A DOA estimation method for circular and non-circular mixed signals based on estimation error energy constraint

Abstract

The present invention discloses a method for estimating the DOA of a mixed circular and non-circular signal based on an estimated error energy constraint, comprising: a linear uniform array passively receives electromagnetic waves that are not correlated with each other and are emitted from a far-field source, and obtains a linear uniform array output; the linear uniform array output and its conjugate form an extended array output signal, and an extended covariance matrix is ​​calculated; an estimated error energy constraint condition is introduced, and a non-circular signal DOA estimation function expression based on the estimated error energy constraint is given, and finally the target angle parameter of the non-circular signal is obtained; S5, according to the target angle parameter of the non-circular signal, a new estimated value of the array output covariance matrix based on the circular signal is further obtained, and finally the target angle parameter of the circular signal is obtained. Based on the DOA estimation algorithm based on atomic norm minimization, this method introduces an estimated error energy constraint to achieve mixed signal DOA estimation in the case of few snapshots.

Description

Technical Field

[0001] The invention relates to array signal processing technology, and in particular to a circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint. Background Art

[0002] With the continuous development of modern communication technology, the spectrum resources occupied by traditional radar and communication are becoming increasingly scarce. Therefore, high-frequency bands, especially millimeter-wave band spectrum, will become the key candidate frequency bands for radar and 5 / 6G communication. How to determine the direction of the signal and distinguish whether the signal comes from radar or communication has become a hot issue in array signal processing. Generally, radar transmission signals are mostly circular signals, and communication system transmissions are mostly non-circular signals. Therefore, this problem can be converted into estimating the Direction-of-Arrival (DOA) parameters of mixed circular and non-circular signals.

[0003] At present, relevant scholars and experts have studied the DOA estimation problem of circular and non-circular mixed signals and achieved certain results, such as the method based on atomic norm minimization (see the literature Teng L, Wang Q, Chen H, et al. AtomicNorm-Based DOA Estimation with Sum and Difference Co-arrays in Coexistence ofCircular and Non-circular Signals[J].Circuits Systems and Signal Processing) and the high-resolution MUSIC algorithm (Wan L, Xie L. An Improved DOA Estimation Algorithm forCircular and Non-Circular Signals with High Resolution[C], 2016IEEE International Conference on Acoustics, Speech and Signal Processing). However, these methods have poor estimation effects on non-circular signals in the case of few snapshots, which will in turn interfere with the direction finding accuracy of circular signals in mixed sources. Therefore, it is necessary to improve the accuracy of non-circular signal estimation in the above situation to accurately estimate the angle of mixed signals. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a DOA estimation method for circular and non-circular mixed signals based on estimation error energy constraint. This method introduces estimation error energy constraint on the basis of a DOA estimation algorithm based on atomic norm minimization to achieve mixed signal DOA estimation in the case of few snapshots.

[0005] Technical solution: A circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint of the present invention comprises the following steps:

[0006] S1, a linear uniform array is formed by M array elements with a spacing of d, and the linear uniform array passively receives K=K c +K nc The electromagnetic waves emitted by far-field sources are unrelated to each other, K nc is the number of non-circular information sources, K c is the number of circular sources, so the linear uniform array output x(t)=As(t)+n(t), where A=[A nc A c ] is the array flow type corresponding to all sources, A nc and A c are the array flow patterns of non-circular signals and circular signals respectively, n(t) is the Gaussian non-uniform noise signal, t=1,…,L is the number of snapshots;

[0007] S2, use the linear uniform array output and its conjugate simultaneously to form the extended array output signal y(t), and calculate the extended covariance matrix R y ;

[0008] S3, calculate the array output pseudo covariance matrix based on non-circular signals The estimated value is Then, define the vector z cn Output pseudo-covariance matrix for array After vectorization, remove the redundant vectors and create vector z cn and and R′ nc Then, the estimation error energy constraint is introduced, and the DOA estimation function expression of non-circular signal based on the estimation error energy constraint is given. The function expression is converted into a convex function form, and finally the convex optimization toolkit is used to solve the function and obtain the Toeplitz matrix

[0009] S4. Toeplitz matrix Perform eigenvalue decomposition (EVD): make is the noise subspace, and finally the target angle parameter of the non-circular signal is obtained by spectrum peak search;

[0010] S5. According to the target angle parameter of the non-circular signal estimated in step S4, the non-circular signal array flow pattern A is first obtained by using the formation of the linear uniform array. nc Estimated value of Then, the pseudo-covariance matrix of the non-circular signal is obtained by using the pseudo-inverse operator Estimated value of Then, according to the estimated value of the pseudo-covariance matrix Get an estimate of the covariance matrix of the non-circular signal Finally, the array output covariance matrix R based on the non-circular signal is obtained nc Estimated value of And the covariance matrix R of the noisy array output signal based on the circular signal c Estimated value of Further solving the problem yields a new estimate of the array output covariance matrix based on the circular signal: Finally, the target angle parameters of the circular signal are obtained through spectrum peak search.

[0011] Furthermore, the non-circular information source in step S1 is a maximum non-circular rate information source.

[0012] Furthermore, in step S2, the extended array output signal y(t) is:

[0013]

[0014] Among them, the superscript * It is represented as the conjugate operator;

[0015] Expanded covariance matrix R y for:

[0016]

[0017]

[0018]

[0019]

[0020] in, They are the circular signal covariance matrix, the non-circular signal covariance matrix, and the non-circular signal pseudo-covariance matrix, respectively. are the first circle signal, the Kth circle signal, c The first circular signal, the first non-circular signal, the Kth nc The power of a noncircular and its noncircular phase, diag{} and superscript H Represented as vector diagonalization and conjugate transpose operators.

[0021] Furthermore, in step S3, the array output pseudo covariance matrix R′ based on the non-circular signal nc Estimated value of for:

[0022]

[0023] in, and △E are the array output pseudo covariance matrices based on non-circular signals, respectively. The estimated value and estimation error of

[0024] The estimated error energy constraint is:

[0025]

[0026] in, is represented as the Kronecker product, ||·||2 is represented as the l2 norm, and Asχ 2 (M 2 ) is expressed as the degree of freedom M 2 Chi-square distribution of ;

[0027] After removing the redundant items through the redundancy removal matrix Γ, we get the (2M-1)×1 dimension z cn The expression is:

[0028]

[0029] Build z cn and and R′ nc The relationship between z cn The expression is modified to:

[0030]

[0031] in, and △z nc The vector z cn The estimated value and estimation error of

[0032] The expression of the DOA estimation function of non-circular signals based on the estimation error energy constraint is:

[0033]

[0034] where η is a variable associated with the chi-square distribution degrees of freedom 2M-1, ||·|| A Expressed as atomic norm;

[0035] The convex function form of the non-circular signal DOA estimation function expression based on the estimation error energy constraint is:

[0036]

[0037]

[0038] in, They correspond to the Toeplitz matrix T(μ nc ), z nc , the intermediate variable q nc Estimation of T(μ nc ) represents the vector μ nc =[μ nc,1 ,...,μ nc,2M-1 ] is determined by the Hermitian Toeplitz matrix, μ nc,1 , μ nc,2M-1 They are represented as the 1st and 2M-1th elements respectively, and the specific expressions are as follows:

[0039]

[0040] Furthermore, the target angle parameter of the non-circular signal obtained in step S4 is:

[0041]

[0042]

[0043] in, It reflects the orthogonality of the guidance vector and the noise subspace. The true angle θ of the non-circular source nc The estimated value is and its true noncircular phase The estimated value is

[0044] Furthermore, in step S5 Estimated value of for:

[0045]

[0046] Superscript Represented as a pseudo-inverse operator.

[0047] The estimated value of the covariance matrix of a non-circular signal and the estimated value of the pseudo-covariance matrix have the following relationship:

[0048]

[0049] Estimation of array output covariance matrix based on non-circular signals Then the estimated value of the covariance matrix of the noisy array output based on the circular signal is for:

[0050]

[0051] The target angle parameters of the circular signal are obtained by using the circular signal DOA estimation method based on denoising constraints.

[0052] Furthermore, a circular signal DOA estimation method based on denoising constraints is adopted, which includes the following steps:

[0053] S51, calculate the noisy array output covariance matrix R based on the circular signal c rank(R c )=K c , the optimization problem based on rank minimization is:

[0054]

[0055] Among them, 1, I and Represented as all-one matrix, unit matrix and direct product operator respectively;

[0056] S52. The optimization problem based on rank minimization is non-convex, which can be transformed into the following solution problem:

[0057]

[0058]

[0059] Among them, W c1 and W c2 are temporary variable matrices, trace(·) is the trace operator, It is shown that the matrix satisfies semi-positive definiteness, and then the CVX convex optimization toolkit is used to solve the formula;

[0060] S53, according to the CVX toolkit to solve the new estimate of the array output covariance matrix based on the circular signal Perform eigenvalue decomposition:

[0061]

[0062] Let U Nc =U c (:,K c +1:M) The corresponding noise subspace, and finally the target angle parameter of the circular signal obtained by spectrum peak search is:

[0063]

[0064] in, It reflects the orthogonality of the guidance vector based on the circular signal and the noise subspace. The true angle of the circular source θ c The estimated value is

[0065] A circular and non-circular mixed signal DOA estimation system based on estimation error energy constraint of the present invention comprises:

[0066] Signal acquisition module, the linear uniform array receives the electromagnetic waves that are not related to each other emitted by the far-field signal source, and obtains the linear uniform array output;

[0067] A signal processing module, which forms an extended array output signal from a linear uniform array output and its conjugate, calculates an extended covariance matrix, and calculates an estimated value of an array output pseudo-covariance matrix based on a non-circular signal;

[0068] The DOA signal estimation module introduces the estimation error energy constraint condition, gives the non-circular signal DOA estimation function expression based on the estimation error energy constraint, and solves it to obtain the Toeplitz matrix The target angle parameters of the non-circular signal are obtained by spectrum peak search; finally, the array output covariance matrix R based on the non-circular signal is obtained nc Estimated value of And the covariance matrix R of the noisy array output signal based on the circular signal c Estimated value of Then, the circular signal DOA estimation method based on denoising constraints is used to obtain the target angle parameters of the circular signal.

[0069] A device of the present invention includes a memory and a processor, wherein:

[0070] A memory for storing computer programs that can be run on the processor;

[0071] The processor is used to execute the steps of the above-mentioned circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint when running the computer program.

[0072] A storage medium of the present invention stores a computer program, which, when executed by at least one processor, implements the steps of the above-mentioned method for estimating DOA of circular and non-circular mixed signals based on estimation error energy constraint.

[0073] Beneficial effects: Compared with the prior art, the advantages of the present invention are:

[0074] (1) By introducing the estimated energy constraint, the DOA estimation accuracy of non-circular signals in the case of few snapshots is improved;

[0075] (2) Most existing mixed signal DOA estimation methods are based on the premise of accurate evaluation of the angle parameters of non-circular signal sources. Therefore, the method proposed in the present invention can further improve the DOA estimation accuracy of circular signals by improving the DOA estimation accuracy of non-circular signals with the help of estimated energy constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 It is a flow chart of the present invention;

[0077] Figure 2 It is a spatial spectrum function diagram of a non-circular signal drawn by the present invention for M=4 uniform linear array, wherein the real non-circular signal angles are 15° and 25° respectively, the experimental signal-to-noise ratio SNR is 0dB, and the number of snapshots is 150;

[0078] Figure 3 This is a graph of the spatial spectrum function of a non-circular signal drawn by the present invention for a uniform linear array of M=4, wherein the angle of the real circular signal is -50°, the experimental signal-to-noise ratio SNR is 15dB, and the number of snapshots is 500;

[0079] Figure 4 This is a curve diagram of the root mean square error (RMSE) versus SNR plotted for the M=4 uniform linear array of the present invention. DETAILED DESCRIPTION

[0080] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0081] In order to improve the accuracy of non-circular signal estimation and accurately estimate the angle of mixed signals, this paper proposes a circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint. This method introduces estimation error energy constraint on the basis of the DOA estimation algorithm based on atomic norm minimization to achieve mixed signal DOA estimation in the case of few snapshots. Figure 1 As shown, the following steps are included:

[0082] S1. Assume that there is a linear uniform array composed of M array elements with a spacing of d. d is generally set to half the wavelength λ. Consider that the linear uniform array passively receives K=K c +K nc Far-field sources (by K nc non-circular sources and K c The non-circular signal sources mentioned in the present invention are mixed together. It should be emphasized that the non-circular signal sources mentioned in the present invention are all maximum non-circular rate signal sources. The non-circular signal sources transmit non-circular signals, and the circular signal sources transmit circular signals. The electromagnetic waves emitted by the non-circular signal sources are unrelated to each other, so the linear uniform array output x(t) is obtained. The calculation formula is:

[0083]

[0084]

[0085] In the formula, k nc (k nc =1,…,K nc ) and k c (k c =1,…,K c ) are the intermediate variables corresponding to the number of non-circular sources and circular sources respectively; A=[A nc A c ] is the array flow type corresponding to all sources, A nc and A c are the array flow types corresponding to the non-circular source and the circular source, that is, A nc and A c are the array manifolds of non-circular signals and circular signals respectively; among them, and They are No. 1, K nc and k nc The corresponding guidance vector is and They are No. 1, K c and k c The guidance vector corresponding to the circular source is, and They are No. 1, K nc and k nc non-circular sources, the first, K c and k c The DOA corresponding to the circular source, superscript T is the transpose operator; is the electromagnetic wave emitted by all sources, s nc (t) and s c (t) are the electromagnetic waves emitted by the non-circular source and the circular source, respectively, where: and They are No. 1, K nc and k nc The electromagnetic wave emitted by a non-circular source, since the maximum non-circularity signal can be obtained by phase shifting the real signal, Respectively represented as 1st and K nc The real signal and noncircular phase corresponding to a noncircular source; and Respectively represented as the 1st and K c and k c The electromagnetic waves emitted by the circular source; n(t) is a Gaussian non-uniform noise signal, that is, it obeys the mean of 0, and the covariance matrix is ​​a diagonal matrix σ with equal diagonal elements 2 I, that is

[0086] n(t)~N(0,σ 2 I), (2)

[0087] Among them, σ 2 is the Gaussian white noise power received by the array element. t=1,…,L is the number of snapshots.

[0088] S2. In order to utilize the non-circular characteristics of the signal, the linear uniform array output x(t) and its conjugate x * (t) are used simultaneously to form the extended array output signal y(t):

[0089]

[0090] Among them, the superscript * It is represented as the conjugate operator. And the extended covariance matrix R is calculated according to formula (3): y :

[0091]

[0092] in, They are the circular signal covariance matrix, the non-circular signal covariance matrix, and the non-circular signal pseudo-covariance matrix, respectively. are the first circle signal, the Kth circle signal, c The first circular signal, the first non-circular signal, the Kth nc The power of a non-circular signal, are the first non-circular signal, the Kth nc The non-circular phase of a non-circular signal; diag{} and superscript H denote the vector diagonalization and conjugate transpose operators, respectively.

[0093] S3. Considering the estimation accuracy error that is inevitable in actual scenes due to the limited snapshot effect, the array output pseudo covariance matrix based on non-circular signals obtained by the present invention is Estimated value of for:

[0094]

[0095] and △E are By using the property that the estimated error of the array output covariance matrix based on circular signals obeys the Gaussian distribution mentioned in the literature (Z.Liu, Z.Huang and Y.Zhou, "Sparsity-Inducing Direction Finding for Narrowband and WidebandSignals Based on Array Covariance Vectors[J], IEEE Transactions on WirelessCommunications), the present invention can also deduce that the energy of the estimated error of the array output pseudo-covariance matrix based on non-circular signals obeys the chi-square distribution, that is:

[0096]

[0097] Among them, W is the weight matrix, Asχ 2 (M 2 ) is expressed as the degree of freedom M 2 The chi-square distribution of is represented as the Kronecker product and ||·||2 is represented as the l2 norm. Then, we define the vector z cn The pseudo covariance matrix of the array output based on the non-circular signal calculated by formula (4) is After vectorization, the vector with redundant items removed can be obtained:

[0098]

[0099] Among them, Γ is the redundancy removal matrix, and p k They correspond to the non-circular phase and power of the kth non-circular source respectively. Then we establish z cn and and R′ nc The relationship is modified and formula (7) is:

[0100]

[0101] in, and △z nc The vector z cn The estimated value and estimation error of the non-circular signal DOA estimation method based on atomic norm minimization (ANM) is given by introducing the estimation error energy constraint as shown in (6) to give the non-circular signal DOA estimation function expression based on the estimation error energy constraint:

[0102]

[0103] Here, η is a variable related to the chi-square distribution degrees of freedom 2M-1, which is generally set by the Matlab code chi2inv(0.001,2M-1). is expressed as the atomic norm. Because With convexity, the present invention converts equation (9) into the following convex function form by using the semi-positive programming theory:

[0104]

[0105] in, They correspond to the Toeplitz matrix T(μ nc ), z nc , the intermediate variable q nc It is worth noting that the constraint It shows that the matrix satisfies semi-positive definiteness. Theoretically, T(μ nc ) is sparse and rank(T(μ nc ))=K nc . T(μ nc ) represents the vector μ nc =[μ nc,1 ,...,μ nc,2M-1 ] is determined by the Hermitian Toeplitz matrix, μ nc,1 , μ nc,2M-1 They are represented as the 1st and 2M-1th elements respectively, and the specific expressions are as follows:

[0106]

[0107] The present invention solves (10) by using the CVX convex optimization toolkit.

[0108] S4. The solution obtained by CVX toolkit Perform eigenvalue decomposition (EVD):

[0109]

[0110] make is the noise subspace, and finally the target angle parameter (i.e., direction of arrival parameter) of the non-circular signal can be obtained by spectrum peak search:

[0111]

[0112] in It reflects the orthogonality of the guidance vector and the noise subspace. The true angle θ of the non-circular source nc The estimated value is and its true noncircular phase The estimated value is Figure 2 The spatial spectrum functions of DOA estimation of non-circular signals based on the ANM method and the method proposed in the present invention were compared, and it was found that the method proposed in the present invention has higher estimation accuracy for non-circular signals. Figure 4 Based on 20 Monte Carlo experiments, the RMSE curves of the two methods were compared. The results showed that the proposed method is better than the method based on the atomic norm.

[0113] S5, according to the target angle parameter of the non-circular signal estimated in step S4, the non-circular signal array flow pattern A is obtained by using the formation of the linear uniform array nc Estimated value of Then with the help of superscript The pseudo-inverse operator of the symbol obtains the pseudo-covariance matrix of the non-circular signal Estimated value of

[0114]

[0115] At the same time, the estimated value of the covariance matrix of the non-circular signal and the estimated value of the pseudo-covariance matrix have the following relationship:

[0116]

[0117] Furthermore, we obtain an estimate of the array output covariance matrix based on non-circular signals: Then the estimated value of the covariance matrix of the noisy array output based on the circular signal is for

[0118]

[0119] Where R = E{x(t)x H (t)}.

[0120] The present invention considers the influence of noise on circular signal estimation and adopts a circular signal DOA estimation method based on denoising constraints. The specific operations are as follows:

[0121] S51, due to rank (R c )=K c , that is, K c For R c rank, so consider the optimization problem based on rank minimization:

[0122]

[0123] Among them, 1, I and Represented as a matrix of all 1s, an identity matrix, and a direct product operator respectively. This constraint is to remove the influence of noise on the DOA estimation based on the circular signal.

[0124] S52. Since the optimization problem shown in formula (17) is non-convex, it is transformed into the following solution problem by borrowing convex optimization theory:

[0125]

[0126] Among them, W c1 and W c2 are temporary weight variable matrices, trace(·) is the trace operator, It shows that the matrix satisfies semi-positive definite. Then the CVX convex optimization toolkit is used to solve formula (18).

[0127] S53, according to the CVX toolkit to obtain the new estimate of the array output covariance matrix based on the circular signal Perform eigenvalue decomposition (EVD):

[0128]

[0129] Let U Nc =U c (:,K c +1:M) The corresponding noise subspace can finally obtain the target angle parameter (i.e., direction of arrival parameter) of the circular signal through spectrum peak search:

[0130]

[0131] in, It reflects the orthogonality of the guidance vector based on the circular signal and the noise subspace. The true angle of the circular source θ c The estimated value is Figure 3 The spatial spectrum function of circular signal DOA estimation based on the ANM method and the method proposed in the present invention is depicted.

[0132] A circular and non-circular mixed signal DOA estimation system based on estimation error energy constraint of the present invention comprises:

[0133] Signal acquisition module, the linear uniform array receives the electromagnetic waves that are not related to each other emitted by the far-field signal source, and obtains the linear uniform array output;

[0134] A signal processing module, which forms an extended array output signal from a linear uniform array output and its conjugate, calculates an extended covariance matrix, and calculates an estimated value of an array output pseudo-covariance matrix based on a non-circular signal;

[0135] The DOA signal estimation module introduces the estimation error energy constraint condition, gives the non-circular signal DOA estimation function expression based on the estimation error energy constraint, and solves it to obtain the Toeplitz matrix The target angle parameters of the non-circular signal are obtained by spectrum peak search; finally, the array output covariance matrix R based on the non-circular signal is obtained nc Estimated value of And the covariance matrix R of the noisy array output signal based on the circular signal c Estimated value of Then, the circular signal DOA estimation method based on denoising constraints is used to obtain the target angle parameters of the circular signal.

[0136] A device of the present invention includes a memory and a processor, wherein:

[0137] A memory for storing computer programs that can be run on the processor;

[0138] The processor is used to execute the steps of the above-mentioned circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint when running the computer program, and achieve the technical effect consistent with the above-mentioned method.

[0139] A storage medium of the present invention stores a computer program on the storage medium. When the computer program is executed by at least one processor, the steps of the above-mentioned circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint are implemented, and the technical effect consistent with the above-mentioned method is achieved.

Claims

1. A circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint, characterized in that: The following steps are involved: S1, a linear uniform array is formed by M array elements with a spacing of d, and the linear uniform array passively receives K=K c +K nc The electromagnetic waves emitted by far-field sources are unrelated to each other, K nc is the number of non-circular information sources, K c is the number of circular sources, so the linear uniform array output x(t)=As(t)+n(t), where A=[A nc A c ] is the array flow type corresponding to all sources, A nc and A c are the array flow patterns of non-circular signals and circular signals respectively, n(t) is the Gaussian non-uniform noise signal, t=1,…,L is the number of snapshots; S2, use the linear uniform array output and its conjugate simultaneously to form the extended array output signal y(t), and calculate the extended covariance matrix R y ; S3, calculate the array output pseudo covariance matrix based on non-circular signals The estimated value is Then, define the vector z cn Output pseudo-covariance matrix for array After vectorization, remove the redundant vectors and create vector z cn and and R n ' c Then, the estimation error energy constraint is introduced, and the DOA estimation function expression of non-circular signal based on the estimation error energy constraint is given. The function expression is converted into a convex function form, and finally the convex optimization toolkit is used to solve the function and obtain the Toeplitz matrix S4. Toeplitz matrix Perform eigenvalue decomposition: make is the noise subspace, and finally the target angle parameter of the non-circular signal is obtained by spectrum peak search; S5. According to the target angle parameter of the non-circular signal estimated in step S4, the non-circular signal array flow pattern A is first obtained by using the formation of the linear uniform array. nc Estimated value of Then, the pseudo-covariance matrix of the non-circular signal is obtained by using the pseudo-inverse operator Estimated value of Then, according to the estimated value of the pseudo-covariance matrix Get an estimate of the covariance matrix of the non-circular signal Finally, the array output covariance matrix R based on the non-circular signal is obtained nc Estimated value of And the covariance matrix R of the noisy array output signal based on the circular signal c Estimated value of Further solving the problem yields a new estimate of the array output covariance matrix based on the circular signal: Finally, the target angle parameters of the circular signal are obtained through spectrum peak search.

2. The method for DOA estimation of circular and non-circular mixed signals based on estimation error energy constraint according to claim 1, characterized in that: In step S1, the non-circular information source is the maximum non-circular rate information source.

3. The method for DOA estimation of circular and non-circular mixed signals based on estimation error energy constraint according to claim 1, characterized in that: The extended array output signal y(t) in step S2 is: Among them, the superscript * It is represented as the conjugate operator; Expanded covariance matrix R y for: in, They are the circular signal covariance matrix, the non-circular signal covariance matrix, and the non-circular signal pseudo-covariance matrix, respectively. are the first circle signal, the Kth circle signal, c The first circular signal, the first non-circular signal, the Kth nc The noncircular power and its noncircular phase, diag{} and superscript H denote the vector diagonalization and conjugate transpose operators.

4. The method for DOA estimation of circular and non-circular mixed signals based on estimation error energy constraint according to claim 1, characterized in that: In step S3, the array output pseudo covariance matrix R based on the non-circular signal n ' c The estimated value of is: in, and △E are the array output pseudo covariance matrices based on non-circular signals, respectively. The estimated value and estimation error of The estimated error energy constraint is: in, It is expressed as Kronecker product, and ||·||2 is expressed as l2 norm; z cn The expression is: Build z cn and and R n ' c The relationship between z cn The expression is modified to: in, and △z nc The vector z cn The estimated value and estimation error of The expression of the DOA estimation function of non-circular signals based on the estimation error energy constraint is: where η is a variable associated with the chi-square distribution degrees of freedom 2M-1, Expressed as atomic norm; The convex function form of the non-circular signal DOA estimation function expression based on the estimation error energy constraint is: in, They correspond to the Toeplitz matrix T(μ nc ), z nc , the intermediate variable q nc Estimation of T(μ nc ) represents the vector The Hermitian Toeplitz matrix, μ, determines nc,1 , Represented as the 1st and 2M-1th elements respectively, the specific expressions are as follows:

5. The method for DOA estimation of circular and non-circular mixed signals based on estimation error energy constraint according to claim 1, characterized in that: The target angle parameter of the non-circular signal obtained in step S4 is: in, It reflects the orthogonality of the guidance vector and the noise subspace.

6. The method for DOA estimation of circular and non-circular mixed signals based on estimation error energy constraint according to claim 1, characterized in that: In step S5 Estimated value of for: The estimated value of the covariance matrix of a non-circular signal and the estimated value of the pseudo-covariance matrix have the following relationship: Estimation of array output covariance matrix based on non-circular signals Then the estimated value of the covariance matrix of the noisy array output based on the circular signal is for: The target angle parameters of the circular signal are obtained by using the circular signal DOA estimation method based on denoising constraints.

7. The method for estimating DOA of circular and non-circular mixed signals based on estimation error energy constraint according to claim 6, characterized in that: The circular signal DOA estimation method based on denoising constraint is adopted, which includes the following steps: S51, calculate the noisy array output covariance matrix R based on the circular signal c rank(R c )=K c , the optimization problem based on rank minimization is: Among them, 1, I and Represented as all-one matrix, unit matrix and direct product operator respectively; S52. The optimization problem based on rank minimization is non-convex, which can be transformed into the following solution problem: Among them, W c1 and W c2 are temporary variable matrices, trace(·) is the trace operator, It is shown that the matrix satisfies semi-positive definiteness, and then the CVX convex optimization toolkit is used to solve the formula; S53, according to the CVX toolkit to solve the new estimate of the array output covariance matrix based on the circular signal Perform eigenvalue decomposition: Let U Nc =U c (:,K c +1:M) The corresponding noise subspace, and finally the target angle parameter of the circular signal obtained by spectrum peak search is: in, It reflects the orthogonality of the guidance vector based on the circular signal and the noise subspace.

8. A system used in the circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint as claimed in claim 1, characterized in that: include: Signal acquisition module, the linear uniform array receives the electromagnetic waves that are not related to each other emitted by the far-field signal source, and obtains the linear uniform array output; A signal processing module, which forms an extended array output signal from a linear uniform array output and its conjugate, calculates an extended covariance matrix, and calculates an estimated value of an array output pseudo-covariance matrix based on a non-circular signal; The DOA signal estimation module introduces the estimation error energy constraint condition, gives the non-circular signal DOA estimation function expression based on the estimation error energy constraint, and solves it to obtain the Toeplitz matrix The target angle parameter of the non-circular signal is obtained by spectrum peak search; finally, the array output covariance matrix R based on the non-circular signal is obtained nc Estimated value of And the covariance matrix R of the noisy array output signal based on the circular signal c Estimated value of Then, the circular signal DOA estimation method based on denoising constraints is used to obtain the target angle parameters of the circular signal.

9. A device, characterized in that: comprising a memory and a processor, wherein: A memory for storing computer programs that can be run on the processor; A processor is used to execute the steps of a circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint as described in any one of claims 1 to 7 when running the computer program.

10. A storage medium, characterized in that: The storage medium stores a computer program, which, when executed by at least one processor, implements the steps of a circular and non-circular mixed signal DOA estimation method based on estimation error energy constraint as described in any one of claims 1 to 7.

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