A target direction estimation algorithm based on covariance matrix imaginary part reconstruction

Abstract

The application aims at the problem that underwater environment is complex and weak signal is difficult to detect, and proposes a target direction estimation algorithm based on imaginary part reconstruction of covariance matrix. The algorithm includes calculating the covariance matrix according to the array receiving data; extracting the imaginary part of the covariance matrix, and reconstructing a new covariance matrix according to the eigenvalue and the corresponding eigenvector; initializing the variable factor and the noise power estimation value; calculating the spatial direction spectrum and the initial value of its sparsity; based on the sparse approximate minimum variance principle, iteratively calculating the spatial direction spectrum until convergence; normalizing the iterative spatial direction spectrum, and the angles corresponding to the first K maximum values are the target direction estimation values, wherein K is the real number of target signals. The application reconstructs the covariance matrix by extracting the imaginary part of the covariance matrix, which weakens the influence of noise on weak signal; on the other hand, by adaptively adjusting the variable factor, the estimation performance of weak signal and the sparsity of direction spectrum are considered, and the resolution ability to weak target is enhanced.

Description

TECHNICAL FIELD

[0001] The application relates to a signal processing method, in particular to a target direction estimation algorithm based on reconstruction of imaginary parts of a covariance matrix. BACKGROUND

[0002] Signal detection technology in a complex background environment is an important research content in the field of signal processing. In engineering applications, under the joint action of internal waves, ocean currents, swells and the like, the underwater background noise environment is very complex, and the signal-to-noise ratio of the signal received by the array is generally not very large. When the interference energy is large, the direction estimation accuracy of the weak target will be affected, and even completely unable to reflect on the spatial direction spectrum.

[0003] In actual working scenarios, the noise received by different array elements is not correlated or has a very small correlation coefficient, and according to the spatial distribution characteristics, the underwater environmental noise source approximately presents the characteristics of statistical symmetry of direction and power, so most components of the noise exist in the real part of the diagonal elements of the covariance matrix of the array received data. Based on this feature of the data covariance matrix, some people have proposed an algorithm of taking zero of the diagonal elements of the data covariance matrix to suppress noise, but this kind of algorithm will cause the loss of signal components in the diagonal elements, and further affect the direction estimation of the target. The basic idea of the diagonal load reduction method is to add a load reduction amount or multiply a load reduction coefficient to the diagonal elements of the data covariance matrix of the array to reduce the diagonal elements, so as to weaken the influence of noise on the signal, but it is difficult to accurately give the load reduction amount or load reduction coefficient in this method.

[0004] Since the noise can be divided into symmetric noise and asymmetric noise, and the symmetric noise only exists in the real part of the diagonal elements of the covariance matrix, theoretically, the influence of the symmetric noise on the array received data can be eliminated by extracting the imaginary part of the covariance matrix. Based on this idea, some researchers have proposed a method of extracting the imaginary part of the covariance matrix and reconstructing the real part thereof by using a particle swarm algorithm to estimate the direction of the target. However, the particle swarm algorithm is sensitive to initial values, and is prone to fall into local optimal solution in the operation process, and the calculation amount of the method increases rapidly with the increase of the number of targets, so there is still room for improvement in the method.

[0005] Therefore, in view of the problem that weak targets are difficult to detect in an underwater complex noise environment, corresponding solutions are urgently needed. SUMMARY

[0006] The present application aims to at least solve one of the technical problems existing in the prior art. To this end, the present application proposes a target direction estimation algorithm based on covariance matrix imaginary part reconstruction, which weakens the interference of symmetric noise on the signal by reconstructing a new covariance matrix. For the problem of weak target detection, the present application makes a compromise between the sparsity of the algorithm and the estimation performance of the weak signal, and through adaptive adjustment of the variable factor, the cancellation of the weak target is avoided on the premise of ensuring the sparsity, to a certain extent, solving the problem that the weak target is difficult to detect in the underwater complex noise environment.

[0007] To achieve the above-mentioned purpose, the present application proposes a target direction estimation algorithm based on covariance matrix imaginary part reconstruction, comprising the following steps:

[0008] S1 calculating the covariance matrix according to the array receiving data;

[0009] S2 taking the imaginary part of the covariance matrix obtained in step S1, performing eigenvalue decomposition, and extracting the non-zero eigenvalues and corresponding eigenvectors thereof;

[0010] S3 reconstructing a new covariance matrix according to the eigenvalues and corresponding eigenvectors obtained in step S2;

[0011] S4 initializing the variable factor and the noise power estimation value;

[0012] S5 calculating the initial value of the spatial direction spectrum and its sparsity;

[0013] S6 iteratively calculating the spatial direction spectrum according to the sparse approximate minimum variance principle until convergence;

[0014] S7 normalizing the iterative spatial direction spectrum to obtain the angles corresponding to the first K maximum values, the angles being the target direction estimation value, wherein K is the true number of target signals.

[0015] Further, the calculation of the covariance matrix is:

[0016] Let the time domain data received by the array be Y, and the number of snapshots be N snap , then the covariance matrix R=Y*Y H / N snap , (·) H is the conjugate transpose operation.

[0017] Further, the extraction of the eigenvalues and corresponding eigenvectors of the imaginary part of the covariance matrix is:

[0018] Take the imaginary part of the covariance matrix R, perform eigenvalue decomposition, and obtain 2K non-zero eigenvalues λ k and corresponding eigenvectors u k .

[0019] Further, the reconstruction of the new covariance matrix comprises the following steps:

[0020] S301 using the eigenvector u k Construct the matrix U=[u1,u2,K,u 2K ] using the eigenvalue λ k Construct the diagonal matrix Λ=diag{[λ1,λ2,K,λ 2K ]} diag{·} returns a diagonal matrix containing the elements in the brackets on the main diagonal or extracts a vector containing the diagonal elements of the matrix in the brackets;

[0021] S303 filter the diagonal elements of the diagonal matrix Λ, set the elements less than zero to zero, and obtain a new diagonal matrix Where max{·} represents the maximum value of the elements in the brackets;

[0022] S305 construct a new covariance matrix, get

[0023] Further, the initialization of the variable factor and the noise power estimate comprises the following steps:

[0024] S401 the variable factor is α0, set the initial value of the variable factor α0 to 1;

[0025] S403 calculate the initial value of the noise power estimate Where trace(·) is the trace of the matrix in the brackets, and M is the total number of array elements.

[0026] Further, the calculation of the initial value of the spatial orientation spectrum and its sparsity comprises the following steps:

[0027] S501 determine the set of scanning angles Θ, the length of Θ is N, for any angle θ i ∈Θ, the expression of the array manifold vector is:

[0028] a(θ i )=[1,e j2πp ,Ke j2π(M-1)p ] T ;

[0029] Where d is the array element spacing, λ is the signal wavelength, j is the imaginary unit, and (·) T is the transpose operation;

[0030] S503 the initial value P0 of the spatial orientation spectrum is expressed as:

[0031]

[0032] where the array manifold matrix A(Θ) = [a(θ1), a(θ2), K, a(θM)], θ N ∈ Θ. i ;

[0033] The initial value β0of the sparsity is expressed as:

[0034] β0= ||P0 / max(P0)||1.

[0035] where ||·||1is the 1-norm of a vector.

[0036] Further, the iteration calculation of the spatial direction spectrum based on the sparse approximation minimum variance principle comprises the following steps:

[0037] S601updating the covariance matrix, the calculation formula of the covariance matrix Pj obtained in the jth iteration is:

[0038]

[0039] where I M is an M × M unit matrix, P j-1 and p n,j-1 are the spatial direction spectrum and noise power estimation value obtained in the (j-1) th iteration;

[0040] S603updating the spatial direction spectrum, the calculation formula of the spatial direction spectrum P j obtained in the jth iteration is:

[0041]

[0042] where (·) -1 is the inverse of the matrix in the parentheses;

[0043] S605updating the noise power estimation value, the calculation formula of the noise power estimation value p n,j obtained in the jth iteration is:

[0044]

[0045] S607updating the sparsity, the calculation formula of the sparsity β j obtained in the jth iteration is:

[0046] β j = ||P j / max(P j )||1.

[0047] S609updating the variable factor, the calculation formula of the variable factor α j obtained in the jth iteration is:

[0048] ​

[0049] wherein abs(·) is an absolute value operation;

[0050] S611 judges the spatial direction spectrum P j whether it converges, a judgment factor Q = abs(β j -β j-1 ) is calculated, when Q≤0.005, the iterative calculation is ended, and the iterative spatial direction spectrum P is obtained.

[0051] Further, the normalization processing of the iterative spatial direction spectrum, namely:

[0052] the calculation formula of the normalized spatial direction spectrum value is:

[0053]

[0054] The angle corresponding to the first K maximum values of the spatial direction spectrum is the target direction estimation value.

[0055] Compared with the prior art, the beneficial effects of the present application are:

[0056] The present application extracts the imaginary part of the covariance matrix, eliminates the real number items of the noise covariance matrix contained in the diagonal elements of the data covariance matrix, thereby weakening the influence of noise on weak signals, and improving the performance of weak target direction estimation in a complex noise environment; on the other hand, by means of adaptive adjustment of the variable factor, the estimation performance of weak signals and the sparsity of the direction spectrum are taken into account, and the resolution capability for weak targets is enhanced. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description, and obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0058] Figure 1 is a flowchart of the present application;

[0059] Figure 2 is a spatial direction spectrum diagram obtained by different algorithms processing the covariance matrix and its imaginary part in the specific embodiment. DETAILED DESCRIPTION

[0060] The technical solutions of the present application will be described clearly and completely below in connection with the embodiments. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present application. Specific embodiment 1

[0062] As Figure 1 shown, according to the embodiments of the present application, the present application proposes a target direction estimation algorithm based on covariance matrix imaginary part reconstruction, and the technical solutions adopted include the following steps:

[0063] Step 1: using an M-element uniform linear array located in the xoy plane as a receiving array, the element spacing is half the wavelength of the signal. Calculate the covariance matrix according to the array receiving data. Let the time domain data received by the array be Y, and the number of snapshots be N snap , then the covariance matrix R=Y*Y H / N snap , (·) H is the conjugate transpose operation.

[0064] Step 2: take the imaginary part of the covariance matrix R in step 1, perform eigenvalue decomposition, and obtain 2K non-zero eigenvalues λ k and corresponding eigenvectors u k .

[0065] Step 3: using the eigenvalues λ k and corresponding eigenvectors u k obtained in step 2, reconstruct a new covariance matrix, and the specific implementation steps are as follows:

[0066] 1) Step 3-1: construct a matrix U=[u1,u2,K,u k ] using the eigenvectors u 2K , and construct a diagonal matrix Λ=diag{[λ1,λ2,K,λ k ]} using the eigenvalues λ 2K , diag{·} is a diagonal matrix that returns the elements in the brackets on the main diagonal or a vector that extracts the diagonal elements of the matrix in the brackets;

[0067] 2) Step 3-2: filter the diagonal elements of the diagonal matrix Λ, and set the elements less than zero to zero to obtain a new diagonal matrix where max{·} represents the maximum value of the elements in the brackets;

[0068] 3) Step 3-3: construct a new covariance matrix

[0069] Step 4: initialize the variable factor, the noise power estimate, the implementation steps are as follows:

[0070] 1) Step 4-1: set the initial value of the variable factor a0 to 1;

[0071] 2) Step 4-2: calculate the initial value of the noise power estimate Where trace(·) is the trace of the matrix in the parentheses, and M is the total number of array elements.

[0072] Step 5: calculate the initial value of the spatial direction spectrum and its sparsity, the implementation steps are as follows:

[0073] 1) Step 5-1: determine the scanning angle set Θ, the length of Θ is N; for any angle θ i ∈ Θ, the expression of the array manifold vector is:

[0074] a(θ i )=[1,e j2πp ,Ke j2π(M-1)p ] T ;

[0075] Where d is the array element spacing, λ is the signal wavelength, j is the imaginary unit, and (·) T is the transpose operation;

[0076] 2) Step 5-2: the initial value P0 of the spatial direction spectrum is expressed as:

[0077]

[0078] Where the array manifold matrix A(Θ)=[a(θ1),a(θ2),K,a(θ N )], θ i ∈ Θ;

[0079] 3) Step 5-3: the initial value β0 of the sparsity is expressed as:

[0080] β0=||P0 / max(P0)||1;

[0081] Where ||·||1 is the 1-norm of the vector.

[0082] Step 6: based on the sparse approximation minimum variance principle, iteratively calculate the spatial direction spectrum until convergence, the implementation steps are as follows:

[0083] 1) Step 6-1: update the covariance matrix, the calculation formula of the covariance matrix obtained in the jth iteration is:

[0084]

[0085] where I M is a MxM identity matrix, P j-1 and p n,j-1 are the spatial direction spectrum and noise power estimation value obtained in the j-1th iteration;

[0086] 2) Step 6-2: update the spatial direction spectrum, the spatial direction spectrum P j obtained in the jth iteration is calculated according to the following formula:

[0087]

[0088] where (·) -1 is the inverse of the matrix in the parentheses;

[0089] 3) Step 6-3: update the noise power estimation value, the noise power estimation value p n,j obtained in the jth iteration is calculated according to the following formula:

[0090]

[0091] 4) Step 6-4: update the sparsity, the sparsity β j obtained in the jth iteration is calculated according to the following formula:

[0092] β j = ||P j / max(P j )||1;

[0093] 5) Step 6-5: update the variable factor, the variable factor α j obtained in the jth iteration is calculated according to the following formula:

[0094]

[0095] where abs(·) is the absolute value operation;

[0096] 6) Step 6-6: judge whether the spatial direction spectrum P j converges, calculate the judgment factor Q = abs(β j - β j-1 ), when Q ≤ 0.005, end the iteration calculation, and obtain the iteration spatial direction spectrum P

[0097] Step 7: normalize the iteration spatial direction spectrum; the calculation formula of the normalized spatial direction spectrum value P is as follows:

[0098]

[0099] The angles corresponding to the first K maximum values of P are the target direction estimation values.

[0100] To further verify the real effect of the technical solution of the present application, the present application further provides a simulation experiment case.

[0101] The simulation experiment uses a 16-element uniform linear array as a receiving array, and the element spacing is half the wavelength of the signal. It is assumed that K=2 far-field narrowband signals are incident on the array, the incident angles are 50° and 120°, the signal frequency is 500 Hz, the sampling frequency is five times the signal frequency, the sampling time is 0.2 seconds, the signal signal-to-noise ratio is -15 dB and 5 dB, and the obtained normalized spatial direction spectrum is shown in Figure 2 .

[0102] From Figure 2 it can be seen that when there are multiple signals with different intensities in the space, the incident direction of the weak signal in the obtained spatial direction spectrum is difficult to identify when the conventional algorithm is used to process the covariance matrix or the imaginary part of the covariance matrix is processed separately. In comparison, the present application successfully estimates the direction of all target signals in the space, and shows strong angle resolution.

[0103] It should be noted that in the above embodiments, the description of each embodiment has its own emphasis, and the parts not described in detail in a certain embodiment can be referred to the related description of other embodiments. Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system or a computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer usable program code.

[0104] The present application is described with reference to flowcharts and / or block diagrams of the method and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded computer, or other programmable data processing devices to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices produce a machine that implements the flowcharts and / or block diagrams. Figure 1 flow or multiple flows and / or blocks Figure 1apparatus for performing each function specified in a flow or flows and / or blocks. These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the flow Figure 1 a flow or flows and / or blocks Figure 1 a flow or flows and / or blocks Figure 1 a flow or flows and / or blocks Figure 1 a flow or flows and / or blocks

[0105] While the preferred embodiments of the application have been described, additional variations and modifications can be made to the embodiments by those skilled in the art once they learn of the basic inventive concepts taught in the description of the preferred embodiments. Such additional variations and modifications have been provided for by this disclosure, which is intended to cover all modifications and variations within the scope and spirit of the present application.

[0106] It will be apparent to those skilled in the art that various modifications and variations can be made to the present application without departing from the spirit or scope of the application. Thus, it is intended that the present application cover modifications and variations of this application provided they come within the scope of the appended claims and their equivalents.

Claims

1. A target orientation estimation algorithm based on reconstruction of the imaginary part of the covariance matrix, characterized in that, Includes the following steps: S1 calculates the covariance matrix based on the underwater target signal data received by the array. ; S2 Take the imaginary part of the covariance matrix obtained in step S1, perform eigenvalue decomposition, and extract its non-zero eigenvalues ​​and corresponding eigenvectors. S3 Reconstructs a new covariance matrix based on the eigenvalues ​​and corresponding eigenvectors obtained in step S2; S4 Initializes the variable factor and noise power estimate; S5 calculates the initial values ​​for the spatial orientation spectrum and its sparsity; S6. Based on the principle of sparse approximation minimum variance, iteratively calculate the spatial orientation spectrum. Until convergence, specifically: S601 Update the covariance matrix, the first... The covariance matrix obtained in the next iteration The calculation formula is: ； in For one The identity matrix, and For the first The spatial orientation spectrum and noise power estimates obtained from the next iteration. For the set of scanning angles, For array manifold matrix, To return a diagonal matrix whose main diagonal contains the elements enclosed in parentheses, This is the conjugate transpose operation; S603 Updates Spatial Orientation Spectrum, Chapter Spatial orientation spectrum obtained in the next iteration The calculation formula is: ； in To calculate the inverse of the matrix within the parentheses; S605 Updates noise power estimates, number... The noise power estimate obtained in the next iteration The calculation formula is: ； S607 updates sparsity, the first Sparsity obtained in the second iteration The calculation formula is: ； S609 Update variable factors, the first The variable factor obtained in the second iteration The calculation formula is: ； in For absolute value operations; S611 Determining Spatial Orientation Spectrum To determine whether the convergence has occurred, calculate the decision factor. ,when The iterative calculation ends when the time is right, and the iterative spatial orientation spectrum is obtained. ; S7 normalizes the iterative spatial orientation spectrum to obtain its previous value. The angles corresponding to the maximum values ​​are the target azimuth estimates, where... It is the actual number of target signals.

2. The target orientation estimation algorithm based on the reconstruction of the imaginary part of the covariance matrix according to claim 1, characterized in that, The calculation of the covariance matrix in step S1 is based on the assumption that the time-domain data received by the array is... The number of quick shots is Then the covariance matrix , This is the conjugate transpose operation.

3. The target orientation estimation algorithm based on the reconstruction of the imaginary part of the covariance matrix according to claim 2, characterized in that, The extraction of the eigenvalues ​​and corresponding eigenvectors of the imaginary part of the covariance matrix involves taking the covariance matrix... The imaginary part is used for eigenvalue decomposition to obtain... non-zero eigenvalues and the corresponding feature vectors .

4. The target orientation estimation algorithm based on the reconstruction of the imaginary part of the covariance matrix according to claim 1, characterized in that, The reconstruction of the new covariance matrix in step S3 includes the following steps: S301 utilizes eigenvectors Constructing a matrix Using eigenvalues Construct a diagonal matrix , To return a diagonal matrix containing the elements within the parentheses on the main diagonal, or to extract a vector containing the diagonal elements of the matrix within the parentheses; S303 Filtering Diagonal Matrix Take the diagonal elements, set the elements less than zero to zero, and obtain a new diagonal matrix. ,in , This indicates that the maximum value of the element within the parentheses is extracted. S305 constructs a new covariance matrix, obtaining .

5. The target orientation estimation algorithm based on the reconstruction of the imaginary part of the covariance matrix according to claim 4, characterized in that, The initialization of the variable factor and the noise power estimate includes the following steps: S401 The variable factor is Set variable factors The initial value is 1; S403 Initial values ​​for calculating noise power estimates ,in To calculate the trace of the matrix within the parentheses, This represents the total number of array elements.

6. The target orientation estimation algorithm based on the reconstruction of the imaginary part of the covariance matrix according to claim 1, characterized in that, The calculation of the initial values ​​of the spatial orientation spectrum and its sparsity in step S5 includes the following steps: S501 determines the set of scanning angles. , The length is For any angle The expression for the array manifold vector is: ； in , For the spacing between array elements, For the signal wavelength, The imaginary unit, This is a transpose operation; S503 Initial values ​​of spatial orientation spectrum The expression is: ； Where the array manifold matrix ; Initial value of S505 sparsity The expression is: ； in To calculate the 1-norm of a vector.

7. The target orientation estimation algorithm based on the reconstruction of the imaginary part of the covariance matrix according to claim 6, characterized in that, The normalization process of the iterative spatial orientation spectrum described in step S7, which normalizes the spatial orientation spectrum values. The calculation formula is: ； The former The angle corresponding to the maximum value is the estimated target azimuth.

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