Rapid high-precision near-field positioning method suitable for non-uniform noise

Abstract

The invention belongs to the technical field of array signal high-precision positioning, and particularly relates to a rapid high-precision near-field positioning method suitable for non-uniform noise. The invention provides a near-field positioning method based on joint symmetric matrix decomposition and noise power estimation aiming at the problems that the positioning precision is reduced, the calculation complexity is high and the like in a non-uniform noise environment in the existing near-field positioning method, and the method adopts rapid inexact block coordinate descent to carry out alternate optimization. A closed-form solution exists in each iteration, analysis and solution can be carried out without line search, and the calculation complexity is reduced. The method breaks through the performance bottleneck of a traditional near-field source positioning method under non-uniform noise, has the advantages of being high in positioning precision, low in calculation complexity, high in environmental adaptability and the like, is more excellent in performance in a large-size antenna array scene, and can be applied to near-field positioning systems of radar, sonar, communication and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-precision positioning of array signals, and in particular relates to a fast and high-precision near-field positioning method suitable for non-uniform noise. Background Art

[0002] Array signal processing technology, a core tool for modern spatial signal detection and localization, plays a crucial role in fields such as sonar, wireless communications, and radar. Traditional far-field source localization techniques, based on the plane wave assumption, achieve high-precision positioning through a single parameter (DOA) estimation. This has led to mature algorithms such as maximum likelihood estimation (MLE) and multiple signal classification (MUSIC). However, these methods are limited by the far-field model and are only applicable to scenarios where the signal source distance is significantly greater than the array aperture. They are unable to meet the demand for short-range, high-precision positioning in emerging fields such as smart device interaction, indoor positioning, and medical imaging. With the deepening of application scenarios and the inevitable development of technology, the importance of near-field source localization is becoming increasingly prominent. In the near-field, the signal wavefront exhibits spherical characteristics, requiring simultaneous estimation of the DOA and the distance from the signal source to the array, which significantly increases the parameter dimensionality and computational complexity. Although existing technologies have attempted to extend far-field algorithms to near-field scenarios, their reliance on two-dimensional spectral peak search exponentially increases the computational cost, making it difficult to meet real-time requirements. While high-order statistical methods can distinguish between far-field and near-field sources, they are time-consuming and therefore prohibitive for practical application. Reference "Zhang X, Chen W, Zheng W, et al. Localization of near-field sources: A reduced-dimension MUSIC algorithm[J]. IEEE Communications Letters, 2018, 22(7): 1422-1425." proposes a reduced-dimensionality (RD) MUSIC algorithm for near-field source localization of uniform linear arrays (ULAs). The complex two-dimensional search is reduced to a one-dimensional search. However, this method has significant limitations: the algorithm modeling in the article adopts a Gaussian white noise model, which assumes that the noise power spectrum is uniform and the amplitude follows a Gaussian distribution, which is significantly different from the actual application scenario. In real environments, noise is often formed by the superposition of multiple sources of interference, physical environment inhomogeneity, and internal noise characteristics of the equipment, resulting in its power spectrum density showing a non-uniform distribution in the frequency domain or spatial domain. Non-uniform noise has the characteristics of band limitation, non-stationarity, multi-dimensional coupling, and statistical complexity. The non-uniform covariance matrix in array signal processing cannot be effectively described by the Gaussian white noise model. However, in environments with non-uniform noise, the search and positioning accuracy of the referenced technique significantly decreases, failing to meet practical requirements. Furthermore, the referenced technique performs an orthogonal decomposition of the signal covariance matrix, which is computationally complex and often requires significant runtime in environments with large antennas.

[0003] To address the problem of near-field positioning in non-uniform noise environments, existing methods have attempted to improve positioning robustness in this environment. The patent "A Method for Localizing Narrowband Near-Field Signal Sources in Non-Uniform Noise" eliminates distance unknowns by constructing a Toeplitz matrix and converting non-uniform noise into uniform noise, achieving step-by-step direction of arrival and distance estimation. However, this dual-parameter joint search requires high-dimensional matrix operations and two-dimensional spectrum peak traversal, resulting in high computational complexity. Furthermore, the guidance vector is not constrained, leading to noise subspace contamination and limited positioning accuracy. The patent "A Method for Localizing Near-Field Sound Sources in Non-Uniform Array Element Noise Conditions Based on Ant Colony Optimization" achieves positioning by constructing a maximum likelihood estimation model and solving it using a continuous space ant colony optimization algorithm. However, this method does not address the highly coupled angle and distance parameters in the near-field guidance vector in non-uniform noise. Consequently, the method is highly sensitive to these parameters in low signal-to-noise ratio conditions, resulting in a lack of significant positioning accuracy advantages.

[0004] Currently, there is an urgent need for a near-field source localization method that can achieve low computational complexity and fast speed in a non-uniform noise environment, so as to break through the bottleneck of traditional technologies that are difficult to strike a balance between accuracy and efficiency, and meet the dual needs of real-time and reliability in emerging fields such as radar and communications. Summary of the Invention

[0005] The present invention proposes a fast and high-precision near-field positioning method suitable for non-uniform noise. It adopts inexact block coordinate descent for alternating optimization, combines symmetric matrix decomposition with noise power estimation, and has a closed-form solution in each iteration. It can be solved analytically without line search, thus reducing the computational complexity.

[0006] The technical solution adopted in the present invention is: A fast, high-precision near-field positioning method suitable for non-uniform noise. The positioning signal source is close to the receiving array, the wavefront is a spherical wave, and the phase difference of the signal reaching different array elements is related not only to the angle but also to the distance. Positioning requires simultaneous estimation of angle and distance parameters. At the same time, the array of signal receiving devices is a uniform linear array. The method includes the following steps: S1. Settings M A uniform linear receiving array is used to receive K A near-field signal, K < M , define the total number of snapshots as J , and the superimposed noise on the array source is non-uniform noise, thus obtaining multiple snapshots of the received signal array containing non-uniform noise ; S2, based on the received signal array , obtain the sample covariance matrix, model the near-field positioning problem under non-uniform noise as a joint symmetric matrix decomposition and non-uniform noise power estimation problem, use the fast inexact block coordinate descent method to obtain the symmetric matrix X and the non-uniform noise power matrix Q, take the column space of the symmetric matrix decomposition as the signal subspace, and take the orthogonal complement of the signal subspace as the noise subspace; S3, directing the array of received signals to the matrix The vector elements in are decoupled into a steering matrix containing only angle information and a phase matrix containing the distance-angle coupling relationship; S4. Based on the orthogonality of the noise subspace and the signal subspace, a search matrix containing only angle parameters is constructed by obtaining the noise subspace and the steering matrix containing only angle information. A one-dimensional search is performed on the angle to obtain the angle estimate. ,in, is the signal wavelength, is the array element spacing, Angle value for one-dimensional search; distance parameter It is directly calculated by the least squares method, where After substituting the one-dimensional angle search result, the phase extracted from the phase matrix containing the distance-angle coupling relationship is combined with the angle parameter and the distance parameter to finally determine the source position.

[0007] Furthermore, the specific process of S2 is as follows: S21. Define the receiving signal array as , the sample covariance matrix is ​​obtained as: , S22. Settings is the initial matrix, where each element in the matrix The real part of Satisfy independent sampling uniform distribution , imaginary part Satisfy independent sampling from the standard normal distribution ,Right now , where 1≤ m ≤ M , 1≤ n ≤ K. ; Set the initial non-uniform noise power ,in , Sampling from a Gaussian distribution , is the absolute value symbol; S23, modeling joint symmetric matrix decomposition and non-uniform noise power estimation, using the inexact block coordinate descent method to obtain the symmetric matrix X and the non-uniform noise power matrix Q; S24, generate the final symmetric matrix The orthogonal basis of ; S25. Solve the orthogonal complement of the signal subspace to obtain the noise subspace .

[0008] Furthermore, the specific process of step S23 is as follows: S231, establish the target optimization problem as , is the Frobenius norm, bring in the initial matrix , ; S232, fixed non-uniform noise power , construct subproblems and transform the optimization problem into: , in, ; S233, optimize with the behavior as the target, select the target row to be optimized, record it as i row, 1≤ i ≤ M : , in, , , is a matrix No. Yuan, , , , , , ; S234. Convert the target row into a single variable optimization problem: , in, , , The matrix currently being iterated is i row, definition is a matrix No. Yuan, ; S235, solve the above single variable optimization problem analytically to obtain i Update vector for rows: , in, , , is a matrix The second norm of ; S236, let the original matrix before this iteration No. i Behavior , the currently obtained i The row update vector is ,but ,use Replace the original matrix before this iteration No. i OK , , , ,in, It only indicates the number of iterations; S237, loop through all rows and get the updated matrix , update the non-uniform noise power , To diagonalize the matrix, steps S232 to S236 are repeated until a convergence threshold is met.

[0009] Furthermore, the specific process of step S3 is as follows: S31. Write out the array steering matrix , where the vector element is the near-field steering vector ; S32, near field steering vector Decompose into two matrices by angle and distance and .

[0010] Furthermore, the near-field steering vector in step S31 is specifically: , in, , represents the angle of the near-field source, represents the distance between the near-field source and the reference point, represents the array element spacing, is the signal wavelength, N The number of signal receiving devices on one side.

[0011] The fast and high-precision near-field positioning method suitable for non-uniform noise according to claim 4 is characterized in that the decomposition matrix in step S32 and Specifically: , , in, N The number of signal receiving devices on one side.

[0012] Furthermore, step S4 is specifically as follows: S41. Using the noise subspace and angle-steering matrix that have been solved, construct a dimension-reduction spectrum function; S42, performing a one-dimensional spectrum search in the angle domain, and estimating precise near-field source angle parameters in a non-uniform noise environment according to the peak value of the reduced-dimensional spectrum function; S43. Based on the estimated value of the angle parameter, directly calculate the distance parameter paired with the angle parameter using a least squares criterion.

[0013] Furthermore, the dimension reduction spectrum function in step S41 is: , in, , is the angle-steering matrix, is the noise subspace, , 1≤ k ≤ K。

[0014] Furthermore, the accurate near-field source angle parameter estimated in the non-uniform noise environment according to the peak value of the dimensionality reduction spectrum function in step S42 is: , in, is the signal wavelength, is the array element spacing.

[0015] Furthermore, the pairing relationship between the angle parameter and the distance parameter in step S43 is determined by the following formula: , in, The phase is extracted from the phase matrix containing the distance-angle coupling relationship after substituting the one-dimensional angle search result.

[0016] The beneficial effects of the present invention are: 1. This method is used in near-field source positioning scenarios with non-uniform noise. A model for receiving near-field signals by multiple signal receiving devices is established to ensure that all signal receiving devices can receive near-field signal arrays containing dual parameters of angle and distance. A method for generating non-uniform noise in a realistic environment is proposed, which forms a signal receiving environment that conforms to reality, solves the problem of over-idealization in positioning, and improves the accuracy of parameter estimation.

[0017] 2. This method aims to address the impact of non-uniform distribution of noise intensity in space or time on the accuracy of subspace decomposition, and establishes a block upper bound continuous iterative algorithm for vectors containing non-uniform noise. By decomposing the target matrix to form a low-rank matrix, an orthogonal basis of the low-rank matrix is ​​generated to obtain the signal subspace, and the orthogonal complement of the signal subspace is taken to obtain the noise subspace.

[0018] 3. To address the problem of long search time of the ordinary Music algorithm, this method proposes a fast uncertain fast coordinate descent algorithm, which effectively reduces the search and positioning time and realizes accurate positioning estimation of near-field sources containing non-uniform noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a flowchart of the method steps of the present invention.

[0020] Figure 2 Schematic diagram of the received signal of the present invention.

[0021] Figure 3 This is a comparison chart of positioning time.

[0022] Figure 4 Schematic diagram of angle domain spatial spectrum comparison.

[0023] Figure 5 A schematic diagram showing the comparison of positioning angle errors.

[0024] Figure 6 A schematic diagram showing the comparison of positioning distance errors. DETAILED DESCRIPTION

[0025] The technical solution of the present invention is described in detail below with reference to the accompanying drawings.

[0026] like Figure 1 As shown, the present invention is a fast and high-precision near-field positioning method suitable for non-uniform noise, and its specific steps are as follows: S1. The located signal source is close to the receiving array, and the wavefront is a spherical wave. The phase difference of the signal reaching different array elements is not only related to the angle, but also to the distance. Positioning requires the simultaneous estimation of angle and distance parameters. At the same time, the array of signal receiving devices is a uniform linear array. M uniform linear receiving arrays are set to receive K near-field signals, K<M, and the total number of snapshots is defined as J, and the superimposed noise on the array source is non-uniform noise, thereby obtaining a receiving signal array with non-uniform noise for multiple snapshots. ; like Figure 2As shown in the figure, there are K near-field uncorrelated signal sources incident on a symmetrical uniform linear array (ULA) arranged along the x-axis. The array consists of M=2N+1 signal receiving devices with an element spacing of d. The central signal receiving device is signal receiving device 0, the leftmost signal receiving device is -N, and the rightmost signal receiving device is N. The direction of arrival (DOA) and distance from the array of the kth signal source (k=1,2,...,K) are respectively given by the parameters ( , ) representation.

[0027] S2. Based on the multi-snapshot received signal, the sample covariance matrix is ​​obtained. The near-field positioning problem under non-uniform noise is modeled as a joint symmetric matrix decomposition and non-uniform noise power estimation problem. A fast inexact block coordinate descent method is used to obtain the symmetric matrix X and the non-uniform noise power matrix Q. The column space of the symmetric matrix decomposition is taken as the signal subspace, and the orthogonal complement of the signal subspace is taken as the noise subspace. Step S2 includes the following steps: S21, based on the received signal array , and obtain the signal covariance matrix: , in, is the number of snaps; In step S21, the signal array is received It is derived from the following: The actual observation signal of the mth (m = -N, ..., -1, 0, 1, ..., N) signal receiving device can be expressed as: , in, , , represents the signal from the kth signal source, represents non-uniform noise, represents the angle of the kth sound source, Represents the range between the kth signal source and the reference point, represents the array element spacing, is the signal wavelength. The actual observed signal array of the array is: , S22. Settings is the initial matrix, where each element in the matrix The real part of Satisfy independent sampling uniform distribution , imaginary part Satisfy independent sampling from the standard normal distribution ,Right now , where 1≤m≤M, 1≤n≤K. Set the initial non-uniform noise power ,in , Sampling from a Gaussian distribution , is the absolute value symbol.

[0028] Modeling joint symmetric matrix decomposition and non-uniform noise power estimation, using the inexact block coordinate descent method, to obtain the symmetric matrix X and the non-uniform noise power matrix Q, that is, step S23 includes the following steps: S231, the target optimization problem is , is the Frobenius norm, and the initial matrix is , ; The intermediate matrix product in step S231 is expressed as: , in, , .

[0029] S232, fixed non-uniform noise power , construct subproblems and transform the optimization problem into: , in, ; Next, optimize with the row as the target, ignore the items irrelevant to the target row, and define is a matrix No. Yuan, then the target row i to be optimized is expressed as: , Expanding the quadratic term yields an expression with the same optimal solution, which is the formula obtained in step S233.

[0030] S233. Optimize with the row as the target, select the target row to be optimized, and record it as the i-th row (1≤i≤M): , in, , , is a matrix No. Yuan, , , , , , ; Due to the quadratic term The Lipschitz continuity of can be used to find the upper bound of the objective function. Specifically, by introducing the Lipschitz continuity constraint and adding a regularization term, the quadratic term of the original objective function is approximated: According to the Lipschitz continuity constraint , in, yes The Lipschitz constant, which can be .

[0031] The target line Target item in Replace the above at point The upper bound of the evaluation is the target row function The optimization problem is transformed into a univariate convex optimization problem, and the formula in step S234 is obtained after sorting.

[0032] S234. Convert the target row into a single variable optimization problem: , in, , , The matrix currently being iterated The i-th row of is a matrix No. Yuan, .

[0033] S235, obtain the update vector of the i-th row by analytically solving the above single variable optimization problem Step S235 analyzes and solves the single variable optimization problem in S234 to obtain the update vector of the i-th row: , in, , .

[0034] S236, let the original matrix before this iteration The i-th behavior , the currently obtained update vector for row i is ,but ,use Replace the original matrix before this iteration No. i OK , , , ,in, It only indicates the number of iterations; S237, loop through all rows and get the updated matrix , update the non-uniform noise power , To diagonalize the matrix, repeat steps S232 to S236 until the convergence threshold is met; S24, generate the final symmetric matrix The orthogonal basis of ; The specific process of step S24 is: Signal subspace By decomposing the matrix After orthogonalization, its mathematical expression is: , Here, orth(⋅) represents the orthogonalization operation on the matrix column vectors, and the generated orthogonal matrix column space is spanned into the column space of the original matrix.

[0035] S25 solves the orthogonal complement of the signal subspace and obtains the noise subspace ; Step S3 directs the array of received signals to the matrix The vector elements in are decoupled into a steering matrix containing only angle information and a phase matrix containing the distance-angle coupling relationship; Step S3 includes the following steps: S31. Write out the array steering matrix , where the vector element is the near-field steering vector ; Step S31: The near-field steering vector is written as : , in, , represents the angle of the near-field source, represents the distance between the near-field source and the reference point, represents the array element spacing, is the signal wavelength, N The number of signal receiving devices on one side.

[0036] S32, near field steering vector Decompose into two matrices by angle and distance and ; The decomposition calculation formula of step S32 is: , Wherein, N is the number of signal receiving devices on a single side.

[0037] S4. Based on the orthogonality of the noise subspace and the signal subspace, a search matrix containing only angle parameters is constructed by obtaining the noise subspace and the steering matrix containing only angle information. A one-dimensional search is performed on the angle to obtain the angle estimate. .in, is the signal wavelength, is the array element spacing, The angle value for one-dimensional search. Distance parameter Directly calculated by the least squares method ,in, After substituting the one-dimensional angle search result, the phase extracted from the phase matrix containing the distance-angle coupling relationship is combined with the angle parameter and the distance parameter to finally determine the source position, specifically: S41. Using the noise subspace and angle-steering matrix that have been solved, construct a dimension-reduction spectrum function; The two-dimensional spectrum function is expressed as: , in, , is the noise subspace. The two-dimensional spectrum function is regarded as an optimization problem with the following constraints: , , written as: . , The Lagrange multiplier method is used to solve the above optimization problem. By introducing the Lagrange constant, the cost function is obtained as: , Where is the Lagrange constant. Take the partial derivative of the cost function, set the partial derivative equal to 0, and combine the constraints to derive: , Substitute the above formula into the two-dimensional spectrum function optimization problem , then the optimization problem can be rewritten as: , Where 1≤ k ≤ K .

[0038] S42, performing a one-dimensional spectrum search in the angle domain, and estimating precise near-field source angle parameters in a non-uniform noise environment according to the peak value of the reduced-dimensional spectrum function; Step S42 solves the optimization problem in step S41 to obtain the precise near-field source angle parameter in the non-uniform noise environment, which can be expressed as: , in, is the signal wavelength, is the array element spacing.

[0039] S43. Based on the estimated value of the angle parameter, directly calculate the distance parameter paired with the angle parameter by using a least squares criterion; Step S43 directly calculates the distance parameter paired with the angle parameter using the least squares criterion. The specific process is as follows: According to the one-dimensional spectrum search results, The estimated vector of is updated as follows: , definition , angle (·) represents the phase extraction operation. Based on the least squares criterion, the optimization objective of the distance can be written as: , in, . is the estimation error (k=1,2,…,K). The least squares solution is: , in, The distance parameter finally paired with the angle parameter is: , in, The phase is extracted from the phase matrix containing the distance-angle coupling relationship after substituting the one-dimensional angle search result.

[0040] like Figure 3 As shown in the reference "Zhang X, Chen W, Zheng W, et al. Localization ofnear-field sources: A reduced-dimension MUSIC algorithm[J]. IEEECommunications Letters, 2018, 22(7): 1422-1425."", the reduced-dimension MUSIC algorithm uses eigendecomposition to obtain the noise subspace, which is relatively inefficient and cannot meet the fast requirements. However, this method greatly improves the calculation speed in large-scale antenna arrays and has extremely excellent performance.

[0041] like Figure 4As shown in the reference "Zhang X, Chen W, Zheng W, et al. Localization of near-field sources: A reduced-dimension MUSIC algorithm[J]. IEEE Communications Letters, 2018, 22(7): 1422-1425.", the reduced-dimension MUSIC algorithm uses eigendecomposition to obtain the noise subspace. Under non-uniform noise interference, the resolution is extremely low and two close near-field sources cannot be distinguished. However, the method of the present invention can clearly and effectively distinguish close near-field sources with extremely high resolution.

[0042] like Figure 5 As shown in the reference "Zhang X, Chen W, Zheng W, et al. Localization of near-field sources: A reduced-dimension MUSIC algorithm[J]. IEEE Communications Letters, 2018, 22(7): 1422-1425.", the reduced-dimension MUSIC algorithm uses eigendecomposition to obtain the noise subspace. The resulting positioning results have a root mean square error (RMSE) of the arrival angle exceeding 1 at low signal-to-noise ratios and only become stable when the signal-to-noise ratio reaches 10 dB or above. However, the method of the present invention has a root mean square error of the arrival angle below 1 at low signal-to-noise ratios and approaches 0 when the signal-to-noise ratio is around 5 dB, and the convergence speed is extremely fast.

[0043] like Figure 6 As shown in the reference "Zhang X, Chen W, Zheng W, et al. Localization of near-field sources: A reduced-dimension MUSIC algorithm[J]. IEEE Communications Letters, 2018, 22(7): 1422-1425."", the reduced-dimension MUSIC algorithm uses eigendecomposition to obtain the noise subspace. The resulting positioning results have a root mean square error of more than 5 at low signal-to-noise ratios, resulting in poor positioning accuracy. However, the root mean square error of the distance of the method proposed in the present invention is less than half of that of the method, and converges rapidly. Compared with the method proposed in the present invention, the accuracy is several times higher, the positioning error is very small, and it is suitable for various environments.

[0044] In summary, the present invention proposes a fast and high-precision near-field positioning method suitable for non-uniform noise. In view of the problems of existing near-field positioning methods such as reduced positioning accuracy and high computational complexity in non-uniform noise environments, the present invention proposes a near-field positioning method based on joint symmetric matrix decomposition and noise power estimation. This method uses fast uncertain block coordinate descent for alternating optimization. Each iteration has a closed-form solution, which can be solved analytically without line search, reducing computational complexity. This method breaks through the performance bottleneck of traditional near-field source positioning methods under non-uniform noise, and has the characteristics of high positioning accuracy, low computational complexity and strong environmental adaptability. It performs better in large-scale antenna array scenarios and can be applied to near-field positioning systems such as radar, sonar, and communications.

Claims

1. A fast and high-precision near-field positioning method suitable for non-uniform noise, characterized in that: The steps include: S1. Settings M A uniform linear receiving array is used to receive K A near-field signal, K < M , define the total number of snapshots as J , and the superimposed noise on the array source is non-uniform noise, thus obtaining multiple snapshots of the received signal array containing non-uniform noise ; S2, based on the received signal array , obtain the sample covariance matrix, model the near-field positioning problem under non-uniform noise as a joint symmetric matrix decomposition and non-uniform noise power estimation problem, use the fast inexact block coordinate descent method to obtain the symmetric matrix X and the non-uniform noise power matrix Q, take the column space of the symmetric matrix decomposition as the signal subspace, and take the orthogonal complement of the signal subspace as the noise subspace; S3, directing the array of received signals to the matrix The vector elements in are decoupled into a steering matrix containing only angle information and a phase matrix containing the distance-angle coupling relationship; S4. Based on the orthogonality of the noise subspace and the signal subspace, a search matrix containing only angle parameters is constructed by obtaining the noise subspace and the steering matrix containing only angle information. A one-dimensional search is performed on the angle to obtain the angle estimate. ,in, is the signal wavelength, is the array element spacing, Angle value for one-dimensional search; distance parameter It is directly calculated by the least squares method, where After substituting the one-dimensional angle search result, the phase extracted from the phase matrix containing the distance-angle coupling relationship is combined with the angle parameter and the distance parameter to finally determine the source position.

2. A fast and high-precision near-field positioning method suitable for non-uniform noise according to claim 1, characterized in that: The specific process of S2 is as follows: S21. Define the receiving signal array as , the sample covariance matrix is ​​obtained as: ， S22. Settings is the initial matrix, where each element in the matrix The real part of Satisfy independent sampling uniform distribution , imaginary part Satisfy independent sampling from the standard normal distribution ,Right now , where 1≤ m ≤ M , 1≤ n ≤ K. ; Set the initial non-uniform noise power ,in , Sampling from a Gaussian distribution , is the absolute value symbol; S23, modeling joint symmetric matrix decomposition and non-uniform noise power estimation, using the inexact block coordinate descent method to obtain the symmetric matrix X and the non-uniform noise power matrix Q; S24, generate the final symmetric matrix The orthogonal basis of ; S25. Solve the orthogonal complement of the signal subspace to obtain the noise subspace .

3. A fast and high-precision near-field positioning method suitable for non-uniform noise according to claim 2, characterized in that: The specific process of step S23 is as follows: S231, establish the target optimization problem as , is the Frobenius norm, bring in the initial matrix , ; S232, fixed non-uniform noise power , construct subproblems and transform the optimization problem into: ， in, ; S233, optimize with the behavior as the target, select the target row to be optimized, record it as i row, 1≤ i ≤ M : ， in, , , is a matrix No. Yuan, , , , , , ; S234. Convert the target row into a single variable optimization problem: ， in, , , The matrix currently being iterated is i Row, definition is a matrix No. Yuan, ; S235, solve the above single variable optimization problem analytically to obtain i Update vector for rows: ， in, , , is a matrix The second norm of ; S236, let the original matrix before this iteration No. i Behavior , the currently obtained i The row update vector is ,but ,use Replace the original matrix before this iteration No. i OK , , , ,in, It only indicates the number of iterations; S237, loop through all rows and get the updated matrix , update the non-uniform noise power , To diagonalize the matrix, steps S232 to S236 are repeated until a convergence threshold is met.

4. The fast and high-precision near-field positioning method applicable to non-uniform noise according to claim 1, characterized in that: The specific process of step S3 is as follows: S31. Write out the array steering matrix , where the vector element is the near-field steering vector ; S32, near field steering vector Decompose into two matrices by angle and distance and .

5. The fast and high-precision near-field positioning method applicable to non-uniform noise according to claim 4, characterized in that: The near-field steering vector in step S31 is specifically: ， in, , represents the angle of the near-field source, represents the distance between the near-field source and the reference point, represents the array element spacing, is the signal wavelength, N The number of signal receiving devices on one side.

6. The fast and high-precision near-field positioning method applicable to non-uniform noise according to claim 4, characterized in that: The decomposition matrix in step S32 and Specifically: ， ， in, N The number of signal receiving devices on one side.

7. The fast and high-precision near-field positioning method applicable to non-uniform noise according to claim 1, characterized in that: Step S4 is specifically as follows: S41. Using the noise subspace and angle-steering matrix that have been solved, construct a dimension-reduction spectrum function; S42, performing a one-dimensional spectrum search in the angle domain, and estimating precise near-field source angle parameters in a non-uniform noise environment according to the peak value of the reduced-dimensional spectrum function; S43. Based on the estimated value of the angle parameter, directly calculate the distance parameter paired with the angle parameter using a least squares criterion.

8. The fast and high-precision near-field positioning method applicable to non-uniform noise according to claim 7, characterized in that: The dimension reduction spectrum function in step S41 is: ， in, , is the angle-steering matrix, is the noise subspace, , 1≤ k ≤ K。 9. The fast and high-precision near-field positioning method applicable to non-uniform noise according to claim 7, characterized in that: The accurate near-field source angle parameter estimated in the non-uniform noise environment according to the peak value of the dimension reduction spectrum function in step S42 is: ， in, is the signal wavelength, is the array element spacing.

10. The fast and high-precision near-field positioning method applicable to non-uniform noise according to claim 7, characterized in that: The pairing relationship between the angle parameter and the distance parameter in step S43 is determined by the following formula: ， in, The phase is extracted from the phase matrix containing the distance-angle coupling relationship after substituting the one-dimensional angle search result.

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