A nested array coherent target direction estimation method, system and terminal based on CLEAN

Abstract

The present invention relates to the technical field of underwater acoustic array signal processing, and discloses a nested array coherent target azimuth estimation method, system and terminal based on CLEAN. The target azimuth estimation method comprises: S1. configuring a nested array, receiving a narrowband signal, and constructing a narrowband signal model; S2. calculating the covariance matrix of a non-undersampled subarray; S3. calculating an estimated value of each target azimuth in the narrowband signal model; S4. constructing clear signals of the nested array for different targets, and calculating the covariance matrix of the clear signals of different targets; S5. vectorizing the covariance matrix of the clear signal to obtain a received signal of a virtual array; S6. calculating an updated estimated value of each target azimuth; S7. using the updated estimated value as input, cyclically executing steps S4 to S6, and repeating three times to obtain a target azimuth estimate. Compared with a method based on a uniform linear array with the same number of array elements, the present invention can achieve higher angular resolution, a narrower mainlobe width, and a lower sidelobe level.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater acoustic array signal processing, and in particular to a CLEAN-based nested array coherent target azimuth estimation method, system and terminal. Background Art

[0002] Array structure plays a crucial role in passive direction of arrival (DOA) estimation of sound sources. Uniform linear arrays (ULAs) are the most commonly used linear array structure, typically arranged with uniform element spacing. To avoid spatial angular ambiguity during target detection, the element spacing is typically less than or equal to half the signal wavelength. Because the aperture of a ULA is limited by the array length, increasing the aperture and improving spatial resolution requires increasing the number of elements, which significantly increases the hardware cost of the array. Sparse arrays are linear arrays with non-uniform spacing. Nested arrays (NAs), a typical example of sparse arrays, offer advantages such as high resolution, high degrees of freedom, and low coupling effects. Consequently, they have garnered extensive attention and research in recent years.

[0003] Furthermore, due to the multipath effect of underwater acoustic propagation, the signals received by underwater acoustic arrays are coherent, making subspace-based high-resolution direction estimation methods, such as the Multiple Signal Classification (MUSIC) method, no longer applicable. Forward / Backward Spatial Smoothing (FBSS), a typical example of a decorrelation method, has been widely used for many years (hereafter referred to as spatial smoothing). However, this method reduces the array aperture and resolution. Furthermore, it is only applicable to uniform linear arrays and cannot be directly applied to nested arrays. While sparse signal processing-based methods are applicable to coherent signal scenarios and can be extended to nested arrays, these methods suffer from high computational complexity and sensitivity to regularization parameters. Therefore, further research is needed on high-resolution direction estimation methods for coherent targets based on nested arrays. Summary of the Invention

[0004] The object of the present invention is to provide a nested array coherent target direction estimation method, system and terminal based on CLEAN, which has a narrower main lobe width and lower side lobe level than the method based on uniform linear array with the same number of array elements.

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

[0006] In a first aspect, the present invention provides a nested array coherent target direction estimation method based on CLEAN, comprising the following steps:

[0007] S1. Configure a nested array to receive narrowband signals from far-field coherent targets and construct a narrowband signal model.

[0008] S2. Calculating the covariance matrix of the non-undersampled sub-arrays included in the nested array;

[0009] S3. Split the non-undersampled subarray into Each contains A linear subarray of array elements is formed, and the covariance matrices of the linear subarrays are weighted summed to obtain a full-rank spatial smoothed covariance matrix. An estimated value of each target direction in the narrowband signal model is calculated based on the full-rank spatial smoothed covariance matrix;

[0010] S4. Based on the estimated value of each target's bearing, construct a nested array of clear signals for different targets and calculate the covariance matrix of the clear signals for different targets;

[0011] S5. Vectorize the covariance matrix of the clean signal to obtain the received signal of the virtual array;

[0012] S6. Split the virtual array into Each contains A virtual linear subarray of array elements is formed; a weighted summation of the covariance matrices of the virtual linear subarrays is performed to obtain a full-rank spatial smoothed covariance matrix of the virtual array; and an updated estimate of each target direction is calculated based on the full-rank spatial smoothed covariance matrix of the virtual array;

[0013] S7. Using the updated estimated value as input, loop through steps S4 to S6. In each loop, the input to step S4 is the updated estimated value obtained in step S6 in the previous loop. Repeat three times to obtain the target direction value.

[0014] As a possible implementation method, S1 specifically includes:

[0015] S10. Configuration by The nested array consists of array elements, where represents the number of array elements in the internal non-undersampled sub-array, Indicates the number of array elements in the outer undersampled subarray;

[0016] S11. Using nested arrays to receive far-field signals incident from different directions a narrowband signal;

[0017] S12. Constructing a narrowband signal model:

[0018] ;

[0019] in, t expresst time, is the array manifold matrix, For the The steering vector corresponding to the target, is the incident signal vector, is an independent and identically distributed Gaussian white noise vector, Represents nested arrays in t The narrowband signal received at all times.

[0020] As a possible implementation, the non-undersampled sub-arrays included in the nested array are specifically: ,

[0021] Among them, m is the array element, Indicates the number of array elements in the internal non-undersampled sub-array;

[0022] The covariance matrix of the non-undersampled subarray is:

[0023] ,

[0024] in, For nested arrays The signal received by each array element.

[0025] As a possible implementation, S3 includes the following sub-steps:

[0026] S30. Split the non-undersampled subarray into Each contains A linear sub-array of elements;

[0027] S31. Perform weighted summation of the covariance matrices of the linear subarrays to obtain a full-rank spatial smoothing covariance matrix;

[0028] S32. Based on the full-rank spatial smoothed covariance matrix, a Root-MUSIC algorithm is used to obtain an estimated value of the direction of each target in the narrowband signal model.

[0029] As a possible implementation, S4 includes the following sub-steps:

[0030] S40 obtains an array manifold estimate of the nested array based on the estimated value of each target orientation;

[0031] S41. Based on the array manifold estimate, the least squares method is used to estimate the source signal, obtaining clear signals for different targets in the nested array.

[0032] S42. Compute the covariance matrix of the clean signals for different targets.

[0033] As a possible implementation, S6 specifically includes the following sub-steps:

[0034] S60. Split the virtual array into Each contains A virtual linear sub-array of elements;

[0035] S61. Weighted summation of the covariance matrix of the virtual linear subarray to obtain a full-rank spatial smoothed covariance matrix of the virtual array;

[0036] S62. Based on the full-rank spatial smoothed covariance matrix of the virtual array, the Root-MUSIC algorithm is used to calculate the updated estimate of each target's position.

[0037] As a possible implementation, S40 is specifically as follows: ,in, Represents the total number of nested array elements, is the array manifold estimate of the nested array, Represents the steering vector in the direction of the estimated value.

[0038] In a second aspect, the present invention provides a CLEAN-based nested array coherent target direction estimation system, comprising:

[0039] Narrowband signal model building unit, configured by The nested array consists of array elements, where represents the number of array elements in the internal non-undersampled sub-array, represents the number of elements in the external undersampling subarray; the nested array is used to receive the far-field incident from different directions. narrowband signal; build a narrowband signal model: ,in, t express t time, is the array manifold matrix, For the The steering vector corresponding to the target, is the incident signal vector, is an independent and identically distributed Gaussian white noise vector, Represents nested arrays in t The narrowband signal received at all times;

[0040] The estimated value solving unit of each target position is based on the spatial smoothing method to divide the non-undersampled subarray into Each contains The linear subarray of array elements is constructed; the covariance matrices of the linear subarrays are weighted and summed to obtain a full-rank spatial smoothed covariance matrix; based on the full-rank spatial smoothed covariance matrix, the Root-MUSIC algorithm is used to obtain an estimated value of each target direction;

[0041] The covariance matrix solving unit for clear signals of different targets obtains the array manifold estimation value of the nested array based on the estimated value of each target's orientation; based on the array manifold estimation value, the least squares method is used to perform source signal estimation to obtain the clear signals of the nested array for different targets; and the covariance matrix of the clear signals of different targets is calculated;

[0042] The estimated value solving unit for each target position update divides the virtual array into Each contains The covariance matrices of the virtual linear subarrays are weighted summed to obtain the full-rank spatial smoothed covariance matrix of the virtual array; based on the full-rank spatial smoothed covariance matrix of the virtual array, the Root-MUSIC algorithm is used to calculate the updated estimate of each target direction.

[0043] In a third aspect, the present invention provides a terminal comprising a processor and a communication interface coupled to the processor, wherein the processor is configured to run a computer program or instruction to implement the CLEAN-based nested array coherent target azimuth estimation method provided in the first aspect.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. The CLEAN-based nested array coherent target azimuth estimation method provided by the present invention utilizes the non-undersampled subarrays in the nested array to perform initial estimation of the coherent target azimuth, and has a certain robustness for the initial estimation. Based on the azimuth estimation value, combined with the CLEAN algorithm, clear signals belonging to different targets are constructed, which can effectively filter out other azimuth signals and noise, greatly reducing the coherence between signals.

[0046] 2. The CLEAN-based nested array coherent target azimuth estimation method proposed in this paper calculates the covariance matrix of the nested array for different targets. It then vectorizes the equivalent virtual domain signal corresponding to the augmented virtual array, using this to perform high-resolution target azimuth estimation, effectively leveraging the aperture advantage of the nested array. After updating the azimuth estimate, it is re-substituted into the CLEAN algorithm for iteration to further improve estimation accuracy, thereby achieving high-resolution azimuth estimation suitable for coherent target scenarios.

[0047] 3. The CLEAN-based nested array coherent target direction estimation method provided by this invention can achieve higher angular resolution with fewer array elements than traditional uniform linear arrays. It can also effectively remove the coherence between signals without sacrificing the array aperture, which is beneficial to improving the performance of subspace-based target direction estimation algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0049] Figure 1 Flowchart of a nested array coherent target direction estimation method based on CLEAN in an embodiment of the present invention;

[0050] Figure 2 Graph showing the input signal-to-noise ratio and the root mean square error of angle estimation calculated using the multiple signal classification method combined with spatial smoothing according to an embodiment of the present invention;

[0051] Figure 3 1. A graph showing a root mean square error (RMS) curve of the snapshot number and angle estimation calculated using a multiple signal classification method combined with spatial smoothing according to an embodiment of the present invention and the method of the present invention;

[0052] Figure 4 The spatial spectrum is calculated by combining a multiple signal classification method with spatial smoothing under the condition of a single sound source in a shallow sea environment according to an embodiment of the present invention;

[0053] Figure 5 This is the spatial spectrum calculated by the method of the present invention under the condition of a single sound source in a shallow sea environment in an embodiment of the present invention. DETAILED DESCRIPTION

[0054] To facilitate a clear description of the technical solutions of the embodiments of the present invention, the words "first" and "second" are used in the embodiments of the present invention to distinguish between identical or similar items with substantially the same functions and effects. For example, the first threshold and the second threshold are merely used to distinguish between different thresholds and do not limit their order. Those skilled in the art will understand that the words "first" and "second" do not limit the quantity or execution order, and the words "first" and "second" do not necessarily mean different.

[0055] It should be noted that, in the present invention, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the present invention should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0056] In the present invention, "at least one" means one or more, and "more" means two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can mean: the existence of A alone, the existence of A and B at the same time, and the existence of B alone, where A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. The following at least one item (item) or similar expressions refers to any combination of these items, including any combination of single items (items) or plural items (items). For example, at least one item (item) of a, b or c can mean: a, b, c, the combination of a and b, the combination of a and c, the combination of b and c, or the combination of a, b and c, where a, b, c can be single or plural.

[0057] Existing coherent target azimuth estimation methods based on nested arrays have problems such as high computational complexity and sensitivity to regularization parameters. To address the above problems, the present invention provides a CLEAN-based nested array coherent target azimuth estimation method, system, and terminal. Compared with methods based on uniform linear arrays with the same number of array elements, the mainlobe width is narrower and the sidelobe level is lower, which can achieve high-resolution azimuth estimation suitable for coherent target scenarios.

[0058] In a first aspect, the present invention provides a nested array coherent target direction estimation method based on CLEAN, comprising the following steps:

[0059] S1. Configure a nested array to receive narrowband signals from far-field coherent targets and construct a narrowband signal model.

[0060] As a possible implementation method, S1 specifically includes:

[0061] S10. Configuration by The nested array consists of array elements, where represents the number of array elements in the internal non-undersampled sub-array, Indicates the number of array elements in the outer undersampled subarray;

[0062] As an example of a nested array, A nested array of hydrophones is placed in the seawater at a certain depth to receive narrowband signals incident from different directions.

[0063] S11. Using nested arrays to receive far-field signals incident from different directions a narrowband signal;

[0064] S12. Constructing a narrowband signal model:

[0065] ;

[0066] in, t express t time, is the array manifold matrix, For the The steering vector corresponding to the target, is the incident signal vector, is an independent and identically distributed Gaussian white noise vector, Represents nested arrays in t The narrowband signal received at all times.

[0067] As an example, the position of each element of the nested array in S1 is available Indicates that is the element spacing of the non-undersampled sub-array in the nested array, and the set Specifically:

[0068]

[0069] Where, represents the number of array elements in the internal non-undersampled sub-array, represents the number of elements in the external undersampled sub-matrix, m represents the number of elements in the non-undersampled sub-matrix, and n represents the number of elements in the undersampled sub-matrix. Direction signal, which guides the vector It can be expressed as follows:

[0070]

[0071] Where, , , l =1,2,…, N 1+ N 2, Represents the total number of nested array elements, is the signal wavelength.

[0072] S2. Calculating the covariance matrix of the non-undersampled sub-arrays included in the nested array;

[0073] As a possible implementation, the non-undersampled sub-arrays included in the nested array are specifically: ,

[0074] in,m is the array element of the non-undersampled sub-array, Indicates the number of array elements in the internal non-undersampled sub-array;

[0075] The covariance matrix of the non-undersampled subarray is:

[0076] ,

[0077] in, represents the expectation of a random variable, represents the conjugate transpose operation, For nested arrays The received signal of an array element is usually approximated by the sampling covariance matrix, which is specifically expressed as:

[0078]

[0079] Where, is the number of sampling points.

[0080] S3. Split the non-undersampled subarray into Each contains A linear subarray of array elements is formed, and the covariance matrices of the linear subarrays are weighted summed to obtain a full-rank spatial smoothed covariance matrix. An estimated value of each target direction in the narrowband signal model is calculated based on the full-rank spatial smoothed covariance matrix;

[0081] As a possible implementation, S3 includes the following sub-steps:

[0082] S30. Split the non-undersampled subarray into Each contains A linear sub-array of elements;

[0083] S31. Perform weighted summation of the covariance matrices of the linear subarrays to obtain a full-rank spatial smoothing covariance matrix;

[0084] As an example, the full-rank spatial smoothing covariance matrix for:

[0085]

[0086] Where, For the The sampling covariance matrix corresponding to the subarrays.

[0087] S32. Based on the full-rank spatial smoothed covariance matrix, a Root-MUSIC algorithm is used to obtain an estimated value of the direction of each target in the narrowband signal model.

[0088] As an example, smooth the covariance matrix of the full-rank space Perform eigendecomposition, sort the eigenvalues ​​from large to small, and obtain the subspace composed of eigenvectors, including the noise subspace , the Root-MUSIC algorithm is used to estimate the target direction, specifically:

[0089]

[0090] in, , represents the steering vector, , Represents the phase difference of each array element relative to the first array element. Solving it can get the estimated value of the target direction .

[0091] S4. Based on the estimated value of each target's bearing, construct a nested array of clear signals for different targets and calculate the covariance matrix of the clear signals for different targets;

[0092] As a possible implementation, S4 includes the following sub-steps:

[0093] S40 obtains an array manifold estimate of the nested array based on the estimated value of each target orientation;

[0094] As a possible implementation method, S40 specifically includes: according to the given target position estimation value , you can directly get the manifold estimate of the nested array :

[0095] ,

[0096] in, Represents the total number of nested array elements, is the nested array manifold estimate, Represents the steering vector in the direction of the estimated value. Represents the number of array elements.

[0097] S41. Based on the array manifold estimate, the least squares method is used to estimate the source signal, obtaining clear signals for different targets in the nested array.

[0098] As an example, the least square method is used to estimate the source signal, specifically:

[0099]

[0100] For the Target, delete No. Column obtained , deleted No. OK , nested array for the first A clear signal of a goal It can be expressed as:

[0101] .

[0102] S42. Compute the covariance matrix of the clean signals for different targets.

[0103] As an example, for The covariance matrix of the clear signal is approximated by the sampling covariance matrix:

[0104]

[0105] Where, is the number of sampling points.

[0106] The CLEAN-based nested array coherent target azimuth estimation method provided by the present invention utilizes the non-undersampled subarrays in the nested array to perform initial estimation of the coherent target azimuth, and has a certain robustness for the initial estimation; based on the azimuth estimation value, combined with the CLEAN algorithm, clear signals belonging to different targets are constructed, which can effectively filter out other azimuth signals and noise, greatly reducing the coherence between signals.

[0107] S5. Covariance matrix of the vectorized clean signal: , obtain the receiving signal of the virtual array;

[0108] In the present invention, the specific method of vectorization is not limited.

[0109] S6. Split the virtual array into Each contains A virtual linear subarray of array elements is formed; a weighted summation of the covariance matrices of the virtual linear subarrays is performed to obtain a full-rank spatial smoothed covariance matrix of the virtual array; and an updated estimate of each target direction is calculated based on the full-rank spatial smoothed covariance matrix of the virtual array;

[0110] As a possible implementation, S6 specifically includes the following sub-steps:

[0111] S60. Split the virtual array into Each contains A virtual linear sub-array of elements;

[0112] S61. Weighted summation of the covariance matrix of the virtual linear subarray to obtain a full-rank spatial smoothed covariance matrix of the virtual array;

[0113] As an example, the spatial smoothing method is used to obtain the full-rank spatial smoothing covariance matrix of the virtual array:

[0114]

[0115] Where, For the The target signal The covariance matrix corresponding to the virtual linear subarrays.

[0116] S62. Based on the full-rank spatial smoothed covariance matrix of the virtual array, the Root-MUSIC algorithm is used to calculate the updated estimate of each target's position.

[0117] As an example, Perform eigendecomposition to obtain the noise subspace composed of eigenvectors , the Root-MUSIC algorithm is used to calculate the estimated value of each target position update:

[0118]

[0119] in, , Solving for each target position update yields an estimate: .

[0120] S7. Using the updated estimated value as input, loop through steps S4 to S6. In each loop, the input to step S4 is the updated estimated value obtained in step S6 in the previous loop. Repeat three times to obtain the target direction value.

[0121] The CLEAN-based nested array coherent target azimuth estimation method proposed in this paper calculates the covariance matrix of the nested array for different targets. It then vectorizes the equivalent virtual domain signal corresponding to the virtual array, using this to perform high-resolution target azimuth estimation, effectively leveraging the aperture advantage of the nested array. After updating the azimuth estimate, it is re-substituted into the CLEAN algorithm for iteration to further improve estimation accuracy, thereby achieving high-resolution azimuth estimation suitable for coherent target scenarios.

[0122] In one possible implementation, an 8-element nested array is used to receive the signal. The input signal-to-noise ratio and the root mean square error of the angle estimation calculated by the multiple signal classification method combined with spatial smoothing (ULA-MUSIC+FBSS) and the method of the present invention (NA-CLEAN) are compared. The comparison results are shown in Figure 2It can be seen that when the same array elements are used, the root mean square error of the method of the present invention is lower than that of the multiple signal classification method under different input signal-to-noise ratios. Using the same 8-element nested array, the root mean square error of the snapshot number and angle estimation calculated by the multiple signal classification method based on uniform linear array combined with spatial smoothing (ULA-MUSIC+FBSS) and the nested array-based method of the present invention (NA-CLEAN) is compared. The comparison results are shown in Figure 3 It can be seen that when the same array elements are used, the root mean square error of the proposed method is lower than that of the multiple signal classification method under different snapshot numbers.

[0123] In another possible implementation, under the condition of a single sound source in a simulated shallow sea environment, an 8-element nested array is used to receive the signal, and the spatial spectra calculated by the multiple signal classification method combined with spatial smoothing (ULA-MUSIC+FBSS) and the method of the present invention (NA-CLEAN) are compared. The comparison results are shown in Figures 4 and 5 It can be seen that the method provided by the present invention has a narrower main lobe width and a lower side lobe level than the former.

[0124] The CLEAN-based nested array coherent target azimuth estimation method provided by the present invention can achieve higher angular resolution with a smaller number of array elements compared to traditional uniform linear arrays, and can effectively remove the coherence between signals without losing the array aperture, which is beneficial to the performance improvement of the subspace target azimuth estimation algorithm.

[0125] In a second aspect, the present invention provides a CLEAN-based nested array coherent target direction estimation system, comprising:

[0126] Narrowband signal model building unit, configured by The nested array consists of array elements, where represents the number of array elements in the internal non-undersampled sub-array, represents the number of elements in the external undersampling subarray; the nested array is used to receive the far-field incident from different directions. narrowband signal; build a narrowband signal model: ,in, t express t time, is the array manifold matrix, For the The steering vector corresponding to the target, is the incident signal vector, is an independent and identically distributed Gaussian white noise vector, Represents nested arrays in t The narrowband signal received at all times;

[0127] The estimated value solving unit of each target position is based on the spatial smoothing method to divide the non-undersampled subarray into Each contains The linear subarray of array elements is constructed; the covariance matrices of the linear subarrays are weighted and summed to obtain a full-rank spatial smoothed covariance matrix; based on the full-rank spatial smoothed covariance matrix, the Root-MUSIC algorithm is used to obtain an estimated value of each target direction;

[0128] The covariance matrix solving unit for clear signals of different targets obtains the array manifold estimation value of the nested array based on the estimated value of each target's orientation; based on the array manifold estimation value, the least squares method is used to perform source signal estimation to obtain the clear signals of the nested array for different targets; and the covariance matrix of the clear signals of different targets is calculated;

[0129] The estimated value solving unit for each target position update divides the virtual array into Each contains The covariance matrices of the virtual linear subarrays are weighted summed to obtain the full-rank spatial smoothed covariance matrix of the virtual array; based on the full-rank spatial smoothed covariance matrix of the virtual array, the Root-MUSIC algorithm is used to calculate the updated estimate of each target direction.

[0130] In a third aspect, the present invention provides a terminal comprising a processor and a communication interface coupled to the processor, wherein the processor is configured to run a computer program or instruction to implement the CLEAN-based nested array coherent target azimuth estimation method provided in the first aspect.

[0131] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art may understand and implement other variations of the disclosed embodiments by reviewing the drawings, the disclosure, and the drawings, etc. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple situations. A single processor or other unit can implement several functions listed in the specification. Certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0132] Although the present invention has been described with reference to specific features and embodiments thereof, it will be apparent that various modifications and combinations thereof may be made without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely illustrative of the present invention and are deemed to cover any and all modifications, variations, combinations or equivalents within the scope of the invention. It will be apparent that various modifications and variations of the present invention may be made by those skilled in the art without departing from the spirit and scope of the invention. Thus, the present invention is intended to include such modifications and variations as fall within the scope of the invention and its equivalents.

Claims

1. A nested array coherent target direction estimation method based on CLEAN, characterized in that: The steps include: S1. Configuring a nested array, using the nested array to receive a narrowband signal from a far-field coherent target, and constructing a narrowband signal model; S2. Calculating the covariance matrix of the non-undersampled sub-arrays included in the nested array; S3. Split the non-undersampled subarray into Each contains A linear subarray of array elements is formed, covariance matrices of the linear subarrays are weighted summed to obtain a full-rank spatial smoothed covariance matrix, and an estimated value of each target direction in the narrowband signal model is calculated based on the full-rank spatial smoothed covariance matrix; S4 based on the estimated value of the direction of each target, constructing a nested array of clear signals for different targets, calculating the covariance matrix of the clear signal of different targets; S5 vectorizes the covariance matrix of the clear signal to obtain a virtual array of received signals; S6. Splitting the virtual array into Each contains A virtual linear subarray of array elements; performing weighted summation on the covariance matrices of the virtual linear subarrays to obtain a full-rank spatial smoothed covariance matrix of the virtual array, and calculating an updated estimate of each target orientation based on the full-rank spatial smoothed covariance matrix of the virtual array; S7. Using the updated estimated value as input, loop through steps S4 to S6. In each loop, the input to step S4 is the updated estimated value obtained in step S6 in the previous loop. Repeat three times to obtain the target direction value.

2. The CLEAN-based nested array coherent target direction estimation method according to claim 1, characterized in that: Said S1 specifically includes: S10. Configuration by The nested array consists of array elements, where represents the number of elements in the inner non-undersampled subarray, represents the number of elements in the outer undersampled subarray; S11. Using the nested array to receive far-field signals incident from different directions a narrowband signal; S12. Constructing a narrowband signal model: ； in, t express t time, is the array manifold matrix, For the The steering vector corresponding to the target, is the incident signal vector, is an independent and identically distributed Gaussian white noise vector, N Indicates the total number of elements in the nested array, Represents nested arrays in t The narrowband signal received at all times.

3. The CLEAN-based nested array coherent target direction estimation method according to claim 2, characterized in that: The non-undersampled subarrays included in the nested array are specifically: ， in, m For the array element, Indicates the number of elements in the internal non-undersampled subarray; The covariance matrix of the non-undersampled subarray is: ， in, Before nested arrays The signal received by each array element.

4. The CLEAN-based nested array coherent target direction estimation method according to claim 1, characterized in that: The S3 includes the following sub-steps: S30. Based on the spatial smoothing method, the non-undersampled subarray is divided into Each contains A linear sub-array of elements; S31. Weighted summation of the covariance matrix of the linear subarray to obtain a full-rank spatial smoothing covariance matrix; S32. Based on the full-rank spatial smoothed covariance matrix, a Root-MUSIC algorithm is used to obtain an estimated value of the direction of each target in the narrowband signal model.

5. The CLEAN-based nested array coherent target direction estimation method according to claim 2, characterized in that: The S4 includes the following sub-steps: S40 obtains an array manifold estimate of the nested array based on the estimated value of each target orientation; S41. Based on the array manifold estimate, the least squares method is used to estimate the source signal to obtain a clear signal for different targets of the nested array; S42. Compute the covariance matrix of the clean signals for different targets.

6. The CLEAN-based nested array coherent target direction estimation method according to claim 1, characterized in that: The S6 specifically includes the following sub-steps: S60. Based on the spatial smoothing method, the virtual array is divided into Each contains A virtual linear sub-array of elements; S61. Weighted summation of the covariance matrices of the virtual linear subarrays to obtain a full-rank spatially smoothed covariance matrix of the virtual array; S62. Based on the full-rank spatial smoothed covariance matrix of the virtual array, a Root-MUSIC algorithm is used to calculate an updated estimate of each target position.

7. The CLEAN-based nested array coherent target direction estimation method according to claim 5, characterized in that: The S40 is specifically: ,in, Represents the total number of nested array elements, is the array manifold estimate for the nested array, Represents the steering vector in the direction of the estimated value.

8. A CLEAN-based nested array coherent target direction estimation system, characterized in that: include: Narrowband signal model building unit, configured by The nested array consists of array elements, where represents the number of elements in the inner non-undersampled subarray, represents the number of elements of the outer undersampling subarray; the nested array is used to receive far-field signals incident from different directions. narrowband signal; build a narrowband signal model: ,in, t express t time, is the array manifold matrix, For the The steering vector corresponding to the target, is the incident signal vector, is an independent and identically distributed Gaussian white noise vector, N Indicates the total number of elements in the nested array, Represents nested arrays in t The narrowband signal received at all times; The estimation value solving unit of each target position is configured to divide the non-undersampled subarray into Each contains A linear subarray of array elements; performing weighted summation on the covariance matrices of the linear subarrays to obtain a full-rank spatial smoothed covariance matrix; and obtaining an estimated value of each target direction using a Root-MUSIC algorithm based on the full-rank spatial smoothed covariance matrix; A covariance matrix solving unit for clear signals of different targets obtains an array manifold estimation value of the nested array based on the estimated value of each target orientation; performs source signal estimation using a least squares method based on the array manifold estimation value to obtain clear signals of the nested array for different targets; and calculates the covariance matrix of the clear signals of different targets; The estimated value solving unit for each target position update vectorizes the covariance matrix of the clear signal to obtain the received signal of the virtual array, and divides the virtual array into Each contains A virtual linear subarray of array elements; performing weighted summation on the covariance matrices of the virtual linear subarrays to obtain a full-rank spatial smoothed covariance matrix of the virtual array; and calculating an updated estimate of each target orientation using a Root-MUSIC algorithm based on the full-rank spatial smoothed covariance matrix of the virtual array; The target direction value solving unit takes the updated estimated value as input, and cyclically executes the covariance matrix solving unit of the clear signals of different targets and the estimated value solving unit of each target direction update. In each cycle, the input of the covariance matrix solving unit of the clear signals of different targets is the updated estimated value obtained by the estimated value solving unit of each target direction update in the previous cycle; the cycle is repeated three times to obtain the target direction value.

9. A terminal comprising a processor and a communication interface coupled to the processor, wherein the processor is configured to execute a computer program or instruction to implement the CLEAN-based nested array coherent target direction estimation method according to any one of claims 1 to 7.

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