CN117540138A - Uniform rectangular array target azimuth estimation method based on array manifold matrix learning - Google Patents

Abstract

Aiming at the problem of high computational complexity of a two-dimensional direct expansion version of a one-dimensional grid sparse target azimuth estimation method, the invention provides a uniform rectangular array target azimuth estimation method based on array manifold matrix learning, which comprises the steps of obtaining an expression of an array manifold matrix according to the array information of the uniform rectangular array; according to the array manifold matrix learning strategy, iteratively calculating a two-dimensional direction angle set, an accuracy vector and a Gaussian white noise accuracy parameter of the candidate target signal to obtain a posterior estimation value of the candidate target signal; and calculating a normalized spatial spectrum value by using the posterior estimation quantity, wherein the two-dimensional direction angle corresponding to the maximum value is the target azimuth estimation value. The number of the two-dimensional direction angles is increased one by one from zero, so that the number of columns of the array manifold matrix is lower, the complexity of parameter iterative computation is reduced, and meanwhile, the invention designs a high-efficiency two-dimensional direction angle computing method which has higher angle estimation precision.

Description

Uniform rectangular array target azimuth estimation method based on array manifold matrix learning

Technical Field

The invention relates to a signal processing method, in particular to a uniform rectangular array target azimuth estimation method based on array manifold matrix learning.

Background

The target direction estimation technology is one of powerful means of target detection and is widely applied to the fields of radar, sonar, wireless communication and the like. The development of the efficient and high-precision target azimuth estimation method is beneficial to the performance improvement of a target detection system. In the existing target azimuth estimation method, the sparse method has high estimation precision, and can still have good estimation performance under the adverse conditions of low signal-to-noise ratio and less snapshot data, so that the sparse method is widely focused and researched. At present, most sparse target azimuth estimation methods process linear array time domain snapshot data and aim at the problem of one-dimensional target azimuth estimation. Generally, the sparse target azimuth estimation method carries out discretization processing on an observation angle space, utilizes the obtained discrete angle points to construct an array manifold matrix for sparse parameter estimation, and obtains a target azimuth estimation value according to the sparse parameter estimation value. Generally we refer to this sparse-class target position estimation method involving angle discretization processing as the grid-class method. For a grid sparse target azimuth estimation method, the density degree of discrete angle points can influence the accuracy and the computational complexity of target azimuth estimation; higher estimation accuracy can be obtained to some extent using denser discrete angle points, but the computational complexity will be greatly increased.

For the two-dimensional target azimuth estimation problem, if the one-dimensional grid sparse target azimuth estimation method is directly expanded to a two-dimensional form, the number of the related discrete angle points is greatly increased, and the dimension of the array manifold matrix is greatly increased, so that the complexity of sparse parameter calculation is obviously increased, and the practical application is not facilitated. On the other hand, if the target azimuth deviates from a preset discrete angle point, namely angle mismatch errors exist, the angle estimation precision of the grid sparse target azimuth estimation method is reduced, and angle refinement processing is required to be introduced to compensate the angle mismatch errors so as to ensure the angle estimation precision. This additional angle refinement process will further increase the computational complexity of the grid-like sparse target bearing estimation method. For another grid-free sparse target azimuth estimation method, although angle discretization processing is not needed, the calculation efficiency is high, the number of targets is often needed to be known in advance, which is not practical in practice, so the practical application of the method is limited.

Therefore, aiming at the problem of high computational complexity of the two-dimensional direct expansion version of the one-dimensional grid sparse target azimuth estimation method, a corresponding solution is needed to be proposed.

Disclosure of Invention

The present invention aims to solve at least one of the technical problems existing in the prior art. Therefore, the invention provides a uniform rectangular array target azimuth estimation method based on array manifold matrix learning, which obtains a two-dimensional direction angle set with elements added one by one from zero through an array manifold matrix learning strategy, constructs an array manifold matrix with fewer column vectors for parameter iterative computation, reduces computation complexity and improves operation efficiency.

In order to achieve the above object, the present invention provides a method for estimating the azimuth of a uniform rectangular array target based on array manifold matrix learning, comprising:

s1, obtaining an expression of an array manifold matrix according to the array information of the uniform rectangular array;

s2, iteratively calculating a two-dimensional direction angle set, an accuracy vector and a Gaussian white noise accuracy parameter of a candidate target signal according to an array manifold matrix learning strategy, updating an array manifold matrix by using the two-dimensional direction angle set in each iteration, and then calculating a posterior estimation value (namely a posterior mean value and a posterior covariance matrix) of the candidate target signal by using the accuracy vector, the Gaussian white noise accuracy parameter and the updated array manifold matrix, wherein the posterior mean value is used as an estimated value of the candidate target signal;

s3, calculating a normalized spatial spectrum value by using the obtained estimated value of the candidate target signal, wherein the two-dimensional direction angles corresponding to the first K maximum values in the normalized spatial spectrum value are target azimuth estimated values, and K is the number of real target signals.

Further, the expression of the array manifold matrix is:

in the method, in the process of the invention,is a set of two-dimensional direction angles of candidate target signals, +.>For the number of candidate target signals, θ _i And->Respectively +.>Pitch and azimuth of the two-dimensional direction angle,for two-dimensional direction angle>The above steering vector has the expression:

in the method, in the process of the invention,is the product of Kronecker> Wherein ( ^T In order to transpose the operator,lambda is the wavelength of the target signal, M _z And M _y The number of array elements in the z-axis and the y-axis of the uniform rectangular array respectively, d _z And d _y The array element intervals of the array elements in the z-axis direction and the y-axis direction are respectively.

Further, the parameter iterative computation according to the array manifold matrix learning strategy comprises the following steps:

s201, initializing a two-dimensional direction angle set, an accuracy vector and Gaussian white noise accuracy parameters of candidate target signals, and setting the maximum iteration times and iteration convergence conditions;

s202, updating a two-dimensional direction angle set theta and an accuracy vectorUpdated value Θ using two-dimensional set of direction angles ^new A new array manifold matrix a (Θ is obtained ^new )；

S203, updating a Gaussian white noise precision parameter beta, wherein a calculation formula is as follows:

where tr (. Cndot.) is a matrix tracing operation,for Moore-Penrose pseudo-inverse matrix operation, I _M For m=m _y ×M _z Dimension Unit matrix>For the sampling covariance matrix, y= [ Y (1), …, Y (T)]For the time domain snapshot data matrix of the uniform rectangular array, T is the number of time domain snapshots, y (T), t=1, …, T is the T-th time domain snapshot data vector, (·) ^H Is conjugate transpose operation;

s204 updates the posterior mean μ= [ μ (1), …, μ (T) of the candidate target signal]And a posterior covariance matrix Sigma, using the posterior mean as the estimated value of the candidate target signal, i.eWherein μ (T), t=1, …, the calculation formulas of T and Σ 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 (alpha) ^new ) To update the value alpha with the precision vector ^new Diagonal matrix for main diagonal element, (·) ^-1 Inverting the matrix;

s205 repeats the above S202, S203, and S204, and performs iteration count; if the iteration count reaches the maximum iteration number or meets the iteration convergence condition, ending the iteration calculation and outputting a two-dimensional direction angle set theta ^new And an estimated value of the candidate target signalThe iteration convergence condition is as follows:

in the method, in the process of the invention,for the estimated value of candidate target signal obtained by last iteration, τ is the iteration convergence decision threshold, size (·) represents the matrix dimension, "&&"means a logical and operation, I.I _F Is the Frobenius norm of the matrix.

Further, the two-dimensional direction angle set Θ and the precision vectorComprises:

firstly, the updating process of theta and alpha involves two updating operations, namely a new angle adding operation and an existing angle updating operation;

in the new angle adding operation, a new two-dimensional direction angle is calculatedTo add to Θ, calculate +.>Accuracy parameter of candidate target signal in direction +.>To be added to alpha, calculate the log-marginal likelihood delta l of the new angle addition operation ₀ ；

In the existing angle updating operation, for each two-dimensional direction angle existing in ΘCalculation of auxiliary parameters +.>And->If->Then enter the existing angle delete operation, i.e. remove +.>Removing the precision parameter alpha from alpha _i Calculating the log-marginal likelihood delta ++for the existing angle deletion operation>If->Then enter the existing angle re-estimation operation, i.e. calculate the updated value +.>For replacing->Calculating an update value +.>For replacing alpha _i Calculating the log-marginal likelihood delta +.>

Wherein the three log-marginal likelihood increments Deltal ₀ 、And->The calculation formulas of (a) are respectively as follows:

in the method, in the process of the invention,for parameter pair->Is +.>The auxiliary parameterAnd->The calculation formulas of (a) are respectively as follows:

in the method, in the process of the invention,

second, in the update process of Θ and α, co-obtainedThe log-marginal likelihood increments, i.e. Deltal ₀ Andcompare this->And obtaining the maximum log-margin likelihood increment. If Deltal ₀ Maximum, the new angle adding operation is executed, and the updated values of theta and alpha are respectively obtainedAnd->And update the number of candidate target signals +.>If->At maximum, the existing angle deleting operation is executed to obtain updated values of theta and alpha which are respectively theta ^new ＝(Θ) _-i And alpha ^new ＝(α) _-i And update the number of candidate target signals +.>Wherein ( _-i Indicating removal of the ith element; if-> At maximum, the existing angle re-estimation operation is performed to obtain updated values of Θ and α as +.>Andand let->Remain unchanged.

Further, in the new angle adding operation and the existing angle re-estimating operation, efficient two-dimensional direction angle calculation and precision parameter calculation of candidate target signals are sequentially performed:

s501 is calculated by two-dimensional boom-FFT:

in the method, in the process of the invention,Z _-k (: q) is a matrix Z _-k Is the q-th column vector of (2); zomFFT 2D (·) represents a two-dimensional zoom-FFT operation; s []Matrix form conversion operation of representing vector, namely converting vector in brackets into M _z ×M _y Dimensional matrices, e.g. vectors Z _-k (:,q)＝vec(S[Z _-k (:,q)]) Vec (·) is a matrix vectorization operation; a is that _-i Removing the angle +.A from the two-dimensional direction for A (Θ)>Related partial matrix, μ _-k (t) μ (t) removal and +.>The vector after the relevant part, Σ _-k For sigma removal and->Matrix behind the relevant part, +.>Is sigma (sigma) _-k Square root of hermitian;

s502 obtaining a two-dimensional frequency estimation value corresponding to the maximum value in GBy->Calculating to obtain a two-dimensional direction angle estimated value +.>The calculation formula is as follows:

s503 calculationAccuracy parameter of candidate target signal in direction +.>The calculation formula is as follows:

in the method, in the process of the invention,and->For two-dimensional direction angle estimate +.>Corresponding auxiliary parameters.

Further, in calculating the normalized spatial spectrum valueWhen in P-> P number _k The calculation formula of (2) is as follows:

in the method, in the process of the invention,μ _k (t) is the kth element of the posterior mean μ (t); /> max (·) represents taking the maximum value.

Compared with the prior art, the invention has the beneficial effects that:

the array manifold matrix used in the parameter iterative computation is obtained by iterative learning from a null matrix, namely the number of column vectors of the array manifold matrix is gradually increased and is always kept at a smaller value (slightly larger than the number of real target signals), so that the matrix dimension of the array manifold matrix is reduced, the complexity of the parameter iterative computation is reduced, and the operation efficiency is improved.

On the other hand, in the invention, the discretization processing is not needed for the observation angle domain in the efficient two-dimensional direction angle calculation, so that the estimation accuracy of the two-dimensional direction angle calculation is not influenced by angle mismatch, and the invention has higher target azimuth estimation accuracy.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a flow diagram illustration of the present invention;

FIG. 2 is a schematic diagram of a uniform rectangular array according to an embodiment;

FIG. 3 is a graph of root mean square error of target bearing estimation results for different methods under different SNR conditions in accordance with an embodiment;

fig. 4 shows the average run time of different methods under different signal-to-noise conditions for the specific embodiment.

Detailed Description

The technical solutions of the present invention will be clearly and completely described in connection with the embodiments, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

According to the embodiment of the invention, the invention provides a uniform rectangular array target azimuth estimation method based on array manifold matrix learning, and the adopted technical scheme comprises the following steps:

step 1: using a M vertically disposed in the plane yoz _y ×M _z Estimating target azimuth by using a meta-uniform rectangular array, wherein M is _y For the number of y-axis array elements, M _z The number of the array elements in the z-axis direction is d, and the distances between the array elements in the y-axis direction and the z-axis direction are respectively _y And d _z . Assume that in the target azimuth estimation process, the obtained two-dimensional direction angle set of the candidate target signals isWherein (1)>For the number of candidate target signals, θ _i And->Respectively the firstThe pitch angle and the azimuth angle of each two-dimensional direction angle are according to the array information of the uniform rectangular array, and the expression of the array manifold matrix is obtained as follows:

in the formula, the firstColumn guide vector +.> Is the product of Kronecker> Lambda is the signal wavelength, ( ^T Is the transpose operator.

Step 2: iteratively computing a two-dimensional directional angle set Θ and an accuracy vector of a candidate target signal using an array manifold matrix learning strategyAnd a Gaussian white noise precision parameter beta. The implementation steps are as follows.

1) Step 21, setting a maximum iteration number MaxIter and an iteration convergence judgment threshold tau; initializing the Θ and the α, including:

step 211, let the gaussian white noise precision parameter β=10 ³ Θ is an empty set, i.e., Θ= []；

Step 212, using the time domain snapshot data matrix y= [ Y (1), …, Y (T) of the uniform rectangular array]According to the efficient two-dimensional angle calculation formula, a first two-dimensional direction angle is calculatedDegree ofCalculating +.>Accuracy parameter of candidate target signal in direction +.>

Step 213, order Number of candidate target signals>Calculating a posterior mean μ (t) =βΣa (Θ) of the candidate target signal ^H y (t) and a posterior covariance matrix Σ= [ diag (α) +βa (Θ) ^H A(Θ)] ^-1 Wherein t=1, …, T is the number of time-domain snapshots, (·) ^-1 And (5) inverting the matrix.

2) Step 22, updating Θ and α to obtain updated value Θ ^new And alpha ^new Comprising:

step 221, calculating relevant parameters of the new angle adding operation. According to the high-efficiency two-dimensional angle calculation formula, a new one is calculatedCalculating according to the accuracy parameter calculation formula of the candidate target signal to obtain +.>Corresponding toCalculating log-marginal likelihood delta for new angle addition operations/>

Step 222, calculating relevant parameters of the existing angle deletion operation and the existing angle re-estimation operation, namely:

for each of Θ Calculating corresponding auxiliary parameters ∈ ->And->

If it isThen calculate the log-marginal likelihood delta +.>

If it isThen the relevant parameters for the existing angular re-estimation parameters are calculated. According to the efficient two-dimensional angle calculation formula, calculating +.>Update value +.>Calculating alpha according to the calculation formula of the precision parameters of the candidate target signals _i Update value +.>Computing log-marginal likelihood delta for existing angle re-estimation operations

Step 223, comparing the obtainedThe log-marginal likelihood increments, i.e. Deltal ₀ And-> Obtaining the maximum log-marginal likelihood increment, and executing the angle updating operation corresponding to the maximum log-likelihood increment, namely:

if Deltal ₀ Maximum, then new angleAdded to Θ, will +.>Added to alpha to obtain an updated valueAnd->And update the number of candidate target signals +.>

If it isMaximum, the existing angle +.>Remove alpha from theta _i Removing from alpha to obtain an updated value theta ^new ＝(Θ) _-i And alpha ^new ＝(α) _-i And update->Wherein ( _-i Indicating removal of the ith element;

if it isMaximum, the existing angle +.>Replaced by->Will be alpha _i Replaced byGet updated value +.>And-> And let->Remain unchanged.

To this end, step 22 ends. In calculating the log marginal likelihood delta in this step,corresponding contribution->Wherein,

3) Step 23, updating the white gaussian noise precision parameter beta, wherein the calculation formula is as follows:

where tr (. Cndot.) is a matrix tracing operation,for Moore-Penrose pseudo-inverse matrix operation, I _M For m=m _y ×M _z Dimension Unit matrix>

4) Step 24, update the posterior mean μ= [ μ (1), …, μ (T) of candidate target signals]Sum a posteriori covariance matrix Σ= [ diag (α) ^new )+βA(Θ ^new ) ^H A(Θ ^new )] ^-1 And taking the posterior mean value as the estimated value of the candidate target signal, namelyWhere t=1, …, T column μ (T) =βΣa (Θ) ^new ) ^H y(t)。

5) Step 25, repeating step 22, step 23 and step 24, and proceedingPerforming row iteration counting; if the iteration count reaches MaxIter, or simultaneously satisfiesAnd->Ending the iteration and outputting Θ ^new And->Wherein (1)>For the estimated value of the candidate target signal obtained in the previous iteration, the size (·) represents the matrix dimension, I.I _F Is the Frobenius norm of the matrix.

So far, step 2 ends. In this step, two-dimensional direction angle estimation valueThe efficient calculation formula of (2) is as follows:

in the method, in the process of the invention,is the two-dimensional frequency estimation value corresponding to the maximum value in the two-dimensional boom-FFT output result G,wherein->Z _-k (: q) is a matrix Z _-k Is represented by the q-th column vector of (2D (-)) from the zomFFT, S [ · representing a two-dimensional zomFFT operation]Matrix form conversion operation of representing vector, namely converting vector in brackets into M _z ×M _y Dimensional matrices, e.g. vectors Z _-k (:,q)＝vec(S[Z _-k (:,q)]) Vec (·) is a matrix vectorization operation, A _-i Remove and +.>Related partial matrix, μ _-k (t) μ (t) removal and +.>The vector after the relevant part, Σ _-k For sigma removal and->Matrix behind the relevant part, +.>Is M _-k Square root of hermitian of (a).

In the step 2 of the process described above,accuracy parameter of candidate target signal in direction +.>The calculation formula of (2) is as follows:

step 3: using estimated values of candidate target signalsCalculating normalized spatial spectral values +.>The two-dimensional direction angles corresponding to the first K maximum values in P are target azimuth estimated values, and K is the number of real target signals. Wherein, the%>The element P _k The calculation formula of (2) is as follows:

in the method, in the process of the invention,μ _k (t) is the kth element of the posterior mean μ (t), ++> max (·) represents taking the maximum value.

Simulation experiment case

The simulation experiment uses a 6X 4 element uniform rectangular array vertically arranged on a yoz plane to carry out target azimuth estimation, wherein the number of y-axis array elements is M _y =6, the number of z-axis array elements is M _z Array element interval d =4 _y And d _z All of half wavelength. A schematic of the uniform rectangular array is shown in fig. 2. Simulation assumes that K=2 far-field narrowband signals are incident on the uniform rectangular array, and the two-dimensional direction angles of the incident signals are respectivelyAnd->The number of snapshots of the time domain snapshot data of the uniform rectangular array is set to be 50, and the signal-to-noise ratio SNR is increased from-10 dB to 20dB. The method and the two reference methods are used for estimating the target azimuth, 200 independent experiments are respectively carried out, root Mean Square Error (RMSE) and average running time of target azimuth estimation results of different methods under different SNR conditions are calculated, and performance curves are drawn as shown in fig. 3 and 4.

As can be seen from fig. 3, the root mean square error of the target bearing estimation result of the present invention is minimal when the signal-to-noise ratio is less than 0 dB; when the signal-to-noise ratio is greater than or equal to 0dB, the root mean square error of the target azimuth estimation result is similar to that of the SAMV-RELAX method, and the target azimuth estimation result is close to the lower boundary of the Clamamaro. Therefore, the target azimuth estimation accuracy of the invention is better than that of the other two methods.

As can be seen from fig. 4, the average run time of the present invention is slightly greater than that of the FGML process, but less than that of the SAMV-RELAX process, and always less than 1 second, under different signal-to-noise ratio conditions. Therefore, the invention has higher operation efficiency.

The preferred embodiments of the invention disclosed above are intended only to assist in the explanation of the invention. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise form disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best understand and utilize the invention. The invention is limited only by the claims and the full scope and equivalents thereof.

Claims (6)

1. A uniform rectangular array target azimuth estimation method based on array manifold matrix learning is characterized by comprising the following steps:

s1, obtaining an expression of an array manifold matrix according to the array information of the uniform rectangular array;

s2, iteratively calculating a two-dimensional direction angle set, an accuracy vector and a Gaussian white noise accuracy parameter of a candidate target signal according to an array manifold matrix learning strategy, updating an array manifold matrix by using the two-dimensional direction angle set in each iteration, and then calculating a posterior estimation value (namely a posterior mean value and a posterior covariance matrix) of the candidate target signal by using the accuracy vector, the Gaussian white noise accuracy parameter and the updated array manifold matrix, wherein the posterior mean value is used as an estimated value of the candidate target signal;

s3, calculating a normalized spatial spectrum value by using the obtained estimated value of the candidate target signal, wherein two-dimensional direction angles corresponding to the first K maximum values of the normalized spatial spectrum value are target azimuth estimated values, and K is the number of real target signals.

2. The method for estimating the target azimuth of the uniform rectangular array based on array manifold matrix learning according to claim 1, wherein the expression of the array manifold matrix is:

in the method, in the process of the invention,is a set of two-dimensional direction angles of candidate target signals, +.>For the number of candidate target signals, θ _i And->Respectively +.>Pitch and azimuth of the two-dimensional direction angle,for two-dimensional direction angle>The above steering vector has the expression:

in the method, in the process of the invention,is the product of Kronecker> Wherein ( ^T For transpose operator +.>Lambda is the wavelength of the target signal, M _z And M _y The number of array elements in the z-axis and the y-axis of the uniform rectangular array respectively, d _z And d _y The array element intervals of the array elements in the z-axis direction and the y-axis direction are respectively.

3. The method for estimating the target azimuth of the uniform rectangular array based on the array manifold matrix learning according to claim 1, wherein the parameter iterative calculation based on the array manifold matrix learning strategy comprises the following steps:

s201, initializing a two-dimensional direction angle set, an accuracy vector and Gaussian white noise accuracy parameters of candidate target signals, and setting the maximum iteration times and iteration convergence conditions.

S202, updating a two-dimensional direction angle set theta and an accuracy vector of a candidate target signalUpdated value Θ using two-dimensional set of direction angles ^new A new array manifold matrix a (Θ is obtained ^new )。

S203, updating a Gaussian white noise precision parameter beta, wherein a calculation formula is as follows:

wherein tr (. Cndot.) is a matrixThe trace-finding operation is carried out,for Moore-Penrose pseudo-inverse matrix operation, I _M For m=m _y ×M _z Dimension Unit matrix>For the sampling covariance matrix, y= [ Y (1), …, Y (T)]For the time domain snapshot data matrix of the uniform rectangular array, T is the number of time domain snapshots, y (T), t=1, …, T is the T-th time domain snapshot data vector, (·) ^H Is a conjugate transpose operation.

S204 updates the posterior mean μ= [ μ (1), …, μ (T) of the candidate target signal]And a posterior covariance matrix Sigma, using the posterior mean as the estimated value of the candidate target signal, i.eWherein μ (T), t=1, …, the calculation formulas of T and Σ 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 (alpha) ^new ) To update the value alpha with the precision vector ^new Diagonal matrix for main diagonal element, (·) ^-1 And (5) inverting the matrix.

S205 repeats the above S202, S203, and S204, and performs iteration count; if the iteration count reaches the maximum iteration number or the iteration convergence condition is met, stopping the iteration calculation and outputting a two-dimensional direction angle set theta ^new And an estimated value of the candidate target signalThe iteration convergence condition is as follows:

in the method, in the process of the invention,for the estimated value of candidate target signal obtained by last iteration, τ is the iteration convergence decision threshold, size (·) represents the matrix dimension, "&&"means a logical and operation, I.I _F Is the Frobenius norm of the matrix.

4. The iterative calculation of parameters based on array manifold matrix learning strategy of claim 3, wherein the two-dimensional set of direction angles Θ and precision vectorsComprises:

firstly, the updating process of theta and alpha involves two updating operations, namely a new angle adding operation and an existing angle updating operation;

in the new angle adding operation, a new two-dimensional direction angle is calculatedTo be added to Θ, calculateAccuracy parameter of candidate target signal in direction +.>To be added to alpha, calculate the log-marginal likelihood delta l of the new angle addition operation ₀ ；

In the existing angle updating operation, for each two-dimensional direction angle existing in ΘCalculation of auxiliary parameters +.>And->If->Then enter the existing angle delete operation, i.e. remove +.>Removing the precision parameter alpha from alpha _i Calculating the log-marginal likelihood delta ++for the existing angle deletion operation>If->Then enter the existing angle re-estimation operation, i.e. calculate the updated value +.>For replacing->Calculating an update value +.>For replacing alpha _i Calculating the log-marginal likelihood delta +.>

Wherein the three log-marginal likelihood increments Deltal ₀ 、And->The calculation formulas of (a) are respectively as follows:

in the method, in the process of the invention,for parameter pair->Is a logarithmic marginal likelihood contribution of (c),the auxiliary parameterAnd->The calculation formulas of (a) are respectively as follows:

in the method, in the process of the invention,

second, in the update process of Θ and α, co-obtainedThe log-marginal likelihood increments, i.e. Deltal ₀ Andcompare this->And obtaining the maximum log-margin likelihood increment. If Deltal ₀ Maximum, the new angle adding operation is executed, and the updated values of theta and alpha are respectively obtainedAnd->And update the number of candidate target signals +.>If->At maximum, the existing angle deleting operation is executed to obtain updated values of theta and alpha which are respectively theta ^new ＝(Θ) _-i And alpha ^new ＝(α) _-i And update the number of candidate target signals +.>Wherein ( _-i Indicating removalAn i-th element; if->At maximum, the existing angle re-estimation operation is performed to obtain updated values of Θ and α as +.> Andand let->Remain unchanged.

5. A method for estimating a target azimuth of a uniform rectangular array based on array manifold matrix learning according to claim 1 or 3, wherein the updating operation involves efficient two-dimensional direction angle calculation and calculation of precision parameters of candidate target signals, the two calculations are used in a new angle adding operation and an existing angle re-estimating operation, and the implementation steps are as follows:

s501 is calculated by two-dimensional boom-FFT:

in the method, in the process of the invention,Z _-k (: q) is a matrix Z _-k Is the q-th column vector of (2); zomFFT 2D (·) represents a two-dimensional zoom-FFT operation; s []Matrix form conversion operation of representing vector, namely converting vector in brackets into M _z ×M _y Dimensional matrices, e.g. vectors Z _-k (:,q)＝vec(S[Z _-k (:,q)]) Vec (·) is a matrix vectorization operation; a is that _-i Removing the angle +.A from the two-dimensional direction for A (Θ)>Related partial matrix, μ _-k (t) μ (t) removal and +.>The vector after the relevant part, Σ _-k For sigma remove and +.>Matrix behind the relevant part, +.>Is sigma (sigma) _-k Square root of hermitian;

s502 obtaining a two-dimensional frequency estimation value corresponding to the maximum value in GBy->Calculating to obtain a two-dimensional direction angle estimated value +.>The calculation formula is as follows:

s503 calculationAccuracy parameter of candidate target signal in direction +.>The calculation formula is as follows:

in the method, in the process of the invention,and->For two-dimensional direction angle estimate +.>Corresponding auxiliary parameters.

6. The method for estimating a uniform rectangular array target orientation based on array manifold matrix learning of claim 1, wherein said normalized spatial spectrum valuesCalculation of (1)/(P)>The element P _k The calculation formula of (2) is as follows:

in the method, in the process of the invention,μ _k (t) is the kth element of the posterior mean μ (t), ++> max (·) represents taking the maximum value.