vector, and Gaussian white noise precision parameters of the candidate target signal according to the array manifold matrix learning strategy. In each iteration, the array manifold matrix is updated using the two-dimensional direction angle set. Then, the posterior estimate of the candidate target signal, namely the posterior mean and the posterior covariance matrix, is calculated using the precision vector, the Gaussian white noise precision parameters, and the updated array manifold matrix. The posterior mean is used as the estimate of the candidate target signal. S3 uses the estimated values of the obtained candidate target signals to calculate the normalized spatial spectrum value. The two-dimensional direction angles corresponding to the first K maximum values of the normalized spatial spectrum value are the target azimuth estimates, where K is the number of real target signals.
2. The method for estimating the azimuth of a uniform rectangular array target based on array manifold matrix learning according to claim 1, characterized in that, The expression for the array manifold matrix is: In the formula, This is the set of two-dimensional directional angles of the candidate target signal. θ represents the number of candidate target signals. i and The first The pitch and azimuth angles in two-dimensional directions. Angle in two dimensions The guide vector on is expressed as: In the formula, For Kronecker product, in,(·) T It is the transpose operator. λ is the wavelength of the target signal, M z and M y d represents the number of elements along the z-axis and y-axis of the uniform rectangular array, respectively. z and d y These represent the element spacing along the z-axis and y-axis, respectively.
3. The method for estimating the azimuth of a uniform rectangular array target based on array manifold matrix learning according to claim 1, characterized in that, The parameter iterative calculation based on the array manifold matrix learning strategy includes the following steps: S201 initializes the two-dimensional direction angle set, precision vector, and Gaussian white noise precision parameters of the candidate target signal, and sets the maximum number of iterations and the iteration convergence condition. S202 updates the two-dimensional direction angle set Θ and precision vector of the candidate target signal. Update value Θ using a set of two-dimensional direction angles new The new array manifold matrix A(Θ) is obtained. new ). The S203 update Gaussian white noise accuracy parameter β is calculated using the following formula: In the formula, tr(·) is the trace operation of a matrix. To perform operations on the Moore-Penrose pseudo-inverse matrix, I M For M=M y ×M z 3D identity matrix Let Y = [y(1), ..., y(T)] be the sampling covariance matrix, Y = [y(1), ..., y(T)] be the time-domain snapshot data matrix of the uniform rectangular matrix, T be the number of time-domain snapshots, and y(t), t = 1, ..., T be the t-th time-domain snapshot data vector. H This is the conjugate transpose operation. S204 updates the posterior mean μ = [μ(1),…,μ(T)] and the posterior covariance matrix ∑ of the candidate target signal, and uses the posterior mean as the estimate of the candidate target signal, i.e. Where, the formulas for calculating μ(t), t=1,…,T and ∑ are respectively: μ(t)=β∑A(Θ new ) H y(t) ∑=[diag(α new )+βA(Θ new ) H A(Θ new )] -1 In the formula, diag(α) new ) is the value α updated using the precision vector. new A diagonal matrix with elements on the main diagonal, (·) -1 Invert a matrix. S205 repeats S202, S203, and S204, and performs iteration counting; if the iteration count reaches the maximum number of iterations, or the iteration convergence condition is met, the iteration calculation stops, and the two-dimensional direction angle set Θ is output. new and the estimated value of the candidate target signal The iterative convergence condition is as follows: In the formula, Let τ be the estimated value of the candidate target signal obtained in the previous iteration, τ be the iteration convergence decision threshold, size(·) represent the matrix dimension, "&&" represent the logical "AND" operation, and ||·|| F Let f be the Frobenius norm of the matrix.
4. The parameter iterative calculation based on the array manifold matrix learning strategy according to claim 3, characterized in that, The two-dimensional direction angle set Θ and precision vector The update calculation includes: First, the update process of Θ and α involves two update operations: adding a new angle and updating an existing angle. In the new angle addition operation, a new two-dimensional direction angle is calculated. Add to Θ, calculate Precision parameters of candidate target signals in the direction To add to α, calculate the logarithmic marginal likelihood increment Δl0 of the new angle addition operation; In the existing angle update operation, for each existing two-dimensional direction angle in Θ Calculate auxiliary parameters and like Then proceed to the existing angle deletion operation, that is, remove from Θ. Remove the precision parameter α from α. i Calculate the logarithmic marginal likelihood increment of the existing angle deletion operation. like Then proceed to the existing angle re-estimation operation, that is, calculate the updated value. Used for replacement Calculation accuracy parameter update value Used to replace α i Calculate the logarithmic marginal likelihood increment of the existing angle re-estimation operation. Among them, the three logarithmic marginal likelihood increments Δl0, and The calculation formulas are as follows: In the formula, For parameter pairs The logarithmic marginal likelihood contribution. The auxiliary parameters and The calculation formulas are as follows: In the formula, Secondly, during the update process of Θ and α, a total of The logarithmic marginal likelihood increments, namely Δl0 and Compare this The maximum log-marginal likelihood increment is obtained by performing a log-marginal likelihood increment operation. If Δl0 is the maximum, then the new angle addition operation is performed, and the updated values of Θ and α are obtained respectively. and And update the number of candidate target signals. like If the value is the maximum, then the existing angle deletion operation is performed, and the updated values of Θ and α are obtained as follows: Θ new =(Θ) -i and α new =(α) -i And update the number of candidate target signals. in(·) -i This indicates removing the i-th element; if If the value is maximum, then the existing angle re-estimation operation is performed to obtain updated values for Θ and α, respectively. and And make It remains unchanged.
5. A method for estimating the azimuth of a uniform rectangular array target based on array manifold matrix learning according to claim 1 or 3, characterized in that, The update operation involves efficient two-dimensional direction angle calculation and accuracy parameter calculation of candidate target signals. These two calculations are used in the new angle addition operation and the existing angle re-estimation operation. The implementation steps are as follows: S501 was calculated using a two-dimensional zoom-FFT: In the formula, Z -k (:,q) is a matrix Z -k The q-th column vector; zoomFFT2D(·) represents the two-dimensional zoom-FFT operation; S[·] represents the vector matrix transformation operation, that is, the vector in parentheses is transformed into an M-column vector. z ×M y 3D matrix, such as vector Z -k (:,q)=vec(S[Z -k (:,q)]), vec(·) is a matrix vectorization operation; A -i Remove the angle between A(Θ) and the two-dimensional direction. The relevant matrix after the part, μ -k (t) is μ(t) removed from the context. The vector following the relevant part, ∑ -k For ∑removal and The relevant part of the matrix For ∑ -k The Hermitian square root; S502 obtains the two-dimensional frequency estimate corresponding to the maximum value in G. use The estimated two-dimensional directional angle values are calculated. The calculation formula is: S503 Calculation Precision parameters of candidate target signals in the direction The calculation formula is: In the formula, and Two-dimensional directional angle estimate The corresponding auxiliary parameters.
6. The method for estimating the azimuth of a uniform rectangular array target based on array manifold matrix learning according to claim 1, characterized in that, The normalized spatial spectral value The calculation of P, the first element P k The calculation formula is: In the formula, μ k (t) is the k-th element of the posterior mean μ(t). max(·) means taking the maximum value.