Related signal DOA estimation method based on Gaussian Newton orthogonal subspace projection

Abstract

The invention discloses a correlation signal DOA estimation method based on Gaussian Newton orthogonal subspace projection, and the method comprises the steps: inputting a radar array signal, and initializing the total number of search directions of arrival; preliminarily estimating direction-of-arrival vectors of all directions of arrival by using an alternating projection method; updating the array time delay by using Gaussian Newton orthogonal subspace projection; judging whether the current cost value is smaller than a preset threshold value; if yes, accurate estimation of all directions of arrival is completed; otherwise, continuing to update the array time delay; and extracting a direction-of-arrival vector by using the array time delay. According to the method, the convergence speed of estimation is increased, the adaptability to environment change is enhanced, and meanwhile, the accuracy and the resolution of the direction-of-arrival estimation of the related signals are remarkably improved.

Description

Technical Field

[0001] The invention relates to the field of target direction estimation, and in particular to a method for estimating DOA of correlation signals of a compact array based on Gauss-Newton orthogonal subspace projection. Background Art

[0002] Reducing the spacing between array elements and miniaturizing arrays are of great significance in modern technology applications. The spacing between elements of traditional arrays is usually set to half the wavelength of the carrier, which makes the array bulky and affects its transportation and use. The spacing between elements of compact arrays is less than half the wavelength of the carrier, which realizes the miniaturization of the array, significantly improves the flexibility and mobility of the system, and enables it to be easily deployed in various complex environments. In many fields such as radar, sonar, communication, detection and medical treatment, direction of arrival (DOA) estimation is widely used as an important technology. In order to achieve DOA estimation, many super-resolution subspace algorithms have been proposed, such as Multiple Signal Classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT). These algorithms usually require that the incident signals are independent of each other, but in actual applications, due to the multipath effect caused by factors such as reflections from mountains and buildings and the influence of co-channel interference, there are not only independent components between the signals, but also a large number of strongly correlated or coherent signals. This situation causes the signal covariance matrix to be rank-deficient, destroying the orthogonal relationship between the array steering vector and the noise subspace, which significantly reduces the performance of algorithms such as MUSIC or even makes them ineffective.

[0003] In addition, the reduction in array element spacing will cause the array main lobe to become wider, thereby reducing the directivity of the signal and affecting the accuracy of DOA estimation. This is particularly critical for applications that require high-precision positioning. At the same time, the wide main lobe makes it impossible to accurately distinguish the contribution of each signal source in the case of similar signal sources, resulting in a decrease in resolution. This has a significant impact on applications such as high-resolution imaging or multi-target tracking, thereby limiting the performance of the system. Therefore, how to improve the accuracy and resolution of DOA estimation of compact array-related signals to promote array miniaturization has become a problem that needs to be urgently solved by those skilled in the art. Summary of the invention

[0004] The purpose of the present invention is to provide a correlation signal DOA estimation method based on Gauss-Newton orthogonal subspace projection to improve the accuracy and resolution of compact array correlation signal DOA estimation.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A method for estimating DOA of a correlation signal based on Gauss-Newton orthogonal subspace projection, comprising:

[0007] S1, input radar array signal S, initialize the search for the total number of wave arrival directions K;

[0008] S2, using the alternating projection method, preliminarily estimate the direction of arrival vector θ of K directions of arrival;

[0009] S3, update the array delay Ψ using Gauss-Newton orthogonal subspace projection;

[0010] S4, determine the current generation value β 2 Is it less than the preset threshold ε? 2 ; If the current generation value β 2 Less than the threshold ε 2 , then the accurate estimation of K wave arrival directions has been completed, and jump to S5; otherwise, continue to update the array delay Ψ and jump to S3;

[0011] S5, extract the direction of arrival vector θ using the array delay Ψ.

[0012] Furthermore, the total number K of searched arrival directions is known or has been estimated using an existing numerical detection method.

[0013] Furthermore, the alternating projection method described in S2 is used to preliminarily estimate the direction of arrival vectors θ of K directions of arrival, including:

[0014] S2.1, initialize the estimated arrival direction vector θ, the previous round of estimated arrival direction vector θ last , the current estimated direction of arrival number k, the counter Count of k k and the previous estimated direction of arrival number k last ;

[0015] S2.2, determine whether the current estimated arrival direction number k is less than the total number K of searched arrival directions; if the current estimated arrival direction number k is less than the total number K of searched arrival directions, jump to S2.3; otherwise, it indicates that the estimation of all arrival directions has been completed, the search ends, and jumps to S3;

[0016] S2.3, determine the current cost β 1 Is it less than the preset threshold ε? 1 ;

[0017] If the current generation value β 1 Less than the threshold ε 1 , the estimation of the first k wave arrival directions has been completed, and then update k = Count k+1, Count k = k, then jump to S2.2;

[0018] If the current generation value β 1 Greater than or equal to the threshold ε 1 , then initialize the counter Count of alternately estimating the wave direction sequence number j=1 and j j = 1, update the estimated direction of arrival vector θ of the previous round last =θ, then jump to S2.4;

[0019] S2.4, update the jth direction of arrival θ according to the current estimated direction of arrival vector θ (j) , the specific formula is:

[0020]

[0021] F(θ m )=tr{[IA(θ now )(A H (θ now )A(θ now )) -1 A(θ now )]R}

[0022] Among them, θ m Indicates the angle to be searched. The matrix superscript H indicates that the conjugate transpose operation is performed on the matrix. [] -1 represents the inverse operation of the matrix, tr{} represents the trace of the matrix, I represents the identity matrix, R represents the complex covariance matrix, and the same below; A(θ now ) represents the steering matrix corresponding to the direction of arrival, and the specific formula is:

[0023]

[0024] Where S represents the radar array signal, e is a natural constant, N represents the number of snapshots, i represents the imaginary symbol, λ is the wavelength of the carrier, the distance vector D of each array element relative to the reference array element and the current wave direction estimation vector θ now1 The specific formula is:

[0025] D=[0,d,2d,...,(M-1)d] T

[0026] θ now =[θ m ,θ (-j) ]

[0027] The matrix superscript T indicates that the matrix is ​​transposed, and d is the array element spacing, which is M is the number of array elements, θ (-j)represents the remaining elements after removing the jth element in θ, [θ m ,θ (-j) ] represents θ m and the matrix formed by the remaining elements;

[0028] S2.5, determining whether the alternate estimated direction of arrival number j is less than the current estimated direction of arrival number k;

[0029] If the alternate estimated direction of arrival number j is less than the current estimated direction of arrival number k, then update j = Count j +1, Count j =j, then jump to S2.4;

[0030] If the alternate estimated direction of arrival number j is greater than or equal to the current estimated direction of arrival number k, then update k last =k, then jump to S2.3.

[0031] Furthermore, the specific initialization formula in S2.1 is: θ=[0]; θ last =[+∞]; k = 1; Count k =1; k last =0; where [0] represents the zero vector.

[0032] Furthermore, the current cost value β 1 The specific formula is:

[0033]

[0034] where θ (n) , They represent θ and θ respectively. last The nth element in .

[0035] Furthermore, the specific formula of the array delay Ψ in S3 is:

[0036]

[0037] Among them, the objective function is:

[0038]

[0039] in, is the orthogonal projection matrix of the steering matrix A(θ), and the specific formula is:

[0040]

[0041] Furthermore, the updating of the array delay Ψ by using Gauss-Newton orthogonal subspace projection in S3 includes:

[0042] S3.1, calculate the first-order derivative matrix Q(Ψ) of the steering matrix A(θ) with respect to the array delay Ψ. The specific formula is:

[0043]

[0044] Where diag means finding the diagonal elements of the matrix. is the imaginary number symbol;

[0045] S3.2, calculate the first-order derivative matrix F(Ψ) and the second-order derivative matrix H(Ψ) of the objective function f(Ψ):

[0046] A + (θ)=(A H (θ)A(θ)) -1 A(θ)

[0047]

[0048] Among them, A + (θ) is the pseudo-inverse matrix of the steering matrix A(θ), represents the real part operation, It means to find the Kronecker product;

[0049] S3.3, update array delay Ψ, the specific formula is:

[0050] ΔΨ=-(H(Ψ)) -1 F(Ψ)

[0051] Ψ=Ψ+μΔΨ

[0052] Where μ is the update step size and ΔΨ is the update increment of the array delay Ψ.

[0053] Furthermore, the cost value β 2 The specific formula is:

[0054]

[0055] Among them, ΔΨ (n) represents the nth element in ΔΨ.

[0056] Furthermore, the array delay Ψ is used to extract the direction of arrival vector θ, and the specific formula is:

[0057]

[0058] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, the method for estimating the DOA of a correlated signal based on Gauss-Newton orthogonal subspace projection is implemented.

[0059] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the method for estimating the DOA of a correlation signal based on Gauss-Newton orthogonal subspace projection is implemented.

[0060] Compared with the prior art, the present invention has the following technical features:

[0061] 1. The present invention optimizes the relevant signal arrival direction vector in each iteration through the alternating projection method, thereby ensuring that the estimation in each step can more accurately approach the true value. The core idea of ​​alternating projection is to decompose the complex optimization problem into multiple simple projection steps, so that each iteration can be optimized within a relatively small calculation range, and at the same time, the residual power is used as an indicator to avoid the influence of the covariance matrix rank deficiency on the DOA estimation. This strategy not only improves the convergence speed of the estimate, but also enhances the adaptability to environmental changes. In addition, the result of alternating projection also provides a good initial value for the subsequent Gauss-Newton orthogonal subspace projection, which reduces the number of iterations in the calculation process to a certain extent, further reducing the computational burden;

[0062] 2. The present invention adopts the Gauss-Newton orthogonal subspace projection method, based on the estimation results of the previous round of DOA, and uses the residual power as an update index to ensure that the new round of search is more accurate, while effectively avoiding the local optimal solution problem caused by improper initial value selection. When the residual power is found to be high, it means that the current DOA estimation has not yet reached the optimal state. At this time, the Gauss-Newton method will adjust the estimation to minimize the residual power, thereby achieving a more accurate DOA estimation. Through such a feedback mechanism, the algorithm can continuously correct and optimize the estimation results in each iteration, thereby significantly improving the accuracy and resolution of the DOA estimation of the relevant signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a flow chart of the method of the present invention;

[0064] Figure 2 Flowchart for searching DOA for preliminary estimation using the alternating projection method;

[0065] Figure 3 This is a comparison chart of simulation results of the present method and the bidirectional smoothing MUSIC method when the incident angle is [10.46°, -20.62°] in Example 1;

[0066] Figure 4 This is a comparison chart of simulation results of the present method and the bidirectional smoothing MUSIC method when the incident angle is [10.46°, 2.46°] in Example 1;

[0067] Figure 5This is a comparison diagram of the root mean square error of the present method and the two-way smoothing MUSIC method as a function of the signal-to-noise ratio when the incident angle is [9.46°] in Example 2;

[0068] Figure 6 This is a comparison diagram of the root mean square error of the present method and the two-way smoothing MUSIC method as a function of the signal-to-noise ratio when the incident angle is [33.46°, -19.63°] in Example 2;

[0069] Figure 7 A comparison chart of the root mean square error of the present method and the bidirectional smoothing MUSIC method versus the angle interval in Example 3. DETAILED DESCRIPTION

[0070] See attached Figure 1 and Figure 2 The present invention provides a method for estimating the DOA of a correlation signal based on Gauss-Newton orthogonal subspace projection, comprising the following steps:

[0071] S1, input radar array signal S, initialize the total number K of search arrival directions; wherein, the total number K of search arrival directions is known or has been estimated using an existing numerical detection method.

[0072] S2, using the alternating projection method, preliminarily estimate the direction of arrival vector θ of K directions of arrival.

[0073] S2.1, initialize the estimated arrival direction vector θ, the previous round of estimated arrival direction vector θ last , the current estimated direction of arrival number k, the counter Count of k k and the previous estimated direction of arrival number k last ; The specific initialization formula is:

[0074] θ=[0]

[0075] θ last =[+∞]

[0076] k=1

[0077] Count k =1

[0078] k last =0

[0079] Among them, [0] represents the zero vector.

[0080] S2.2, determine whether the current estimated arrival direction number k is less than the total number K of searched arrival directions; if the current estimated arrival direction number k is less than the total number K of searched arrival directions, jump to S2.3; otherwise, it indicates that the estimation of all arrival directions has been completed, the search ends, and jumps to S3;

[0081] S2.3, determine the current cost β 1 Is it less than the preset threshold ε? 1 ;

[0082] If the current generation value β 1 Less than the threshold ε 1 , the estimation of the first k wave arrival directions has been completed, and then update k = Count k +1, Count k = k, then jump to S2.2; in this scheme, the threshold ε 1 The value can be set to 0.001.

[0083] If the current generation value β 1 Greater than or equal to the threshold ε 1 , then initialize the counter Count of alternately estimating the wave direction sequence number j=1 and j j = 1, update the estimated direction of arrival vector θ of the previous round last =θ, then jump to S2.4;

[0084] Among them, the current generation value β 1 The specific formula is:

[0085]

[0086] where θ (n) , They represent θ and θ respectively. last The nth element in .

[0087] S2.4, update the jth direction of arrival θ according to the current estimated direction of arrival vector θ (j) , the specific formula is:

[0088]

[0089] F(θ m )=tr{[IA(θ now )(A H (θ now )A(θ now )) -1 A(θ now )]R}

[0090] Among them, θ m Indicates the angle to be searched. The matrix superscript H indicates that the conjugate transpose operation is performed on the matrix. [] -1 Indicates the inverse operation of the matrix, tr{} indicates the trace of the matrix, that is, the sum of the diagonal elements of the main diagonal of the matrix, I indicates the identity matrix, R indicates the complex covariance matrix, and the same below; A(θ now) represents the steering matrix corresponding to the direction of arrival, and the specific formula is:

[0091]

[0092] Where S represents the radar array signal, e is a natural constant, N represents the number of snapshots, i represents the imaginary symbol, λ is the wavelength of the carrier, the distance vector D of each array element relative to the reference array element and the current wave direction estimation vector θ now1 The specific formula is:

[0093] D=[0,d,2d,...,(M-1)d] T

[0094] θ now =[θ m ,θ (-j) ]

[0095] The matrix superscript T indicates that the matrix is ​​transposed, and d is the array element spacing, which is M is the number of array elements, θ (-j) represents the remaining elements after removing the jth element in θ, [θ m ,θ (-j) ] represents θ m The matrix formed with the remaining elements.

[0096] S2.5, determining whether the alternate estimated direction of arrival number j is less than the current estimated direction of arrival number k;

[0097] If the alternate estimated direction of arrival number j is less than the current estimated direction of arrival number k, then update j = Count j +1, Count j =j, then jump to S2.4;

[0098] If the alternate estimated direction of arrival number j is greater than or equal to the current estimated direction of arrival number k, then update k last =k, then jump to S2.3.

[0099] S3, update the array delay Ψ using Gauss-Newton orthogonal subspace projection.

[0100] The specific formula of array delay Ψ is:

[0101]

[0102] Among them, the objective function is:

[0103]

[0104] in, is the orthogonal projection matrix of the steering matrix A(θ), and the specific formula is:

[0105]

[0106] S3.1, calculate the first-order derivative matrix Q(Ψ) of the steering matrix A(θ) with respect to the array delay Ψ. The specific formula is:

[0107]

[0108] Where diag means finding the diagonal elements of the matrix. Is the imaginary number symbol.

[0109] S3.2, calculate the first-order derivative matrix F(Ψ) and the second-order derivative matrix H(Ψ) of the objective function f(Ψ):

[0110] A + (θ)=(A H (θ)A(θ)) -1 A(θ)

[0111]

[0112] Among them, A + (θ) is the pseudo-inverse matrix of the steering matrix A(θ), represents the real part operation, It means to find the Kronecker product.

[0113] S3.3, update array delay Ψ, the specific formula is:

[0114] ΔΨ=-(H(Ψ)) -1 F(Ψ)

[0115] Ψ=Ψ+μΔΨ

[0116] Wherein, the update step size μ=0.01, and ΔΨ is the update increment of the array delay Ψ.

[0117] S4, determine the current generation value β 2 Is it less than the preset threshold ε? 2 ;

[0118] If the current generation value β 2 Less than the threshold ε 2 , the accurate estimation of K wave arrival directions has been completed, and jump to S5; in this scheme, the threshold ε 2 The value can be set to 0.0001.

[0119] If the current generation value β 2 Greater than or equal to the threshold ε 2 , then continue to update the array delay Ψ and jump to S3.

[0120] Among them, the cost value β 2 The specific formula is:

[0121]

[0122] Among them, ΔΨ (n) represents the nth element in ΔΨ.

[0123] S5, use the array delay Ψ to extract the accurate wave arrival direction vector θ, the specific formula is:

[0124]

[0125] Example:

[0126] In the embodiment of the present invention, the model of the simulation array signal S is:

[0127]

[0128] Among them, θ k represents the kth wave arrival angle, A k (θ k ) represents the steering vector corresponding to the kth wave arrival angle, n is 0, and the variance is σ 2 Additive Gaussian white noise, s represents the signal source, the specific formula is:

[0129]

[0130] D=[0,d,2d,...,(M-1)d] T

[0131] s=[s(1),s(2),...,s(u),...,s(N)]

[0132]

[0133] Where d is the array element spacing, which is M is the number of array elements, which is 4. The signal amplitude is A s =1, sampling rate F s =10kHz, f is the frequency of the signal, is the initial phase of the signal, and the number of snapshots N=2000.

[0134] In order to verify the accuracy and resolution of the present invention in the estimation of the DOA of the correlation signal, the present invention considers the extreme case that the incident signals are exactly the same and only the incident angles are different. In the embodiment of the present invention, the frequency of the signal source is f=1kHz and the initial phase is

[0135] The size of the additive white Gaussian noise n is determined by the interference-to-noise ratio SNR, and the specific formula is:

[0136]

[0137] In order to accurately evaluate the effect of DOA estimation, the root mean square error of DOA is used as the evaluation index. The specific formula is:

[0138]

[0139] Among them, θ r (k) is the true direction of arrival, θ (k) To estimate the direction of arrival.

[0140] Embodiment 1:

[0141] In this embodiment, two groups of incident angles are set, namely [10.46°, -20.62°] and [10.46°, 2.62°]. Other simulation parameters are the same as the initial parameters given in the example. The compact array DOA estimation method based on alternating projection and golden section search method and the bidirectional smoothed MUSIC method are used to analyze the two groups of array simulation signals. The results are shown in Figure 2. Figure 3 and Figure 4 When the incident angle is [10.46°, -5.46°], both methods can distinguish the target angle. At this time, the root mean square error of the compact array DOA estimation method based on the alternating projection and golden section search method is 0.049, and the root mean square error of the bidirectional smoothing MUSIC method is 0.467, which proves that the method of the present invention can effectively perform DOA estimation and improve the accuracy; when the incident angle is [10.46°, 2.62°], the bidirectional smoothing MUSIC method has only one spectral peak and cannot distinguish two targets, while the compact array DOA estimation method based on the alternating projection and golden section search method can accurately identify the target, which proves that the method of the present invention can effectively improve the resolution.

[0142] Embodiment 2:

[0143] 3100 Monte Carlo experiments were conducted, with the signal-to-noise ratio ranging from -10dB to 20dB. Two groups of incident angles were set, namely [9.46°] and [33.46°, -19.63°]. Other simulation parameters were the same as the initial parameters given in the example. The compact array DOA estimation method based on alternating projection and golden section search method and the bidirectional smoothed MUSIC method were used to analyze the simulation signal, and the root mean square error results were obtained as shown in the figure. Figure 5 and Figure 6 As shown. Figure 5 and Figure 6Analysis shows that under the same parameters, the root mean square error of the compact array DOA estimation method based on alternating projection and golden section search method is significantly better than that of the bidirectional smoothed MUSIC algorithm. The above results show that the compact array DOA estimation method based on alternating projection and golden section search method proposed in the present invention can improve the accuracy.

[0144] Embodiment 3:

[0145] 1500 Monte Carlo experiments were conducted, with the angle interval ranging from 4° to 15°. The other simulation parameters were the same as the initial parameters given in the example. The compact array DOA estimation method based on alternating projection and golden section search method and the bidirectional smoothed MUSIC method were used to analyze the simulation signal, and the root mean square error results were obtained as shown in the figure. Figure 7 As shown. Figure 7 The analysis shows that the root mean square error of the compact array DOA estimation method based on alternating projection and golden section search method is significantly smaller than that of the bidirectional smoothing MUSIC algorithm. Figure 3 , Figure 4 and Figure 7 ,The simulation results show that the method described in the ,presentation can improve the resolution when estimating DOA.

[0146] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for estimating DOA of correlated signals based on Gauss-Newton orthogonal subspace projection, characterized in that: include: S1, input radar array signal S, initialize the search for the total number of wave arrival directions K; S2, using the alternating projection method, preliminarily estimate the direction of arrival vector θ of K directions of arrival; S3, update the array delay Ψ using Gauss-Newton orthogonal subspace projection; S4, determine whether the current cost value β2 is less than the preset threshold ε2; if the current cost value β2 is less than the threshold ε2, the accurate estimation of K wave arrival directions has been completed, and jump to S5; otherwise, continue to update the array delay Ψ and jump to S3; S5, extract the direction of arrival vector θ using the array delay Ψ.

2. The method for estimating DOA of correlation signals based on Gauss-Newton orthogonal subspace projection according to claim 1, characterized in that: S2 uses the alternating projection method to preliminarily estimate the direction of arrival vector θ of K directions of arrival, including: S2.1, initialize the estimated arrival direction vector θ, the previous round of estimated arrival direction vector θ last , the current estimated direction of arrival number k, the counter Count of k k and the previous estimated direction of arrival number k last ; S2.2, determine whether the current estimated arrival direction number k is less than the total number K of searched arrival directions; if the current estimated arrival direction number k is less than the total number K of searched arrival directions, jump to S2.3; otherwise, it indicates that the estimation of all arrival directions has been completed, the search ends, and jumps to S3; S2.3, determining whether the current cost value β1 is less than a preset threshold ε1; If the current cost value β1 is less than the threshold ε1, the estimation of the first k directions of arrival has been completed, and the update k=Count is executed. k +1, Count k = k, then jump to S2.2; If the current cost value β1 is greater than or equal to the threshold ε1, the counter Count of the alternately estimated wave direction sequence number j=1 and j is initialized j = 1, update the estimated direction of arrival vector θ of the previous round last =θ, then jump to S2.4; S2.4, update the jth direction of arrival θ according to the current estimated direction of arrival vector θ (j) , the specific formula is: F(θ m )=tr{[IA(θ now )(A H (i now )A(θ now )) -1 A(θ now )]R} Among them, θ m Indicates the angle to be searched. The matrix superscript H indicates that the conjugate transpose operation is performed on the matrix. [] -1 represents the inverse operation of the matrix, tr{} represents the trace of the matrix, I represents the identity matrix, R represents the complex covariance matrix, and the same below; A(θ now ) represents the steering matrix corresponding to the direction of arrival, and the specific formula is: Where S represents the radar array signal, e is a natural constant, N represents the number of snapshots, i represents the imaginary symbol, λ is the wavelength of the carrier, the distance vector D of each array element relative to the reference array element and the current wave direction estimation vector θ now1 The specific formula is: D=[0,d,2d,...,(M-1)d] T i now =[θ m ,i (-j) ] The matrix superscript T indicates that the matrix is ​​transposed, and d is the array element spacing, which is M is the number of array elements, θ (-j) represents the remaining elements after removing the jth element in θ, [θ m ,θ (-j) ] represents θ m and the matrix formed by the remaining elements; S2.5, determining whether the alternate estimated direction of arrival number j is less than the current estimated direction of arrival number k; If the alternate estimated direction of arrival number j is less than the current estimated direction of arrival number k, then update j = Count j +1, Count j =j, then jump to S2.4; If the alternate estimated direction of arrival number j is greater than or equal to the current estimated direction of arrival number k, then update k last =k, then jump to S2.

3.

3. The method for estimating DOA of correlation signals based on Gauss-Newton orthogonal subspace projection according to claim 2, characterized in that: The specific initialization formula in S2.1 is: θ = [0]; θ last =[+∞]; k = 1; Count k =1; k last =0; where [0] represents the zero vector.

4. The method for estimating DOA of correlation signals based on Gauss-Newton orthogonal subspace projection according to claim 2, characterized in that: The specific formula of the current cost value β1 is: where θ (n) , They represent θ and θ respectively. last The nth element in .

5. The method for estimating DOA of correlation signals based on Gauss-Newton orthogonal subspace projection according to claim 1, characterized in that: The specific formula of the array delay Ψ in S3 is: Among them, the objective function is: in, is the orthogonal projection matrix of the steering matrix A(θ), and the specific formula is:

6. The method for estimating DOA of correlation signals based on Gauss-Newton orthogonal subspace projection according to claim 5, characterized in that: The method of updating the array delay Ψ by using Gauss-Newton orthogonal subspace projection in S3 includes: S3.1, calculate the first-order derivative matrix Q(Ψ) of the steering matrix A(θ) with respect to the array delay Ψ. The specific formula is: Where diag means finding the diagonal elements of the matrix. is the imaginary number symbol; S3.2, calculate the first-order derivative matrix F(Ψ) and the second-order derivative matrix H(Ψ) of the objective function f(Ψ): A + (θ)=(A H (θ)A(θ)) -1 A(θ) Among them, A + (θ) is the pseudo-inverse matrix of the steering matrix A(θ), represents the real part operation, It means to find the Kronecker product; S3.3, update array delay Ψ, the specific formula is: ΔΨ=-(H(Ψ)) -1 F(Ψ) Ψ=Ψ+μΔΨ Where μ is the update step size and ΔΨ is the update increment of the array delay Ψ.

7. The method for estimating DOA of correlation signals based on Gauss-Newton orthogonal subspace projection according to claim 1, characterized in that: The specific formula of the cost value β2 is: Among them, ΔΨ (n) represents the nth element in ΔΨ.

8. The method for estimating DOA of correlation signals based on Gauss-Newton orthogonal subspace projection according to claim 1, characterized in that: The specific formula for extracting the direction of arrival vector θ using the array delay Ψ is:

9. A terminal device comprising a processor, a memory and a computer program stored in the memory; characterized in that: When the processor executes the computer program, the correlation signal DOA estimation method based on Gauss-Newton orthogonal subspace projection according to any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the method for estimating DOA of a correlation signal based on Gauss-Newton orthogonal subspace projection according to any one of claims 1 to 8 is implemented.

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