Information source number estimation method based on orthogonal matching pursuit and signal subspace matching

Abstract

The invention relates to an information source number estimation method, in particular to an information source number estimation method based on orthogonal matching pursuit and signal subspace matching. The invention aims to solve the problems that the signal-to-noise ratio of array snapshot data in an underwater acoustic environment is generally not high, the array snapshot data is easily interfered by colored noise and coherent signal sources, and for a high-speed moving target, the number of effective snapshots is small, so that the accuracy of traditional signal source number estimation is low. According to the method, an orthogonal matching pursuit method is utilized to iteratively solve a support vector and a feature vector corresponding to a residual maximum feature value of the support vector to construct two subspaces, and signal source number estimation is realized through a signal subspace matching criterion. Simulation results show that compared with an existing signal source number estimation method, the method has the advantages that the requirement for the signal-to-noise ratio is lower, the performance is better under the condition of small snapshots, and meanwhile the method is not sensitive to coherent signal sources and colored noise. Lake test data processing results show that the method can effectively estimate the number of fixed and moving underwater acoustic targets.

Description

Technical Field

[0001] The invention relates to a method for estimating the number of information sources. Background Art

[0002] Source number estimation has a wide range of key applications in underwater acoustic signal processing. For example, when using subspace algorithms for azimuth estimation, the number of sources needs to be known to correctly distinguish the signal subspace from the noise subspace. [1] ; When performing blind source separation on underwater acoustic signals, many algorithms take the number of signal sources as a known condition [2] ; When using the multi-target tracking algorithm based on joint probability data association for target tracking, the number of signal sources is required to be constant and known. [3] .

[0003] In a complex and changing underwater acoustic environment, the collected data will be superimposed with strong noise, which leads to the use of the Akaike information criterion (AIC). [4] , minimum description length (MDL) criterion [5] and Geiger radius [6] The performance of traditional methods for signal source number estimation has seriously deteriorated. Therefore, in order to effectively estimate the signal source number of underwater acoustic targets, predecessors have done a lot of research on reducing the requirements of the above methods on the signal-to-noise ratio. [7-10] . Reference [8] designed a criterion value to characterize the contribution of signal and noise in the covariance matrix, and estimated the number of signal sources through this criterion value. When the signal-to-noise ratio is low and there is unequal power, its estimation performance is better than the Gaussian radius method. Reference

[10] proposed a spatial focusing method for rotating uniform circular arrays, which increased the number of snapshots that can be used per frame in the estimation of the number of static target source numbers. The above method relies on a large amount of snapshot data to achieve effective source number estimation in an underwater acoustic environment with a low signal-to-noise ratio. However, for high-speed moving targets, the number of snapshots that can be used for estimation per frame is relatively small.

[11] ,Therefore, the estimation performance of the above method will be affected.

[0004] In recent years, many scholars have conducted in-depth research on the estimation of the number of information sources under short snapshot conditions. [12-15]. Reference

[12] used the large random matrix theory to improve the AIC method and improved the estimation performance under small snapshot conditions. Reference

[13] used the linear shrinkage method to reduce the estimation error of the noise eigenvalue under small snapshot conditions, thereby improving the estimation performance of the MDL method. Reference

[15] combined the ideas of information granules and granular computing with fuzzy set theory to realize the estimation of the number of signal sources under small snapshots and low signal-to-noise ratio conditions. The above methods all assume that the noise received by the array is Gaussian white noise, that is, the noise power of each array element is equal and independent. However, the actual ocean environment is very complex, and the array elements are easily interfered by various noises, which makes it difficult to meet the assumption of Gaussian white noise.

[16] , which leads to the degradation of the estimation performance of these methods.

[0005] In order to achieve effective source number estimation in the scenario of small snapshots and colored noise, the reference

[17] first increases the proportion of uncorrelated noise through the adaptive diagonal loading method to reduce the influence of correlated noise, and then estimates the number of sources by using the law of linear shrinkage coefficient changing with the number of sources. This method shows good estimation effect in the case of small snapshots and low degree of colored noise, but has high requirements on signal-to-noise ratio. Wax proposed the signal subspace matching (SSM) criterion for source number estimation [18-19] Initially, Wax used this criterion to match the subspace generated by the original sampled data and the eigenvectors of the covariance matrix

[18] , which can achieve good signal source number estimation results under small snapshots and colored noise conditions, but has high requirements on the signal-to-noise ratio. In order to reduce the requirements on the signal-to-noise ratio, Wax is based on the array rotation invariance.

[20] , using the signal subspace matching (ISSM) generated by the two subarrays to achieve the number of signal sources estimation

[19] , this method significantly improves the estimation performance under low signal-to-noise ratio conditions. Inspired by the ISSM method, reference

[21] characterizes the vector difference by calculating the generalized cosine square value between the single eigenvectors of the two subarrays, and then uses the characteristic that the difference between the signal eigenvectors is smaller than the noise eigenvector, combined with the sequence ratio to estimate the number of sources. This method requires that the difference between the noise eigenvectors of the two subarrays is large, so the requirement for the number of array elements is high. The above-mentioned SSM, ISSM and reference

[21] methods use the matching idea to estimate the number of sources. Although the requirements for the number of snapshots are lower than those of traditional source number estimation methods, they all estimate the number of sources based on the eigenvectors of the covariance matrix. Under small snapshot conditions, if the covariance matrix is ​​to be accurately estimated, the signal-to-noise ratio requirement is high. In addition, the above methods generally assume that the sources are independent of each other, while in the underwater acoustic environment, interface reflections may generate a large number of coherent signals.

[22] , which results in the failure of estimating the eigenvalues ​​and eigenvectors, and in turn causes errors in estimating the number of information sources. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that the signal-to-noise ratio of array snapshot data in an underwater acoustic environment is usually not high and is easily interfered by colored noise and coherent signal sources, and for high-speed moving targets, the number of effective snapshots is small, resulting in low accuracy of traditional signal source number estimation. A signal source number estimation method based on orthogonal matching pursuit and signal subspace matching is proposed.

[0007] The specific process of the source number estimation method based on orthogonal matching pursuit and signal subspace matching is as follows:

[0008] Step 1: Obtain an M×L dimensional matrix X=[X(1),X(2),...,X(t),...,X(L)] consisting of L snapshots collected by the array;

[0009] Wherein, t = 1, 2, ..., ..., L; M represents the number of array elements; X(1) represents the snapshot data collected by the array at time 1, X(2) represents the snapshot data collected by the array at time 2, X(t) represents the snapshot data collected by the array at time t, and X(L) represents the snapshot data collected by the array at time L;

[0010] Step 2: Set the total number of iterations to M-1;

[0011] Step 3: Initialize the number of iterations i = 0; Initialize r 0,t =X(t), t=1,...,L; Initialization

[0012] Among them, r 0,t represents the residual error of the t-th snapshot data collected by the array at the 0th iteration, Λ 0 represents the set of support vector indices obtained in the first 0 iterations, represents the empty set;

[0013] Step 4: Set the number of iterations i = i + 1;

[0014] Step 5: Complete the dictionary Each a(θ v ) and the residuals of all snapshot data are inner-producted, and the absolute values ​​of all inner-products are summed, and then the a(θ v ) as the support vector obtained in the i-th iteration where β i For the selected a(θ v ) index; v = 1, 2, ..., J; J represents the total number of observable angles; column vector a(θ v) is the steering vector of the vth far-field narrowband source;

[0015] Step 6: Support vector obtained based on the i-th iteration The corresponding index β i The set of indices Λ corresponding to the support vectors obtained in the previous i-1 iterations i-1 , obtain the set of indices Λ corresponding to the support vectors obtained in the previous i iterations i ;

[0016] The set Λ of indices corresponding to the support vectors obtained in the previous i iterations i , get the matrix composed of the support vectors obtained in the previous i iterations

[0017] Step 7: Calculate the residual r of the i-1th iteration i-1 The covariance matrix of the residual at the i-1th iteration is obtained, and the eigenvector matrix U corresponding to the residual is obtained. i-1 ;

[0018] Step 8: Matrix composed of support vectors obtained from the previous i iterations and the eigenvector matrix U i-1 , the signal subspace matching criterion is used to calculate the distance between the i-th iteration subspaces

[0019] Among them, (U i-1 ) 1 Denotes the eigenvector matrix U i-1 Column 1;

[0020] Represented by the matrix The subspace generated by the column vectors of

[0021] Represented by the matrix The column vector and eigenvector (U i-1 ) 1 The subspace generated by the column vectors of

[0022] <·> represents the subspace generated by the column vectors of the matrix in brackets;

[0023] represents the i-th iteration subspace and subspace The distance between

[0024] SSM i Represents the distance between subspaces calculated at the i-th iteration;

[0025] Step 9: Order

[0026] Among them, B i Represents the matrix composed of support vectors obtained in the previous i iterations;

[0027] Solve for z using least squares i,t =argmin z ||X(t)-B i z|| 2 ,t=1,...,L;

[0028] Where z represents the coefficient vector obtained by least squares optimization, z = z i,1 ,z i,2 ,…,z i,t ,…,z i,L ;z i,t Indicates B i The coefficient vector of ;

[0029] Step 10: Based on the t-th snapshot data X(t), B collected by the array i and z i,t , calculate the residual r of the i-th iteration i,t ;

[0030] Step 11: Determine whether i <M-1;

[0031] If yes, repeat steps 4 to 11 until i=M-1;

[0032] If not, output the source estimation result

[0033] The beneficial effects of the present invention are:

[0034] In complex underwater acoustic environments, the estimation of the number of signal sources faces many challenges. The signal-to-noise ratio of array snapshot data is usually not high, and it is easily interfered by colored noise and coherent sources. In addition, for high-speed moving targets, the number of effective snapshots is small. These factors cause the performance of traditional signal source number estimation methods to drop significantly. However, the orthogonal matching pursuit method can still estimate relatively accurate support vectors in the above complex scenarios. In order to perform robust signal source number estimation for underwater acoustic targets, the present invention uses the orthogonal matching pursuit method to iteratively solve the support vectors and the eigenvectors corresponding to the maximum eigenvalues ​​of their residuals to construct two subspaces, and realizes the estimation of the number of signal sources through the signal subspace matching criterion. Simulation results show that compared with the existing signal source number estimation methods, the method of the present invention has lower signal-to-noise ratio requirements, performs better under small snapshot conditions, and is insensitive to coherent sources and colored noise. The results of lake test data processing show that this method can effectively estimate the number of fixed and moving underwater acoustic targets.

[0035] In view of the above-mentioned shortcomings of using the covariance matrix eigenvector to estimate the number of information sources, the present invention introduces a more robust eigenvector estimation method. Orthogonal Matching Pursuit (OMP)

[23] It is a greedy sparse recovery method that can effectively estimate the steering vector corresponding to the source under the conditions of small snapshots and colored noise, and has a low signal-to-noise ratio requirement. It is also suitable for coherent sources. When the number of iterations is less than or equal to the number of sources, the support vector estimated by the OMP method in each iteration corresponds to the steering vector of a source; however, when the number of iterations exceeds the number of sources, the support vector corresponds to the eigenvector of the noise. When the noise intensity is large, these noise eigenvectors may be mistaken for signal steering vectors, so the number of sources needs to be known.

[0036] In order to perform robust source number estimation for high-speed moving underwater acoustic targets, the present invention generates two subspaces by combining the support vector obtained by the OMP method and the eigenvector corresponding to the maximum eigenvalue of its residual in a specific manner, and estimates the number of sources through the SSM criterion. This method is referred to as OMP-SSM. Simulation results show that OMP-SSM has the advantage of SSM-type methods being insensitive to colored noise, and performs better under small snapshot conditions. It is also suitable for scenarios with coherent sources. The processing results of the lake test data further verify the effectiveness of the OMP-SSM method.

[0037] When estimating the number of signal sources in a complex environment, we are faced with the challenges of low signal-to-noise ratio, small number of snapshots, non-white noise and the presence of coherent signal sources. To this end, this paper proposes a method for robust estimation of the number of signal sources using orthogonal matching pursuit and signal subspace matching. This method uses the support vector obtained by the orthogonal matching pursuit method and the eigenvector of its residual to construct two subspaces, and calculates the distance between them through the subspace matching criterion, and takes the number of iterations corresponding to the minimum distance as the estimation result of the number of signal sources. Theoretical analysis and simulation results show that compared with the traditional signal source number estimation method based on eigenvalues, when the noise eigenvalue does not meet the assumption of the Gaussian white noise model, the OMP-SSM method still has better estimation performance; compared with the ISSM method which is also based on the signal subspace matching criterion, the OMP-SSM method has a lower requirement for signal-to-noise ratio under small snapshot conditions; in addition, the maximum number of signal sources that the OMP-SSM method can estimate can reach the theoretical value and is suitable for scenarios with coherent signal sources. The results of lake test data processing show that this method can effectively estimate the number of underwater acoustic targets. In summary, this method has the potential for practical application and can be considered for application in the following scenarios: the target moves quickly, resulting in a small number of snapshots; the noise intensity in complex waters is large and presents non-white characteristics; and the scene where coherent signals are generated due to interface reflection. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of the present invention;

[0039] Figure 2 The diagram of the sub-array division method of the ISSM method, (a) the sub-array 1 division method diagram; (b) the sub-array 2 division method diagram;

[0040] Figure 3 It is the calculation process diagram of ISSM method;

[0041] Figure 4 It is the calculation process diagram of the ith iteration of the OMP-SSM method;

[0042] Figure 5 This is a graph showing how the estimation performance varies with the signal-to-noise ratio;

[0043] Figure 6 The analysis results of a single Monte Carlo experiment when the signal-to-noise ratio is -5dB are as follows: (a) Normalized covariance matrix eigenvalues; (b) The distance between the subspace generated by the first k support vectors of OMP and the first k eigenvectors of the covariance matrix and the signal subspace; (c) The subspace matching results of ISSM and OMP-SSM;

[0044] Figure 7 This is a graph showing how the estimation performance changes with the degree of noise color;

[0045] Figure 8 The analysis results of a single Monte Carlo experiment when the signal-to-noise ratio is 5dB and α is 0.6, (a) normalized covariance matrix eigenvalues; (b) the distance between the subspace generated by the first k support vectors of OMP and the first k eigenvectors of the covariance matrix and the signal subspace; (c) the subspace matching results of ISSM and OMP-SSM;

[0046] Fig. 9 The performance of the estimation varies with the number of snapshots. (a) SNR is -10dB; (b) SNR is 0dB; (c) SNR is 5dB; (d) SNR is 10dB.

[0047] Fig.10 The figure shows how the estimation performance changes with the number of signal sources. (a) Gaussian white noise and signal-to-noise ratio is 0dB; (b) colored noise and signal-to-noise ratio is 0dB, α is 0.3;

[0048] Fig.11 The estimation performance diagram when there is a coherent signal source, (a) the estimation performance changes with the signal-to-noise ratio under the background of Gaussian white noise; (b) the estimation performance changes with the degree of noise color when the SNR is 5dB under the background of colored noise;

[0049] Fig.12The estimation performance diagrams for different incident angle spacings are as follows: (a) Under the background of Gaussian white noise, the estimation performance changes with the incident angle spacing when the SNR is 0dB; (b) Under the background of colored noise, the estimation performance changes with the incident angle spacing when the SNR is 0dB and α is 0.3;

[0050] Fig.13 The experimental condition diagram is as follows: (a) experimental situation diagram; (b) receiving array; (c) true position of the sound source ship; (d) distance between the sound source ship and the receiving ship; (e) sound speed profile diagram;

[0051] Fig.14 Background noise analysis diagram, (a) time-frequency spectrum of background noise; (b) normalized covariance matrix eigenvalue;

[0052] Fig.15 Comparison chart of the estimated number of sources of each method and the actual number of sources, (a) OMP-SSM method; (b) ISSM method; (c) ISSR method; (d) LS-MDL method; (e) NE-AIC method; (f) ADL-LS method;

[0053] Fig.16 The results of the 41st second lake test data analysis are as follows: (a) Normalized covariance matrix eigenvalues; (b) The distance between the subspace generated by the first k support vectors of OMP and the first k eigenvectors of the covariance matrix and the signal subspace; (c) Subspace matching results of ISSM and OMP-SSM. DETAILED DESCRIPTION

[0054] Specific implementation method 1: The specific process of the method for estimating the number of signal sources based on orthogonal matching pursuit and signal subspace matching in this implementation method is as follows:

[0055] Step 1: Obtain an M×L dimensional matrix X=[X(1),X(2),...,X(t),...,X(L)] consisting of L snapshots collected by the array;

[0056] Wherein, t = 1, 2, ..., ..., L; M represents the number of array elements; X(1) represents the snapshot data collected by the array at time 1, X(2) represents the snapshot data collected by the array at time 2, X(t) represents the snapshot data collected by the array at time t, and X(L) represents the snapshot data collected by the array at time L;

[0057] Step 2: Set the total number of iterations to M-1;

[0058] Step 3: Initialize the number of iterations i = 0; Initialize r 0,t =X(t), t=1,...,L; Initialization

[0059] Among them, r 0,trepresents the residual error of the t-th snapshot data collected by the array at the 0th iteration, Λ 0 represents the set of support vector indices obtained in the first 0 iterations, represents the empty set;

[0060] Step 4: Set the number of iterations i = i + 1;

[0061] Step 5: Complete the dictionary Each a(θ v ) and the residuals of all snapshot data are inner-producted, and the absolute values ​​of all inner-products are summed, and then the a(θ v ) as the support vector obtained in the i-th iteration where β i For the selected a(θ v ) index; v = 1, 2, ..., J; J represents the total number of observable angles; column vector a(θ v ) is the steering vector of the vth far-field narrowband source;

[0062] Step 6: Support vector obtained based on the i-th iteration The corresponding index β i The set of indices Λ corresponding to the support vectors obtained in the previous i-1 iterations i-1 , obtain the set of indices Λ corresponding to the support vectors obtained in the previous i iterations i ;

[0063] The set Λ of indices corresponding to the support vectors obtained in the previous i iterations i , get the matrix composed of the support vectors obtained in the previous i iterations

[0064] Step 7: Calculate the residual r of the i-1th iteration i-1 The covariance matrix of the residual at the i-1th iteration is obtained, and the eigenvector matrix U corresponding to the residual is obtained. i-1 ; r i-1 =[r i-1,1 ,r i-1,2 ,...,r i-1,t ,...,r i-1,L ];

[0065] Step 8: Matrix composed of support vectors obtained from the previous i iterations and the eigenvector matrix U i-1 , the signal subspace matching criterion is used to calculate the distance between the i-th iteration subspaces

[0066] Among them, (U i-1 ) 1 Denotes the eigenvector matrix U i-1The first column (the first column is U i-1 The eigenvector corresponding to the largest eigenvalue in );

[0067] Represented by the matrix The subspace generated by the column vectors of

[0068] Represented by the matrix The column vector and eigenvector (U i-1 ) 1 The subspace generated by the column vectors of

[0069] <·> represents the subspace generated by the column vectors of the matrix in brackets;

[0070] represents the i-th iteration subspace and subspace The distance between

[0071] SSM i Represents the distance between subspaces calculated at the i-th iteration;

[0072] Step 9: Order

[0073] Among them, B i Represents the matrix composed of support vectors obtained in the previous i iterations;

[0074] Solve for z using least squares i,t =argmin z ||X(t)-B i z|| 2 ,t=1,...,L;

[0075] X(1) corresponds to z i,1 ; X(2) corresponds to z i,2 ; X(L) corresponds to z i,L ;

[0076] Where z represents the coefficient vector obtained by least squares optimization, z = z i,1 ,z i,2 ,…,z i,t ,…,z i,L ;z i,t Indicates B i The coefficient vector of ;

[0077] Step 10: Based on the t-th snapshot data X(t), B collected by the array i and z i,t , calculate the residual r of the i-th iteration i,t ;

[0078] Step 11: Determine whether i <M-1;

[0079] If yes, repeat steps 4 to 11 until i=M-1;

[0080] If not, output the source estimation result

[0081] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the specific process of step 1 is as follows:

[0082] Assume that K far-field narrowband signal sources are incident on an M-element uniform linear array, and the incident direction θ is the angle between the signal direction and the array normal direction;

[0083] Let X = [X(1), X(2), ..., X(t), ..., X(L)] be an M × L dimensional matrix consisting of L snapshots collected by the array, X(1) represents the snapshot data collected by the array at time 1, X(2) represents the snapshot data collected by the array at time 2, X(t) represents the snapshot data collected by the array at time t, and X(L) represents the snapshot data collected by the array at time L;

[0084] Let S = [S(1), S(2), ..., S(t), ..., S(L)] be a K × L dimensional matrix of information sources in L snapshots, S(1) represents a vector of K information source amplitudes at time 1, S(2) represents a vector of K information source amplitudes at time 2, S(t) represents a vector of K information source amplitudes at time t, and S(L) represents a vector of K information source amplitudes at time L;

[0085] Let N = [N(1), N(2), ..., N(t), ..., N(L)] be an M × L dimensional matrix composed of the noise in L snapshots, N(1) represents a vector composed of the noise amplitudes of M array elements at time 1, N(2) represents a vector composed of the noise amplitudes of M array elements at time 2, N(t) represents a vector composed of the noise amplitudes of M array elements at time t, and N(L) represents a vector composed of the noise amplitudes of M array elements at time L;

[0086] The array observation model is expressed as

[0087] X=AS+N (1)

[0088] A=[a(θ 1 ),a(θ 2 ),...,a(θ k ),...,a(θ K )] (2)

[0089]

[0090] Among them, A is the array manifold matrix, and the column vector a(θ 1 ) is the steering vector of the first far-field narrowband source, and the column vector a(θ 2 ) is the steering vector of the second far-field narrowband source, and the column vector a(θ k ) is the steering vector of the kth far-field narrowband source, and the column vector a(θ K ) is the steering vector of the Kth far-field narrowband source;

[0091] λ represents the signal wavelength, d represents the array element spacing, represents the intermediate variable, θ k represents the angle between the kth far-field narrowband source direction and the array normal direction, j represents the imaginary unit, j 2 =-1; the superscript T means transposition;

[0092] In order to sparsely represent the array signal model, an overcomplete dictionary of array manifold matrix is ​​introduced.

[0093]

[0094] Among them, J represents the total number of observable angles, which is much larger than the actual number of signal sources K;

[0095] Column vector a(θ v ) is the steering vector of the vth far-field narrowband source, and the column vector a(θ J ) is the steering vector of the Jth far-field narrowband source;

[0096] {θ 1 ,θ 2 ,...,θ J} represents the set of observable angles of the linear array, which is obtained by quantizing the far field space [-90°, 90°] at certain angle intervals;

[0097] The source of L snapshots is represented by a J×L matrix The J-dimensional column vector corresponding to each snapshot has only K non-zero elements, corresponding to the set {θ 1 ,θ 2 ,...,θ v ,...,θ J} are the K angular positions {θ 1 ,θ 2 ,...,θ k ,...,θ K};

[0098] Represents the vector composed of the amplitudes of all incident signal sources within the observable angle at time 1, Represents the vector composed of the amplitudes of all incident signal sources within the observable angle at time 2, Represents the vector composed of the amplitudes of all incident signal sources within the observable angle at time L;

[0099] In {θ 1 ,θ 2 ,...,θ k ,...,θ K} corresponding column vector a(θ v ) are called the support vectors of X;

[0100] The sparse representation of the array signal model is

[0101]

[0102] The other steps and parameters are the same as those in the first embodiment.

[0103] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that the specific process of step five is as follows:

[0104] Among them, β i represents the support vector obtained at the i-th iteration The corresponding index;

[0105] a(θ v ) represents the steering vector of the vth far-field narrowband source, v = 1, 2, …, J;

[0106] θ v represents the angle between the direction of the v-th far-field narrowband source and the array normal direction, v represents the v-th;

[0107] The superscript H indicates that conjugation is sought;

[0108] r i-1 represents the residual obtained from the i-1th iteration, r i-1 =[r i-1,1 ,r i-1,2 ,...,r i-1,t ,...,r i-1,L ],r i-1,1 Represents r i-1 The residual corresponding to X(1) in r i-1,2 Represents r i-1 The residual corresponding to X(2) in r i-1,t Represents r i-1 The residual corresponding to X(t), r i-1,L Represents r i-1 The corresponding residual of X(L).

[0109] The other steps and parameters are the same as those in the first or second embodiment.

[0110] Specific implementation method 4: This implementation method is different from the specific implementation methods 1 to 3 in that the specific process of step 6 is as follows:

[0111] 1) Support vector obtained based on the i-th iteration The corresponding index β i The set of indices Λ corresponding to the support vectors obtained in the previous i-1 iterations i-1 , obtain the set of indices Λ corresponding to the support vectors obtained in the previous i iterations i ; expressed as:

[0112] Λ i =Λ i-1 ∪β i

[0113] Λ i-1 =[β 1 ,β 2 ,...,β i-1 ],Λ i =[β 1 ,β 2 ,...,β i ];

[0114] Among them, β 1 represents the index corresponding to the support vector obtained in the first iteration, β 2 represents the index corresponding to the support vector obtained in the second iteration, β i-1 represents the index corresponding to the support vector obtained in the i-1th iteration, β i Represents the index corresponding to the support vector obtained in the i-th iteration;

[0115] 2) The index set Λ corresponding to the support vector obtained based on the previous i iterations i , get the matrix composed of the support vectors obtained in the previous i iterations

[0116]

[0117] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0118] Specific implementation method 5: This implementation method is different from specific implementation methods 1 to 4 in that the specific process of step 8 is as follows:

[0119] 1) Calculation subspace The projection matrix

[0120] 2) Calculate subspace The projection matrix

[0121] 3) Calculate the projection matrix and the projection matrix The difference between the two, the norm of the difference is obtained to obtain the subspace and The distance between

[0122] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0123] Specific implementation method 6: This implementation method is different from any one of the specific implementation methods 1 to 5 in that the subspace is calculated in 1) The projection matrix It is expressed as:

[0124]

[0125] The other steps and parameters are the same as those in Specific Implementations 1 to 5.

[0126] Specific implementation method 7: This implementation method is different from any one of the specific implementation methods 1 to 6 in that the subspace is calculated in 2). The projection matrix It is expressed as:

[0127]

[0128] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0129] Specific implementation eight: This implementation differs from any one of the specific implementations one to seven in that the projection matrix is ​​calculated in 3). and the projection matrix The difference between the two, the norm of the difference is obtained to obtain the subspace and The distance between It is expressed as:

[0130]

[0131] Where <·> represents the subspace generated by the column vectors of the matrix in brackets; Represents the square of the Frobenius norm.

[0132] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0133] Specific implementation method 9: This implementation method is different from any one of the specific implementation methods 1 to 8 in that in step 10, the t-th snapshot data X(t) and B collected based on the array are i and zi,t , calculate the residual r of the i-th iteration i,t ;

[0134] r i,t =X(t)-B i z i,t ,t=1,...,L.

[0135] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0136] 2. Derivation of OMP-SSM method and related theoretical introduction:

[0137] 2.1 Signal subspace matching criteria

[0138] The key to using the signal subspace matching criterion to estimate the number of signal sources is to construct two groups of vectors, where the first K vectors are signal feature vectors and the rest are noise feature vectors, and the signal feature vectors in the two groups are required to be different. When both groups select the first i vectors to generate subspaces, the subspaces generated by the two groups are equal only when i=K, that is, both are signal subspaces.

[0139] Next, the signal subspace matching criterion is further introduced through the ISSM method. The uniform linear array of M array elements is divided into two sub-arrays, which are composed of array elements with serial numbers 1:MI and I+1:M, respectively, where 1≤I≤M-1, Figure 2 The sub-array division method is shown when I = 1 and I = 2. According to the rotation invariance of the array, we know

[20] , when the noise is 0, the covariance matrix signal eigenvectors of the two subarrays can generate the same signal subspace. The ISSM method uses the covariance matrix eigenvectors of the two subarrays to match the signal subspace and estimate the number of signal sources. In order to improve the robustness of the method, the literature

[19] uses the two groups of subarrays obtained when I is 1 and 2 for matching, which is referred to as the multiple ISSM method.

[0140] When I = 1, the subarray element numbers are 1:M-1 and 2:M. The calculation process is as follows Figure 3 First, the covariance matrix of the two subarrays is estimated using the snapshot data, and the eigenvalues ​​are decomposed to obtain the eigenvectors, which are denoted as U = [u 1 ,u 2 ,...,u M-1 ] and V = [v 1 ,v 2 ,...,v M-1. It satisfies that the first K vectors are signal feature vectors and the last M - K - 1 vectors are noise feature vectors. Then, the first i eigenvectors are selected from U and V to generate a subspace, where i ∈ {1, 2,..., M - 1}. Finally, the distance between subspaces is calculated using the subspace matching criterion. When the distance is minimized, the corresponding i is the estimated number of signal sources. To characterize the distance between subspaces, first calculate the projection matrix of the subspace generated by the first i eigenvectors

[0141] P(U 1:i ) = U 1:i (U 1:i H U 1:i ) -1 U 1:i H , (7)

[0142] P(V 1:i ) = V 1:i (V 1:i H V 1:i ) -1 V 1:i H , (8)

[0143] U 1:i and V 1:i are matrices composed of the first i column vectors of U and V respectively. Then calculate the difference between the projection matrices of the two subspaces and find its Frobenius norm

[0144]

[0145] where, "<·>" represents the subspace generated by the column vectors of the matrix in the parentheses. The value of this norm characterizes the distance between the subspaces generated by U 1:i and V 1:i .

[0146] When i takes different values, the distance between <U 1:i > and <V 1:i > is analyzed as follows:

[0147] (1) When i = K, <U 1:i > and <V 1:i > are generated by all the estimated signal feature vectors. At this time, the distance between subspaces only depends on the estimation accuracy of the signal feature vectors. If the signal feature vectors can be accurately estimated, then the distance is 0.

[0148] (2) When i < K, <U 1:i > and <V 1:i>Generated by partially estimated signal eigenvectors. Since U and V are obtained through different subarrays, the subspaces generated by some signal eigenvectors will not be equal. If the signal eigenvectors can be accurately estimated, then 1:i > and <V 1:i > will be greater than when i=K. It is worth noting that the eigenvectors corresponding to the largest eigenvalues ​​in the two sets of eigenvectors have a high similarity, and after being interfered by noise, it is easy for the distance between the subspaces to be smaller than i=K when i=1. This is because when i=1, only one estimated signal eigenvector is selected to generate the subspace, and the noise interference is smaller than when i=K. At the same time, since the two vectors are similar, the distance between the generated subspaces is also small, so this phenomenon is easy to occur.

[0149] (3) When i>K, 1:i > and <V 1:i >The signal eigenvector U estimated by all 1:K and V 1:K , and the noise feature vector U K+1:i and V K+1:i Generate. K+1:i and V K+1:i It is random, so when the signal feature vector can be accurately estimated,

[0150] 1:i > and <V 1:i > will be greater than the case where i = K. When i is slightly larger than K, fewer noise feature vectors are selected.

[0151] K+1:i > and <V K+1:i >The similarity is low, so add U 1:K and V 1:K back, 1:i > and <V 1:i >The distance between them increases with the increase of i and reaches the maximum when it reaches a certain value. i and v i are all M-1 dimensional feature vectors. When i approaches M-1 and continues to increase, 1:i > and <V 1:i >Gradually approaching the same M-1 dimensional linear space, so that the similarity between the two gradually increases. When i = M-1, 1:i > and <V 1:i > is the same M-1 dimensional linear space, and the distance between them is 0. This also shows that the maximum number of sources that this method can detect in theory is M-2.

[0152] ​​​​​​​When I = 2, the subarray element numbers are 1:M-2 and 3:M, and the calculation and analysis process is similar to the above case of I = 1. At this time, the maximum number of estimated information sources is reduced to M-3. The multiple ISSM method adds the calculation results of equation (9) when I = 1 and I = 2, and takes the iteration number i corresponding to the minimum value after the addition as the estimation result of the number of information sources.

[0153] Currently, many signal source estimation methods have high requirements on the number of snapshots. [4-10] and sensitive to color noise [12-15] According to the above analysis, when using the signal subspace matching criterion to estimate the number of signal sources, it is not assumed that the noise model is Gaussian white noise. When the degree of colored noise is not very high and has little impact on the performance of signal feature vector estimation, the signal subspace matching criterion can still maintain good estimation performance. In addition, this criterion is based on the idea of ​​matching for estimation, and its requirement for the number of snapshots is relatively low. [18-19] Existing methods for estimating the number of signal sources using signal feature vector matching [18-19,21] , both obtain eigenvectors through eigendecomposition of the covariance matrix. However, to obtain a more accurate covariance matrix through estimation, there are still high requirements for the signal-to-noise ratio and the number of snapshots. Moreover, when there is a coherent source, the eigenvector estimation of the above method will fail. Therefore, it is necessary to adopt an eigenvector estimation method that has low requirements for the signal-to-noise ratio under small snapshot conditions and is suitable for coherent sources. Then, based on this method, two groups of eigenvectors for matching are constructed, and it is required that when i=1, the similarity of the two eigenvectors used for matching is low. Finally, the number of sources is estimated by the signal subspace matching criterion.

[0154] 2.2 Orthogonal Matching Pursuit Method

[0155] OMP is a greedy sparse recovery method. When the number of information sources K is known, it can be used to recover the snapshot data X and the overcomplete dictionary. The steering vector corresponding to the signal source is iteratively obtained. The standard OMP method is only applicable to the sparse recovery of a single snapshot. When the data is multiple snapshots, the array signal model satisfies the multiple measurement vector model in the compressed sensing theory, and the OMP method can be expanded to achieve joint sparse recovery of multiple snapshot data.

[24] .

[0156] 2.2.1 OMP method calculation process

[0157] The calculation process of the OMP method is shown in Table 1. i represents the support vector index obtained in the i-th iteration; Λ i represents the set of the first i support vector indices, Λ i ∈{β 1 ,β 2 ,...,β i}; is the matrix composed of the first i support vectors; r i,t Remove X(t) The residual after the correlation part, r i =[r i,1 ,r i,2 ,...,r i,L After initialization, in step (b), the overcomplete dictionary Each atom in the inner product is made with all snapshot residuals, and the absolute values ​​of all snapshot inner products are summed up, and then the atom corresponding to the maximum sum is selected as the support vector obtained in this iteration. In steps (c) to (e), the support vector obtained in the current iteration is included in The residual is updated by solving the least squares problem. This iterative process is repeated until K support vectors are selected, which correspond to the estimated steering vectors of the K sources.

[0158] Table 1 Calculation steps of orthogonal matching pursuit method

[0159]

[0160] If the number of sources K is known, the azimuth estimation can be achieved through the OMP method, and the angle corresponding to the estimated steering vector is the incident angle of the source. When the number of sources is unknown, if the number of iterations exceeds the number of sources K, the support vector obtained will be determined by the residual dominated by noise. If the noise energy is large, the amplitude of its corresponding support vector may be close to the support vector corresponding to the source, which is easy to cause misjudgment.

[0161] The focus of the present invention is not to use the OMP method to perform azimuth estimation, but to generate two subspaces using the support vector estimated by the OMP method and the eigenvector corresponding to its residual maximum eigenvalue, and to achieve information source number estimation through the SSM criterion.

[0162] 2.2.2 Performance comparison between OMP and feature decomposition methods under short snapshot conditions

[0163] The following further analysis shows that under the condition of small snapshots, the error of estimating support vectors using OMP is smaller than that of estimating eigenvectors using the covariance matrix. To simplify the analysis, assume that when solving the support vectors in the i-th iteration of OMP, the residual r i-1 It only contains noise N and support vectors When the signal model is single snapshot

[0164]

[0165] In step (b), each atom is i-1 Perform inner product to select support vectors. When the atom is The corresponding inner product result is the largest when

[0166]

[0168] In formula (11) When the array element noise is independent Gaussian white noise, because Modulo 1, we get

[0169] It can be seen that the variance σ of the noise part 2 / M decreases with the increase of the number of array elements. Therefore, even if the support vector is estimated under the condition of a single snapshot, the influence of the noise will be weakened as the number of array elements increases. When the array element noise is colored noise, the noise intensity of each array element is not equal and may be correlated. At this time, the corresponding is no longer independent and identically distributed. But when the degree of color is not very high, The variance of can still decrease with the increase of the number of array elements. In the case of multiple snapshots, the above inner product operation is performed on each snapshot, and the results are summed, and then the support vector is selected based on the summation result. The influence caused by the large error of individual snapshot data when selecting the support vector can be reduced, thereby improving the estimation performance.

[0170] Array covariance matrix is ​​R X =E(X(t)X(t) H ), when using snapshot data for estimation, it approximates the statistical average by calculating the time average

[0171]

[0172] According to the literature

[26] , The estimated error of follows the following multivariate complex Gaussian distribution

[0173]

[0174] in, "vec" means converting a matrix into a vector; It means to calculate the Kronecker product of two matrices. It can be seen that the variance of the covariance matrix estimation error increases as the number of snapshots L decreases. Therefore, under the condition of small snapshots, using The eigenvector error obtained by eigendecomposition is large.

[0175] 2.2.3 Performance comparison between OMP and eigendecomposition methods in the presence of coherent sources

[0176] There are K information sources S(t)=[s 1 (t),s2 (t),...,s K (t)] T ,A=[a(θ 1 ),a(θ 2 ),...,a(θ K )], from formula (1) we can know

[0177] X(t)=AS(t)+N(t)(14)

[0178] Assumptions 1 (t) and s 2 (t) is coherent, then s 2 (t) = γs 1 (t), γ is a constant. Let Available

[0179]

[0180] According to the literature

[27] , if the covariance matrix is ​​used for eigendecomposition, the steering vector a(θ 1 ) and a(θ 2 ) will be merged into a(θ 1 )+γa(θ 2 ), so the estimation result of the source number estimation method based on the eigendecomposition of the covariance matrix is ​​K-1.

[0181] When there is a coherent source, assuming that the residual r of the OMP method at the i-1th iteration is i-1,t for

[0182] r i-1,t =s 1 (t)a(θ 1 )+γs 1 (t)a(θ 2 )+C (16)

[0183] Where C represents the product of noise and incoherent signal sources and their corresponding steering vectors. The inner product operation of the OMP method in step (b) when solving the support vector in Table 1 is:

[0184]

[0185] Among them, when the vector performs the inner product operation, s 2 (t) = γs 1 (t) and s 1 (t) as a scalar only plays the role of scaling the result. Therefore, when there is a coherent signal source, it does not affect the OMP method to solve the support vector using the inner product.

[0186] 2.3 Estimation of the number of sources using orthogonal matching pursuit and signal subspace matching

[0187] 2.3.1 Theoretical derivation

[0188] Table 2 Calculation steps of OMP-SSM method

[0189]

[0190] According to the analysis in Section 2.2, compared with the eigendecomposition method, the OMP method has a higher estimation accuracy for the steering vector under small snapshot conditions and is insensitive to colored noise and coherent sources. At the same time, when estimating the support vector, the OMP method first obtains the source steering vector and then obtains the noise eigenvector, which meets the requirements for signal subspace matching in Section 2.1. Therefore, the present invention uses the OMP method and the signal subspace matching criterion to achieve source number estimation. In order to minimize the use of covariance matrix eigenvectors and make the method applicable to coherent sources, in the i-th iteration, one subspace used for matching is generated by the first i support vectors of the OMP method, and the other subspace is generated by the first i-1 support vectors and the eigenvector corresponding to the maximum eigenvalue of its residual.

[0191] The calculation process of the OMP-SSM method is shown in Table 2. In steps (a) to (c), the calculation process of the OMP-SSM method is the same as that of the OMP method, and both find the support vectors through the inner product. And get the matrix composed of support vectors In step (d), calculate the residual r i-1 The covariance matrix of i-1 Next, step (e) uses the SSM criterion in equation (9) to calculate and The distance of the generated subspace, where (U i-1 ) 1 Denotes the eigenvector matrix U i-1 The first column (the first column is U i-1 The eigenvector corresponding to the maximum eigenvalue in (f) and (g) is updated by solving the least squares problem. Finally, the number of iterations corresponding to the minimum subspace distance is selected as the estimated value of the number of sources.

[0192] The calculation process of the i-th iteration is as follows Figure 4 For the convenience of the following discussion, it is assumed that the source incident angle interval is large and the correlation between the steering vectors is small, so that the OMP method can obtain the correct sparse recovery results under noise-free conditions.

[0193] (1) When i = K, Figure 4 In for contains exactly all estimated steering vectors. i-1 For r K-1 ,express exist Since the correlation between the steering vectors is small, the residual r K-1 Still keep Most of the information, therefore (U K-1 ) 1 for The normalized vector of the main component. and The distance is mainly affected by noise. When the noise intensity is close to 0, (U K-1 ) 1 Very close Make and The distance is close to 0.

[0194] (2) When i>K, assuming i=K+1, then Figure 4 In for It contains the noise support vector r i-1 For r K , indicating that the noise is The residual of the projection on K ) 1 It is also a noise vector. Since the noise vector is highly random, and The distance is greater than and distance.

[0195] (3) When i<K, assuming i=K-1, then Figure 4 In for It does not include all estimated steering vectors. i-1 For r K-2 ,express and exist Similarly, due to the small correlation between the steering vectors, the residual r K-2 Still retain and But at this time (U K-2 ) 1 no or The normalized vector of the main component, so and The distance is greater than and It is worth noting that when i = 1, the two subspaces used for matching are and <[(U 0 ) 1 ]>. Among them, represents the first support vector estimated by the OMP method, corresponding to the steering vector of a certain source; (U 0 ) 1 represents the eigenvector corresponding to the maximum eigenvalue obtained by eigendecomposition of the covariance matrix. At this time, the similarity between the two is low, which reduces the probability that the distance between the subspaces when i=1 is greater than when i=K.

[0196] The above discussion does not take the independence of information sources as a prerequisite, so this method is also applicable to the case where there are coherent information sources.

[0197] 2.3.2 Computational complexity analysis

[0198] In the ith iteration of the OMP-SSM method, the computational complexity of the inner product of the residual of a single snapshot and a single atom of the overcomplete dictionary in step (b) is O(M), so the computational complexity of the inner product of L snapshots and J atoms is O(LJM); the computational complexity of the eigendecomposition in step (d) is O(M 3 ); When calculating the subspace distance in step (e), the computational complexity of the projection matrix calculated by formula (7) is O(iM 2 ), the computational complexity of formula (9) to find the norm of two projection matrices is O(M 2 ), so the computational complexity of this step is O(iM 2 ); The computational complexity of updating the single snapshot residual by least squares in steps (f) and (g) is O(iM)

[23] , then the computational complexity of L snapshots is O(iLM).

[0199] Under the condition of small snapshots, the number of snapshots L is close to the number of array elements M, and the dictionary is overcomplete. The total number of atoms J is greater than M. Therefore, the computational complexity of the OMP-SSM method in the i-th iteration is O(LJM). This method performs M-1 iterations in total, and its computational complexity is O(LJM 2 ).

[0200] 2.3.3 Advantages and limitations of the method

[0201] According to the analysis in Section 2.2, under the condition of small snapshots, the OMP method has higher estimation accuracy than the eigendecomposition method. The matching subspace of the OMP-SSM method is mainly generated by the support vectors of the OMP. Therefore, compared with the method that only uses the eigenvectors of the covariance matrix to estimate the number of sources, the OMP-SSM method performs better under the condition of small snapshots. Moreover, under the condition of colored noise, when the degree of color of the noise is not high, the OMP method can still maintain good estimation performance. Finally, this method is also applicable to the case of coherent sources.

[0202] The limitations of the SSM-OMP method mainly come from the inherent limitations of the OMP method itself. As an overcomplete dictionary, when the OMP method is used to estimate the steering vector of the incident signal, the estimation accuracy is not only affected by the noise, but also by the incident angle spacing of the signal source. [28-29] When the source incident angle is close and the aperture is small, the support vectors corresponding to the source will have a high correlation, which may cause the support vectors estimated in step (b) to fail. In addition, when calculating the residual in steps (f) and (g), if the correlation of the steering vectors is large, the residual r is K-1 Only A small amount of information. K-1 ) 1 Will deviate make and Therefore, when there are adjacent incident sources, it is necessary to increase the array aperture to reduce the correlation of the steering vector. [30-31] .

[0203] Example:

[0204] The following simulation analyzes the impact of noise, snapshot number, target source number, coherent source and adjacent source angular spacing on the estimation performance of the OMP-SSM method.

[19] 、ISSR

[21] , NE-AIC

[12] LS-MDL

[13] and ADL-LS

[17] The performance of the two methods was compared. In order to improve the robustness of the estimation results, the multiple ISSM recommended in reference 19 was used to estimate the number of sources when simulating the ISSM method. The simulation used an isotropic uniform linear array with 16 array elements, an array element spacing equal to the half wavelength of the narrowband source, and an azimuth grid spacing of 0.5°. The signal-to-noise ratio (SNR) is defined as 10lg 10 (p / σ n 2 ), where p represents the source power, σ n2 Represents the variance (power) of Gaussian white noise. 1000 Monte Carlo experiments were conducted under each condition, and the estimation performance of each method was characterized by the estimation accuracy, which was defined as the ratio of the number of experiments to the total number of experiments to accurately estimate the number of sources.

[0205] 3.1 Analysis of the impact of noise on the estimation of the number of signal sources:

[0206] Assume that there are four independent sources of narrowband random phase, with incident angles of [-24°, 2°, 10°, 25°], and the number of snapshots is 20. Consider white noise and colored noise respectively. The colored noise model is a strip-shaped colored noise.

[19] , as shown in equations (18) and (19)

[0207]

[0208] Among them, n i (t) represents the white noise of the ith array element, cn m (t) represents the colored noise obtained after the mth array element is affected by the adjacent array elements. The parameter α is used to characterize the degree of color of the noise. When α is 0, cn m (t) becomes white noise.

[0209] 3.1.1 Analysis of the impact of Gaussian white noise on the estimation of the number of signal sources

[0210] Figure 5 It shows how the estimation accuracy of different signal source number estimation methods changes with SNR under the background of Gaussian white noise. Figure 5 It can be observed that when SNR≤-5dB, the estimation accuracy of the OMP-SSM method is better than that of other comparison methods. When SNR≥-4dB, the NE-AIC and LS-MDL methods are slightly better than OMP-SSM. In addition, the overall performance of the OMP-SSM method is significantly better than that of the ISSM and ISSR methods. In particular, when SNR=-3dB, the estimation accuracy of the OMP-SSM method is close to 0.9, while the estimation accuracy of the ISSM and ISSR is less than 0.5.

[0211] Figure 6 The analysis results of a single Monte Carlo experiment when the signal-to-noise ratio is -5dB are shown. Figure 6(a) shows the normalized covariance matrix eigenvalues, which are sorted from large to small. There are 4 incident signal sources in the simulation, so the first 4 eigenvalues ​​correspond to the signal eigenvalues, and the remaining 12 are noise eigenvalues. Theoretically, under the background of Gaussian white noise, the noise eigenvalues ​​should tend to be equal, reflecting the uniformity and unbiasedness of the noise. However, when the number of snapshots is small, the estimation error of the sample covariance is large, resulting in large differences between the noise eigenvalues, deviating from the theoretical flat distribution. Nevertheless, from Figure 6 In (a), it can still be observed that the change of the noise characteristic value is relatively gentle, showing an overall linear decreasing trend.

[0212] Figure 6 (b) shows the subspace generated by the first k support vectors of OMP And the subspace generated by the first k eigenvectors of the covariance matrix <U 1,...,k >, the distance from the signal subspace . It can be observed that since the number of signal sources is 4, when k = 4, and<U 1,...,k However, due to the low signal-to-noise ratio and the small number of snapshots, the eigenvector error estimated by the covariance matrix is ​​large, resulting in a large error when k = 4. 1,...,k > is far from , close to 1. According to the analysis in Section 2.2, the OMP method has a better ability to suppress noise when the number of snapshots is small. Therefore, when k=4, The distance from is small and close to 0.

[0213] Figure 6 (c) shows the distance change between the subspaces used for matching when the number of iterations i is different for the ISSM and OMP-SSM methods. It can be seen that when i = 4, the distance between the subspaces of the OMP-SSM method is the smallest, and the number of sources is successfully estimated. For the ISSM method, according to the analysis in Section 2.1, the similarity of the first eigenvector in the two groups of eigenvectors is high. When the noise intensity is large (SNR = -5dB), the following may occur: Figure 6 The matching result shown in (c) is that the distance between subspaces when i=1 is smaller than that when i=4. In addition, since multiple ISSMs are used to estimate the number of information sources, the maximum number of information sources that can be estimated theoretically is 13. Figure 6 It can also be seen in (c) that when i>4, the distance between the subspaces of the ISSM method shows a trend of increasing first and then decreasing as i increases, which is consistent with the analysis in Section 2.1. Figure 4It can be seen that in the two sets of vectors used by the OMP-SSM method to generate matching subspaces, only the last vector is different, so the distance between subspaces mainly depends on the difference of the last vector. Figure 6 In (c), when i>4, the distance between subspaces of the OMP-SSM method fluctuates greatly.

[0214] 3.1.2 Analysis of the impact of colored noise on the estimation of the number of signal sources

[0215] Figure 7 The paper shows how the estimation accuracy of each source number estimation method changes with α when the SNR is 5dB under the background of colored noise. Figure 7 It can be seen that as α increases, the performance of OMP-SSM and ADL-LS methods is least affected. Among them, the estimation accuracy of the OMP-SSM method remains above 0.9, while the estimation accuracy of the ADL-LS method drops from 0.85 to 0.72. The robustness of the ISSM and LS-MDL methods is poor, and significant jumps occur when α is 0.7 and 0.5, respectively. The NE-AIC and ISSR methods are easily affected by colored noise, and their estimation accuracy is close to 0 when α is 0.5.

[0216] Figure 8 The analysis results of a single Monte Carlo experiment are shown in the background of colored noise, when the SNR is 5dB and α is 0.6. Figure 6 By comparing the noise type (Gaussian white noise becomes colored noise) with the eigenvalue, we can analyze the effect of the change in noise type (Gaussian white noise becomes colored noise) on the eigenvalue, and the effect of the improvement in signal-to-noise ratio (from -5dB to 5dB) on the distance between the subspace generated by the eigenvector of the covariance matrix and the signal subspace. Figure 8 It can be seen from (a) that under the background of colored noise, the noise eigenvalue no longer shows a linear change trend. The first few noise eigenvalues ​​drop rapidly, and the 10th eigenvalue is close to 0. In this case, if the number of signal sources is estimated only by eigenvalues, the rapidly decreasing part of the noise eigenvalue may be mistaken for the signal eigenvalue, resulting in an overestimation of the number of signal sources. Figure 8 In (b), we can see that as the SNR increases from -5dB to 5dB, the interference of noise decreases, which reduces the distance between the signal subspace generated by the covariance matrix and the real signal subspace. In addition, Figure 8 (c) shows that both OMP-SSM and ISSM methods can accurately estimate the number of target sources in the presence of colored noise, verifying their effectiveness in the presence of colored noise.

[0217] 3.2 Analysis of the impact of snapshot number on the estimation of the number of sources

[0218] Assume that there are four independent narrowband random phase signal sources with incident angles of [-24°, 2°, 10°, 25°] respectively. Fig. 9 Medium (a) to Fig. 9 (d) shows the change of estimation accuracy of different signal source number estimation methods with the number of snapshots under Gaussian white noise background when the signal-to-noise ratio is -10dB, 0dB, 5dB and 10dB. Fig. 9 It can be seen in (a) that when the signal-to-noise ratio is -10dB and the number of snapshots is 80, the estimation accuracy of the OMP-SSM method reaches 0.8, while that of the ADL-LS method is 0.6, and that of other methods is less than 0.5. Fig. 9 (b) shows that when the signal-to-noise ratio is 0dB, the probability curve of the OMP-SSM method is relatively stable, and its estimation accuracy can reach 0.8 when the number of snapshots is 7, while other methods are all lower than 0.5. Fig. 9 Figures (c) and (d) in Figure 9 show that when the signal-to-noise ratio is 5dB and 10dB respectively, the OMP-SSM method can achieve an estimation accuracy of 0.9 when the number of snapshots is 5 and 4.

[0219] 3.3 Analysis of the impact of the number of target information sources on the number of information sources estimated

[0220] In order to analyze the impact of the number of target sources on the performance of each method, 15 narrowband random phase independent sources are first constructed with incident angles of [0°, 8°, 15°, 23°, 31°, 40°, 51°, 63°, -8°, -15°, -23°, -31°, -40°, -51°, -63°]. Then, the first k sources are selected from the constructed source group to generate the signal for simulation, k∈{1,2,...,15}, and the number of snapshots is 20. Fig.10 (a) in Figure 10 and (b) in Figure 10 show how the estimation accuracy changes with the number of sources when the signal-to-noise ratio is 0dB under the background of Gaussian white noise. Among them, the α of colored noise is 0.3. It can be seen that the estimation accuracy of the OMP-SSM method always remains above 0.9, and the maximum number of target sources that can be estimated also reaches the theoretical value. In contrast, the estimation accuracy of other methods gradually decreases with the increase in the number of target sources. It is worth noting that according to the analysis in Sections 2.1 and 3.1.1, when the number of iterations i=1 and i=13 of the ISSM method, the distance between the two matching subspaces is small. Therefore, when the number of real sources is 1 and 13, the source estimation accuracy of this method is very high. Fig.10 In (b), due to the addition of colored noise, the performance of NE-AIC, LS-MDL and ISSR methods has declined significantly. The estimation accuracy of the ISSM method has large fluctuations due to its poor robustness. Only the performance of the OMP-SSM and ADL-LS methods remains almost unchanged.

[0221] 3.4 Analysis of the influence of coherent sources on the estimation of the number of sources

[0222] Assume that there are four narrowband signal sources with incident angles of [-24°, 2°, 10°, 25°], and the corresponding signal sources are s 1 、s 2 、s 3 and 4 , the number of snapshots is 20. Among them, s 1 and 4 coherent, and s 1 (s 4 ),s 2 and 3 Independent of each other. Fig.11 Figures (a) and (b) show how the estimation accuracy of different signal source number estimation methods changes with SNR and α under the background of Gaussian white noise and colored noise, respectively. Figure 5 and Figure 7 By comparison, the estimation performance of the OMP-SSM method remains almost unchanged in the presence of coherent sources, while the other methods have failed. This is because when the snapshot data containing coherent sources are eigendecomposed, the eigenvectors and eigenvalues ​​of the coherent sources are merged. Therefore, the eigenvector-based source number estimation methods (such as ISSM and SR-ISSM) and the eigenvalue-based methods (such as LS-MDL, NE-AIC, and ADL-LS) cannot accurately estimate the number of sources in this case.

[0223] 3.5 Analysis of the influence of the incident angle spacing between adjacent sources on the estimation of the number of sources

[0224] Assuming that there are four independent narrowband random phase signal sources, the incident angles are [-24°, 2°, 10°, 10°+Δ], Δ∈{1°, 2°, ..., 15°}, and the number of snapshots is 20, the estimation accuracy of the OMP-SSM and ISSM methods based on signal subspace matching at different incident angle intervals is compared. Fig.12 Figures 12(a) and 12(b) show how the estimation accuracy changes with the incident angle spacing under the conditions of Gaussian white noise and colored noise with an SNR of 0 dB, respectively, where the α of the colored noise is 0.3. Fig.12 As can be seen in (a), the estimation accuracy of the OMP-SSM and ISSM methods reaches 0.8 when the incident angle interval is 6° and 7° respectively. In addition, the curve of the OMP-SSM method changes more smoothly, showing better robustness. Fig.12 It can be observed in (b) that under the condition of colored noise, the estimation accuracy curves of the OMP-SSM and ISSM methods are very close, but the curve of the OMP-SSM method changes more smoothly.

[0225] 4 Lake test data verification

[0226] 4.1 Lake test conditions

[0227] The effectiveness of the method is verified using lake test data. Fig.13 As shown, there are three sound source ships and one receiving ship in the experiment, and the AD sampling rate of the receiving ship is 200kHz. The sound source ships include fixed sound source ship 1, fixed sound source ship 2 and motorized sound source ship. Fixed sound source ships 1 and 2 are dropped into the water about 8m by lead blocks, and the motorized sound source ship is fixedly connected with steel pipes and is about 5m deep in the water. Among them, fixed sound source 1 emits a single-frequency signal of 25kHz per second, fixed sound source 2 emits 14 to 30kHz broadband interference noise for 6 seconds every 6 seconds, and the motorized sound source moves in the direction of the arrow and emits a single-frequency signal of 25kHz per second. Fig.13 (b) shows the regular hexagonal receiving array of the receiving ship, each side of which is a uniform linear array of 16 array elements, with an array element spacing of 0.03 meters. The data of the side with the best reception effect is selected for the estimation of the number of signal sources. Fig.13 (c) shows the changes in the true positions of the three sound source ships over time. Fig.13 (d) shows the distance between each sound source ship and the receiving ship changing with time. Fig.13 (e) is the sound velocity profile of the lake area. When calculating the guidance vector, the sound velocity is set to 1460m / s.

[0228] 4.2 Background noise analysis

[0229] When the sound source is turned off, the collected data of a single array element is taken out, and the background noise spectrum is calculated by short-time Fourier transform. The window length is set to 0.05 seconds, and the result is Fig.14 (a). Fig.14 It can be observed that the power spectral density of background noise at different frequencies is not equal. For example, the power spectral density near 50kHz is significantly larger, which does not conform to the characteristics of white noise.

[0230] In order to further analyze the eigenvalue distribution of the array covariance matrix in the frequency band of interest, the array sampling data is filtered using FIR digital filtering, with an order of 128 and a passband range of 15kHz to 30kHz. After filtering, the data is processed in segments, and FFT is performed with each segment of 0.05 seconds, and the frequency domain amplitude of the 24.5kHz to 25.5kHz frequency band is extracted as the frequency domain snapshot. When performing FFT, the sampling rate is set to 200kHz, so that there are 10,000 sampling points in 0.05 seconds, the spectrum interval is 20Hz, and there are 51 frequency domain snapshots from 24.5kHz to 25.5kHz. Therefore, there are 1020 frequency domain snapshots in 1 second for calculating the covariance matrix, and the eigenvalues ​​obtained are as follows: Fig.14As shown in (b), it can be seen that the downward trend of the noise eigenvalue does not show a slow, linear trend, which is inconsistent with the expected characteristics of the white noise model.

[0231] 4.3 Estimation of the number of information sources

[0232] When the sound source is turned on, the data preprocessing process of the array collection is as in Section 4.2, and the data is filtered and processed in segments. Among them, the sampling rate is 200kHz, the passband range is 15kHz~30kHz, and FFT is performed in each segment of 0.05 seconds, and then the frequency domain amplitude of the 24.5kHz~25.5kHz frequency band is extracted as the frequency domain snapshot. The cumulative 1020 frequency domain snapshots of 1 second constitute 1 frame of data, which is used to estimate the number of signal sources. 80 seconds of data are intercepted for signal source number estimation, and the estimation results of each method are compared with the actual number of signal sources. The results are as follows Fig.15 shown. Fig.15 The “6+” on the middle vertical axis scale indicates that the number of signal sources is ≥6.

[0233] Fig.15 (a) shows the comparison between the estimated number of sources per second by the OMP-SSM method and the actual number of sources. The angle quantization interval of the overcomplete dictionary constructed by the OMP-SSM method is 0.5°. Since the fixed sound source ship 2 does not send signals every second, the actual number of sources will fluctuate periodically between 2 and 3. From the 1st to the 15th second, the number of sources cannot be accurately estimated because the azimuth angles of the mobile sound source ship and the fixed sound source ship 1 are relatively close. When the time reaches 16 seconds, according to Fig.13 As can be seen from (c), at this time, the azimuth angles of the mobile sound source ship and the fixed sound source ship 1 are close to 7 degrees, and the OMP-SSM method can estimate the actual number of signal sources more accurately. It can be seen that the performance of OMP-SSM in the actual environment is mainly limited by the angular spacing (array aperture) of adjacent signal sources, which is consistent with the discussion in Section 2.3.3 and the simulation in Section 3.5. In addition, the fixed sound source ship 2 emits a broadband signal, and only the data in the 24.5kHz to 25.5kHz frequency band is used in this data processing, resulting in the inability to detect 3 signal sources in all time periods when the sound source ship 2 emits signals. Therefore, from Fig.15 It can be seen in (a) that since the 20th second, the OMP-SSM method has under-estimated the first second of each transmission cycle of the sound source ship 2.

[0234] observe Fig.15 From (b) to (f) in Figure 15, it can be found that the remaining signal source number estimation methods are almost all ineffective. In order to further explore the reasons for the failure, the data at the 41st second is selected for in-depth analysis. Figure 6 and Figure 8 , Fig.16 The analysis results at the 41st second are shown. Fig.13 From (c), we can see that there are 3 incident signal sources at the 41st second, so the 4th to 16th eigenvalues ​​correspond to the noise eigenvalues. Fig.16 It can be seen from (a) that the downward trend of these noise eigenvalues ​​does not show a slow, linear trend. In particular, the decline from the 4th to the 5th eigenvalue is significantly greater than the decline of the subsequent eigenvalues, which is inconsistent with the expected characteristics of the Gaussian white noise model. According to the analysis in Section 3.1.2, the eigenvalue-based source number estimation method is likely to lead to an overestimation in this case. Therefore, in Fig.15 It can be observed from (d) to (f) in Figure 15 that the estimated results of LS-MDL, NE-AIC and ADL-LS methods are all greater than the true number of sources. It is worth noting that Figure 7 It is shown that the LS-MDL and ADL-LS methods have a certain ability to resist colored noise, but the estimation is almost ineffective when facing measured data. This is mainly because in the actual environment, after the acoustic signal passes through a complex underwater acoustic channel, the distribution of its noise eigenvalue does not conform to the standard Gaussian white noise or colored noise under simulation conditions. Therefore, the performance of the method that only uses eigenvalues ​​to estimate the number of signal sources decreases, resulting in the failure of the LS-MDL and ADL-LS methods to estimate.

[0235] Depend on Fig.16 From (b), we can see that the distance between the signal subspace generated by the support vector of the OMP method and the true signal subspace is slightly smaller than the distance between the subspace generated by the eigenvector of the covariance matrix and the true signal subspace. However, according to the analysis in Sections 2.1 and 3.1.1, the similarity of the first eigenvector in the two sets of eigenvectors used for matching by the ISSM method is higher, which leads to Fig.16 The matching result shown in (c) is that when the number of iterations i = 1, the distance between subspaces is smaller than the distance when i = K (K is the number of real information sources). Fig.15 As can be seen in (b), the source number estimation result of the ISSM method is almost always 1. Fig.15 The ISSR method in (c) has a small number of array elements and is interfered by colored noise, resulting in almost ineffective estimation.

[0236] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

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Claims

1. A method for estimating the number of signal sources based on orthogonal matching pursuit and signal subspace matching, characterized in that: The specific process of the method is: Step 1: Obtain an M×L dimensional matrix X=[X(1),X(2),...,X(t),...,X(L)] consisting of L snapshots collected by the array; Wherein, t=1,2,…,…,L; M represents the number of array elements; X(1) represents the snapshot data collected by the array at time 1, X(2) represents the snapshot data collected by the array at time 2, X(t) represents the snapshot data collected by the array at time t, and X(L) represents the snapshot data collected by the array at time L; Step 2: Set the total number of iterations to M-1; Step 3: Initialize the number of iterations i = 0; Initialize r 0,t =X(t), t=1,...,L; Initialization ; Among them, r 0,t represents the residual of the t-th snapshot data collected by the array at the 0th iteration, Λ0 represents the set of support vector indexes obtained at the first 0 iterations, represents the empty set; Step 4: Set the number of iterations i = i + 1; Step 5: Complete the dictionary Each a(θ v ) and the residuals of all snapshot data are inner-producted, and the absolute values ​​of all inner-products are summed, and then the a(θ v ) as the support vector obtained in the i-th iteration , where β i For the selected a(θ v ) index; v = 1, 2, ..., J; J represents the total number of observable angles; column vector a(θ v ) is the steering vector of the vth far-field narrowband source; Step 6: Support vector obtained based on the i-th iteration The corresponding index β i The set of indices Λ corresponding to the support vectors obtained in the previous i-1 iterations i-1 , obtain the set of indices Λ corresponding to the support vectors obtained in the previous i iterations i ; The set Λ of indices corresponding to the support vectors obtained in the previous i iterations i , get the matrix composed of the support vectors obtained in the previous i iterations ; Step 7: Calculate the residual r of the i-1th iteration i-1 The covariance matrix of the residual at the i-1th iteration is obtained, and the eigenvector matrix U corresponding to the residual is obtained. i-1 ; Step 8: Matrix composed of support vectors obtained from the previous i iterations and the eigenvector matrix U i-1 , the signal subspace matching criterion is used to calculate the distance between the i-th iteration subspaces ; in, (U i-1 )1 represents the eigenvector matrix U i-1 Column 1; Represented by the matrix The subspace generated by the column vectors of ; Represented by the matrix The column vector and eigenvector (U i-1 )1's column vector generates the subspace, ; <·> represents the subspace generated by the column vectors of the matrix in brackets; represents the i-th iteration subspace and subspace The distance between SSM i Represents the distance between subspaces calculated at the i-th iteration; Step 9: Order ; Among them, B i Represents the matrix composed of support vectors obtained in the previous i iterations; Solve for z using least squares i,t =argmin z ||X(t)-B i z||2,t=1,...,L; Where z represents the coefficient vector obtained by least squares optimization, z = z i,1 ,z i,2 ,…,z i,t ,…,z i,L ; z i,t Indicates B i The coefficient vector of ; Step 10: Based on the t-th snapshot data X(t), B collected by the array i and z i,t , calculate the residual r of the i-th iteration i,t ; Step 11, determine whether i<M-1; If yes, repeat steps 4 to 11 until i=M-1; If not, output the source estimation result .

2. The method for estimating the number of information sources based on orthogonal matching pursuit and signal subspace matching according to claim 1, characterized in that: In the step 1, an M×L dimensional matrix X=[X(1), X(2), ..., X(t), ..., X(L)] consisting of L snapshots collected by the array is obtained; Wherein, t=1,2,…,…,L; M represents the number of linear arrays; X(1) represents the snapshot data collected by the array at time 1, X(2) represents the snapshot data collected by the array at time 2, X(t) represents the snapshot data collected by the array at time t, and X(L) represents the snapshot data collected by the array at time L; The specific process is: Assume that K far-field narrowband signal sources are incident on an M-element uniform linear array, and the incident direction θ is the angle between the signal direction and the array normal direction; Let X = [X(1), X(2), ..., X(t), ..., X(L)] be an M × L dimensional matrix consisting of L snapshots collected by the array, X(1) represents the snapshot data collected by the array at time 1, X(2) represents the snapshot data collected by the array at time 2, X(t) represents the snapshot data collected by the array at time t, and X(L) represents the snapshot data collected by the array at time L; Let S = [S(1), S(2), ..., S(t), ..., S(L)] be a K × L dimensional matrix of information sources in L snapshots, S(1) represents a vector of K information source amplitudes at time 1, S(2) represents a vector of K information source amplitudes at time 2, S(t) represents a vector of K information source amplitudes at time t, and S(L) represents a vector of K information source amplitudes at time L; Let N = [N(1), N(2), ..., N(t), ..., N(L)] be an M × L dimensional matrix composed of the noise in L snapshots, N(1) represents a vector composed of the noise amplitudes of M array elements at time 1, N(2) represents a vector composed of the noise amplitudes of M array elements at time 2, N(t) represents a vector composed of the noise amplitudes of M array elements at time t, and N(L) represents a vector composed of the noise amplitudes of M array elements at time L; The array observation model is expressed as X = AS + N (1) A=[a(θ1),a(θ2),...,a(θ k ),...,a(θ K )] (2) Where A is the array manifold matrix, column vector a(θ1) is the steering vector of the first far-field narrowband source, column vector a(θ2) is the steering vector of the second far-field narrowband source, and column vector a(θ k ) is the steering vector of the kth far-field narrowband source, and the column vector a(θ K ) is the steering vector of the Kth far-field narrowband source; λ represents the signal wavelength, d represents the array element spacing, represents the intermediate variable, θ k represents the angle between the kth far-field narrowband source direction and the array normal direction, j represents the imaginary unit, j 2 =-1; the superscript T means transposition; Introducing an overcomplete dictionary of array manifold matrices ; Among them, J represents the total number of observable angles, which is much larger than the actual number of signal sources K; Column vector a(θ v ) is the steering vector of the vth far-field narrowband source, and the column vector a(θ J ) is the steering vector of the Jth far-field narrowband source; {θ1,θ2,...,θ J } represents the set of observable angles of the linear array; The source of L snapshots is represented by a J×L matrix The J-dimensional column vector corresponding to each snapshot has only K non-zero elements, corresponding to the set {θ1,θ2,...,θ v ,...,θ J } are the K angular positions {θ1,θ2,...,θ k ,...,θ K }; Represents the vector composed of the amplitudes of all incident signal sources within the observable angle at time 1, Represents the vector composed of all incident signal source amplitudes within the observable angle at time 2, Represents the vector composed of the amplitudes of all incident signal sources within the observable angle at time L; In {θ1,θ2,...,θ k ,...,θ K } corresponding column vector a(θ v ) are called the support vectors of X; The sparse representation of the array signal model is 3. The method for estimating the number of information sources based on orthogonal matching pursuit and signal subspace matching according to claim 2, characterized in that: In step 5, the overcomplete dictionary Each a(θ v ) and the residuals of all snapshot data are inner-producted, and the absolute values ​​of all inner-products are summed, and then the a(θ v ) as the support vector obtained in the i-th iteration where β i For the selected a(θ v ) index; v = 1, 2, ..., J; J represents the total number of observable angles; the column vector a(θ) is the steering vector of the vth far-field narrowband source; the specific process is: in, β i represents the support vector obtained at the i-th iteration The corresponding index; a(θ v ) represents the steering vector of the vth far-field narrowband source, v = 1, 2, …, J; θ v represents the angle between the direction of the v-th far-field narrowband source and the array normal direction, v represents the v-th; The superscript H indicates that conjugation is sought; r i-1 represents the residual obtained from the i-1th iteration, r i-1 =[r i-1,1 ,r i-1,2 ,...,r i-1,t ,...,r i-1,L ],r i-1,1 Represents r i-1 The residual corresponding to X(1) in r i-1,2 Represents r i-1 The residual corresponding to X(2) in r i-1,t Represents r i-1 The residual corresponding to X(t), r i-1,L Represents r i-1 The corresponding residual of X(L).

4. The method for estimating the number of information sources based on orthogonal matching pursuit and signal subspace matching according to claim 3, characterized in that: The support vector obtained based on the i-th iteration in step 6 The corresponding index β i The set of indices Λ corresponding to the support vectors obtained in the previous i-1 iterations i-1 , obtain the set of indices Λ corresponding to the support vectors obtained in the previous i iterations i ; The set Λ of indices corresponding to the support vectors obtained in the previous i iterations i , get the matrix composed of the support vectors obtained in the previous i iterations The specific process is: 1) Support vector obtained based on the i-th iteration The corresponding index β i The set of indices Λ corresponding to the support vectors obtained in the previous i-1 iterations i-1 , obtain the set of indices Λ corresponding to the support vectors obtained in the previous i iterations i ; expressed as: L i =L i-1 ∪β i L i-1 =[β1,β2,...,β i-1 ],L i =[β1,β2,...,β i ]; in, β1 represents the index corresponding to the support vector obtained in the first iteration, β2 represents the index corresponding to the support vector obtained in the second iteration, and β i-1 represents the index corresponding to the support vector obtained in the i-1th iteration, β i Represents the index corresponding to the support vector obtained in the i-th iteration; 2) The index set Λ corresponding to the support vector obtained based on the previous i iterations i , get the matrix composed of the support vectors obtained in the previous i iterations ; 5. The method for estimating the number of information sources based on orthogonal matching pursuit and signal subspace matching according to claim 4, characterized in that: The matrix composed of the support vectors obtained in the previous i iterations in step eight and the eigenvector matrix U i-1 , the signal subspace matching criterion is used to calculate the distance between the i-th iteration subspaces in, (U i-1 )1 represents the eigenvector matrix U i-1 Column 1; Represented by the matrix The subspace generated by the column vectors of Represented by the matrix The column vector and eigenvector (U i-1 )1's column vector generates the subspace, <·> represents the subspace generated by the column vectors of the matrix in brackets; represents the i-th iteration subspace and subspace The distance between SSM i Represents the distance between subspaces calculated at the i-th iteration; The specific process is: 1) Calculation subspace The projection matrix 2) Calculate subspace The projection matrix 3) Calculate the projection matrix and the projection matrix The difference between the two, the norm of the difference is obtained to obtain the subspace and The distance between 6. The method for estimating the number of information sources based on orthogonal matching pursuit and signal subspace matching according to claim 5, characterized in that: The subspace is calculated in 1) The projection matrix It is expressed as:

7. The method for estimating the number of information sources based on orthogonal matching pursuit and signal subspace matching according to claim 6, characterized in that: The subspace is calculated in 2) The projection matrix It is expressed as:

8. The method for estimating the number of information sources based on orthogonal matching pursuit and signal subspace matching according to claim 7, characterized in that: The projection matrix is ​​calculated in 3) and the projection matrix The difference between the two, the norm of the difference is obtained to obtain the subspace and The distance between It is expressed as: Where <·> represents the subspace generated by the column vectors of the matrix in brackets; Represents the square of the Frobenius norm.

9. The method for estimating the number of information sources based on orthogonal matching pursuit and signal subspace matching according to claim 8, characterized in that: In step 10, the t-th snapshot data X(t), B collected based on the array i and z i,t , calculate the residual r of the i-th iteration i,t ; r i,t =X(t)-B i z i,t ,t=1,...,L。

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