MUSIC direction finding method and system

Abstract

The invention discloses a MUSIC direction finding method and system, and belongs to the field of array signal processing and high-performance numerical calculation. According to the method, in the MUSIC characteristic decomposition step, a row maximum value set is innovatively introduced and maintained, after each Givens rotation, a maximum value record is selectively updated by judging whether a non-direct change row meets the condition of'failure of a historical maximum value 'or'appearance of a new maximum value' or not, so that the maximum value of the non-direct change row does not meet the condition of'failure of a historical maximum value 'or'appearance of a new maximum value'. Therefore, the accuracy of tracking information is ensured without global scanning, and the addressing complexity is reduced from O (M2) to O (k * M) (k is far less than M) while the convergence of the algorithm is ensured. According to the method, on the premise of ensuring the direction finding precision, the real-time processing capability of the characteristic decomposition and the whole direction finding process is greatly improved, and the method is suitable for a direction-of-arrival estimation scene in which a large-scale array has a high requirement on the real-time performance.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing and high-performance numerical computing, and relates to a fast MUSIC direction finding method and device based on Jacobi eigendecomposition with maximum tracking, which is particularly suitable for large-scale arrays with high real-time requirements for direction of arrival (DOA) estimation. Background Technology

[0002] Direction of arrival (DOA) estimation is one of the core technologies of modern radar, sonar, and wireless communication systems. The MUSIC algorithm, as a super-resolution direction finding algorithm, is widely used, but its core step of "eigenvalue decomposition of array covariance matrix" has high computational complexity, which has become the main bottleneck restricting real-time performance.

[0003] For an M×M covariance matrix, the Jacobi method is commonly used for eigenvalue decomposition. This method requires a full matrix scan in each iteration to find the off-diagonal element with the largest absolute value as the rotation target. The time complexity of this addressing operation is O(M). 2 When the number of array elements is large or the system requires a high update rate, this step is time-consuming and difficult to meet the real-time processing requirements.

[0004] Existing acceleration solutions either rely on parallel computation on general-purpose processors (which consumes a lot of power) or sacrifice accuracy by simplifying the algorithm, neither of which effectively solves the inherent addressing efficiency problem of the Jacobi method. Therefore, a novel eigenvalue decomposition method is needed that can significantly reduce the addressing overhead while maintaining the numerical accuracy of the Jacobi method. Summary of the Invention

[0005] The purpose of this invention is to overcome the problems of complex computation and poor real-time performance of the feature decomposition steps in existing MUSIC algorithms, and to provide a fast MUSIC direction finding method and device based on Jacobi feature decomposition with maximum value tracking, which significantly improves the real-time performance of MUSIC direction finding algorithms.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A fast MUSIC direction finding method based on maximum value tracking Jacobi eigendecomposition specifically includes the following process:

[0008] Step 1: Receive spatial signals through an N-element sensor array to obtain an array output data matrix X of K snapshots; and perform preprocessing on the data matrix X, including down-conversion, filtering, and digitization.

[0009] Step 2, according to the formula in(·) HThe conjugate transpose is used to calculate the sampling covariance matrix R, and the correlation between the received signals of each array element is obtained. Through the real-valued method based on the real part-imaginary part solution, a 2N×2N real symmetric matrix A corresponding to R is obtained. Matrix A contains all the information of the original complex covariance matrix R.

[0010] Step 3: Using the real symmetric matrix A as input, perform Jacobi eigenvalue decomposition based on maximum value tracking to obtain its eigenvalues ​​D_A and eigenvectors V_A;

[0011] Step 4: Based on the correspondence used in the realization process, extract N effective eigenvalues ​​from D_A to form the eigenvalues ​​D_R corresponding to the covariance matrix R; at the same time, recover the complex eigenvector matrix V_R of the covariance matrix R from the column vectors of V_A through linear combination or selection.

[0012] Step 5: Sort the recovered feature values ​​D_R, and select the feature vectors corresponding to the smallest MD feature values ​​to form the noise subspace Un based on the estimated number of sources D;

[0013] Step 6: Construct a spatial spectrum function using the noise subspace Un, calculate the spectrum function within the angle search range, and obtain the DOA estimate through peak detection.

[0014] Furthermore, the specific process of step 3 is as follows:

[0015] Step 301: Initialize the eigenvector matrix V, where V is an M×M identity matrix, and M = 2N;

[0016] Initialize a candidate set of maximum values; this set is used to store the information of the element with the largest absolute value among the off-diagonal elements of each row, specifically a one-dimensional array maxValues ​​of length M and a one-dimensional array maxIndices of length M; maxValues[i] stores the maximum value among the off-diagonal elements of the i-th row, and maxIndices[i] stores the column index corresponding to maxValues[i].

[0017] Step 302: Calculate the global maximum value in the candidate set of maximum values, globalMax = max(maxValues[i]). If globalMax is less than the preset tolerance ε, the algorithm converges, outputs the eigenvalues ​​and eigenvector matrix V, and proceeds to step 5; otherwise, execute step 303.

[0018] Step 303: From the candidate set of maximum values, find the row index p corresponding to globalMax and obtain its corresponding column index q = maxIndices[p]; (p, q) is the optimal rotation pair for this iteration;

[0019] Step 304: Based on the element A[p,q] at position (p,q) in the real symmetric matrix A and the corresponding diagonal elements A[p,p] and A[q,q], calculate the Givens rotation sine parameter s and cosine parameter c used to clear A[p,q].

[0020] Step 305: Update the p-th row, q-th row, p-th column, and q-th column of matrix A using parameters c and s; simultaneously, update the p-th column and q-th column of the eigenvector matrix V.

[0021] Step 306: Update the candidate set of maximum values ​​using the following update strategy:

[0022] Rescan all off-diagonal elements in rows p and q, and update their corresponding maxValues ​​and maxIndices in the maximum value candidate set;

[0023] Determine if the historical maximum value is in column p or column q. If it is, the historical maximum value is invalid, and all off-diagonal elements in the row need to be rescanned, updating their corresponding maxValues ​​and maxIndices in the maximum value candidate set. If the historical maximum value is not in column p or column q, determine if the value in column p or column q is greater than the historical maximum value. If the updated element in column p or q is greater than the element in the maximum value candidate set for that row, then directly update the corresponding maxValues ​​in the maximum value candidate set for that row to the element in column p or q, and maxIndices to p or q.

[0024] Then return to step 302 to perform the next judgment iteration until convergence.

[0025] A fast MUSIC direction finding system based on maximum tracking Jacobi eigendecomposition, used to implement a fast MUSIC direction finding method based on maximum tracking Jacobi eigendecomposition, characterized by comprising:

[0026] The signal acquisition and preprocessing module is used to convert the analog signals received by the array into digital signals and perform step 1.

[0027] The covariance matrix calculation and realization module is connected to the signal acquisition and preprocessing module. It is used to calculate the sampling covariance matrix and output the corresponding real symmetric matrix, and to execute step 2.

[0028] The fast feature decomposition module is used to implement Jacobi feature decomposition based on maximum value tracking and to execute step 3. The input of this module is a real symmetric matrix A, and this module contains a hardware-based candidate set management unit, which is responsible for implementing the maintenance and update logic of the dynamic maximum value candidate set, thereby efficiently completing feature decomposition.

[0029] The feature pair recovery module selects or calculates the eigenvalues ​​and eigenvectors corresponding to the complex covariance matrix from the eigenvalues ​​and eigenvectors obtained from the eigenvalues ​​and eigenvectors of the real symmetric matrix eigenvalue decomposition, based on the inverse transformation relationship of the realization step; and then executes step 4.

[0030] The noise subspace extraction module is used to perform step 5;

[0031] The spatial spectrum calculation and DOA estimation module is used to perform step 6;

[0032] The system control unit is used to schedule the orderly collaboration of various modules and control the entire data processing logic.

[0033] The beneficial effects of this invention are:

[0034] In the Jacobi eigendecomposition process, a candidate set of maximum values ​​is dynamically maintained, recording the maximum value and its position of the off-diagonal elements in each row of the matrix. Each iteration only performs local updates on a finite number of rows and columns affected by Givens rotations, quickly determining the optimal rotation pair for the next iteration without a global scan.

[0035] This method reduces the addressing complexity from O(M) 2 The computation time is reduced to approximately O(k·M) (k is much smaller than M), significantly improving the decomposition speed without sacrificing numerical accuracy. Furthermore, the algorithm is hardware-friendly, easily implementing dedicated high-performance processing modules, making it particularly suitable for real-time direction-of-arrival (DOA) estimation of large-scale arrays. Examples show that for a 256×256 matrix, the computation time is reduced by approximately 16%, while maintaining the same accuracy as traditional methods. Attached Figure Description

[0036] Figure 1 This is the overall flowchart of the method of the present invention;

[0037] Figure 2 This is a comparison test result diagram of the method of the present invention and the traditional Jacobi classical large value method;

[0038] Figure 3 This is the flowchart of the core part of the method of this invention - fast feature decomposition;

[0039] Figure 4 This is a hardware principle block diagram of a device according to an embodiment of the present invention. Detailed Implementation

[0040] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0041] Firstly, a fast MUSIC direction finding method based on Jacobi eigendecomposition with maximum value tracking is provided, including the following steps:

[0042] Step S1: Array signal acquisition and preprocessing

[0043] (1) Receive spatial signals through an N-element sensor array and obtain the array output data matrix X of K snapshots;

[0044] (2) Preprocess the data matrix X, including downconversion, filtering and digitization.

[0045] Step S2: Covariance Matrix Calculation and Realization

[0046] Calculate the sampling covariance matrix in(·) H This represents the conjugate transpose. Using a real-valued method based on the real-imaginary partial solutions, we obtain a 2N×2N dimensional real symmetric matrix A corresponding to R, which serves as the input for the eigenvalue decomposition.

[0047] Step S3: Fast Feature Decomposition

[0048] (1) Initialization

[0049] Initialize the eigenvector matrix V as an M×M (M=2N) identity matrix.

[0050] Initialize a candidate set of maximum values. This set is used to store the information of the element with the largest absolute value among the off-diagonal elements of each row. Specifically, it is a one-dimensional array of length M, maxValues ​​and maxIndices. maxValues[i] stores the maximum value among the off-diagonal elements of the i-th row, and maxIndices[i] stores the column index corresponding to maxValues[i].

[0051] (2) Convergence judgment

[0052] Calculate the global maximum value in the candidate set of maximum values, globalMax = max(maxValues[i]). If globalMax is less than the preset tolerance ε, the algorithm converges and outputs the eigenvalues ​​(diagonal elements of matrix A) and eigenvectors V, and proceeds to step S5; otherwise, execute step (3).

[0053] (3) Select the optimal rotation pair

[0054] From the candidate set of maximum values, find the row index p corresponding to globalMax and obtain its corresponding column index q = maxIndices[p]. (p, q) is the optimal rotation pair for this iteration.

[0055] (4) Calculate the Givens rotation parameters

[0056] Calculate the Givens rotation sine parameter s and cosine parameter c used to clear A[p,q] based on the element A[p,q] at position (p,q) in matrix A and its corresponding diagonal elements A[p,p] and A[q,q].

[0057] (5) Apply Givens rotation update matrices A and V

[0058] The p-th row, q-th row, p-th column, and q-th column of matrix A are updated using parameters c and s. Simultaneously, the p-th column and q-th column of the eigenvector matrix V are updated.

[0059] (6) Locally update the candidate set of maximum values

[0060] Since the rotation operation in step (5) only changes the p-th row, q-th row, p-th column, and q-th column of matrix A, the maximum value candidate set update strategy is designed as follows:

[0061] Rescan all off-diagonal elements in rows p and q, and update their corresponding maxValues ​​and maxIndices in the maximum value candidate set.

[0062] For other rows, determine if the historical maximum value is in column p or column q. If it is, the historical maximum value is invalid, and all off-diagonal elements of the row need to be rescanned, updating their corresponding maxValues ​​and maxIndices in the maximum value candidate set. If the historical maximum value is not in column p or column q, determine if the value in column p or column q is greater than the historical maximum value. If the updated element in column p or q is greater than any element in the maximum value candidate set for that row, then directly update the corresponding maxValues ​​in the maximum value candidate set for that row to the element in column p or q, and maxIndices to p or q.

[0063] Then return to step (2) to perform the next judgment iteration until convergence.

[0064] Step S4: Recover complex feature pairs

[0065] After performing eigenvalue decomposition on the extended-dimensional real symmetric matrix A, its eigenvalues ​​D_A and eigenvectors V_A are obtained. Based on the correspondence used in the realization process, N effective eigenvalues ​​are extracted from D_A to form the eigenvalues ​​corresponding to the original covariance matrix R; simultaneously, the complex eigenvector matrix of the original covariance matrix R is recovered from the column vectors of V_A through linear combination or selection.

[0066] Step S5: Extract the noise subspace

[0067] The recovered feature values ​​are sorted, and the feature vectors corresponding to the smallest MD feature values ​​are selected to form the noise subspace Un based on the estimated number of sources D.

[0068] Step S6: MUSIC Spatial Spectrum Calculation and DOA Estimation

[0069] A spatial spectral function is constructed using the noise subspace Un. The spectral function is calculated within the angular search range, and the DOA estimate is obtained through peak detection.

[0070] Secondly, a fast MUSIC direction finding hardware device for implementing the above method is provided. The device employs a modular pipeline design and includes:

[0071] 1. Signal acquisition and preprocessing module: used to convert the analog signals received by the array into digital signals, for executing step S1.

[0072] 2. Covariance matrix calculation and realization module: connected to the preprocessing module, used to calculate the sampling covariance matrix and output the corresponding real symmetric matrix, used to execute step S2.

[0073] 3. Fast Feature Decomposition Module: This module implements Jacobi feature decomposition based on maximum value tracking, used to execute step S3. The input to this module is a real symmetric matrix. Its core includes a hardware-based candidate set management unit, specifically responsible for maintaining and updating the dynamic maximum value candidate set, thereby efficiently completing feature decomposition. Specifically, it stores the row maximum value and its column index in a hardware register file, achieves fast global addressing through a comparator network, and implements the "intelligent local update" strategy through customized logic circuits, thus solidifying and efficiently executing the innovative steps of the method at the hardware level.

[0074] 4. Feature Pair Recovery Module: Based on the inverse transformation relationship of the realization step, this module selects or calculates the eigenvalues ​​and eigenvectors corresponding to the original complex covariance matrix from the eigenvalues ​​and eigenvectors obtained from the eigenvalues ​​and eigenvectors of the real symmetric matrix eigenvalue decomposition. This is used to execute step S4.

[0075] 5. Noise subspace extraction module: used to execute step S5.

[0076] 6. Spatial Spectrum Calculation and DOA Estimation Module: Used to perform step S6.

[0077] 7. System Control Unit: Used to schedule the orderly collaboration of the above modules and control the entire data processing pipeline.

[0078] The following is a more specific example:

[0079] Example 1: Fast MUSIC direction finding applied to a 128-element large-scale array.

[0080] 1. Method Implementation

[0081] This embodiment uses the MATLAB software platform to simulate and verify the entire process of the method described in this invention, to demonstrate its feasibility and technical effectiveness. The simulated array is a uniform linear array direction finding scenario with 128 elements. The array receives 8 signals from the far field with azimuth angles of -50°, -40°, -30°, -10°, 0°, 10°, 30°, and 60°, respectively. The number of received snapshots is set to 1024, and the signal-to-noise ratio is 10dB.

[0082] Step S1: Array signal acquisition and preprocessing

[0083] Spatial signals are received by a 128-element sensor array, and an array output data matrix X of 1024 snapshots is obtained, with a dimension of 128×1024.

[0084] Step S2: Covariance Matrix Calculation and Realization

[0085] Calculate the 128×128 complex covariance matrix R, and directly obtain a 256×256 real symmetric matrix A by using a real-valued method based on the real part-imaginary part solution.

[0086] Step S3: Perform Jacobi eigendecomposition based on maximum tracking on the 256×256 real symmetric matrix A.

[0087] (1) Initialization

[0088] Initialize the eigenvector matrix: V = eye(256), which is a 256×256 identity matrix.

[0089] Set the convergence tolerance: ε = 1e -2

[0090] Initialize the maximum value candidate set. Extract the maximum value of all rows maxValues[1:256] and store the column index corresponding to maxValues[1:256] into maxIndices[1:256].

[0091] (2) Convergence judgment

[0092] Calculate the global maximum value in the candidate set of maximum values, globalMax = max(maxValues). If globalMax < ε, the algorithm converges and outputs the eigenvalues ​​(diagonal elements of matrix A) and eigenvectors V; otherwise, execute step (3).

[0093] (3) Select the optimal rotation pair

[0094] Find the row index p of globalMax in maxValues: [~, p] = max(maxValues).

[0095] Get the column index q = maxIndices[p] corresponding to globalMax.

[0096] At this point, the optimal rotation pair (p, q) for this iteration has been determined.

[0097] (4) Calculate the Givens rotation parameters

[0098] Based on the element A[p,q] at position (p,q) in matrix A and its corresponding diagonal elements A[p,p] and A[q,q], calculate the Givens rotation sine parameter s and cosine parameter c used to clear A[p,q]. The core calculation logic is as follows:

[0099]

[0100] (5) Apply Givens rotation update matrices A and V

[0101] Update the rows and columns of A:

[0102] A([p,q],:)=[c,s;s-,c]*A([p,q],:);

[0103] A(:,[p,q])=A(:,[p,q])*[c,-s;s,c];

[0104] Update the eigenvector matrix V:

[0105] V(:,[p,q])=V(:,[p,q])*[c,-s;s,c];

[0106] (6) Locally update the candidate set of maximum values

[0107] Only for rows p and q, rescan all off-diagonal elements of these two rows, and update the maximum values ​​maxValues[p] and maxValues[q] and their corresponding maxIndices[p] and maxIndices[q] of rows p and q of matrix A. For other rows, determine if the historical maximum value is in column p or column q. If it is, the historical maximum value is invalid, and all off-diagonal elements of that row need to be rescanned, updating their corresponding maxValues ​​and maxIndices in the maximum value candidate set. If the historical maximum value is not in column p or column q, determine if the value in column p or column q is greater than the historical maximum value. If the updated element in column p or q is greater than the element in the maximum value candidate set for that row, directly update the corresponding maxValues ​​in the maximum value candidate set for that row to the element in column p or q, and maxIndices to p or q.

[0108] Then return to step (2) to perform the next judgment iteration until convergence.

[0109] Step S4: Recover complex feature pairs

[0110] After performing eigenvalue decomposition on the extended-dimensional real symmetric matrix A, its eigenvalues ​​D_A and eigenvectors V_A are obtained. Based on the correspondence used in the realization process, 64 effective eigenvalues ​​are extracted from D_A to form the eigenvalues ​​corresponding to the original covariance matrix R; simultaneously, the complex eigenvector matrix of the original covariance matrix R is recovered from the column vectors of V_A through linear combination or selection.

[0111] Step S5: Extract the noise subspace

[0112] The recovered feature values ​​are sorted, and based on the number of sources (8), the feature vectors corresponding to the 120 smallest feature values ​​are selected to form the noise subspace Un.

[0113] Step S6: MUSIC Spatial Spectrum Calculation and DOA Estimation

[0114] A spatial spectral function is constructed using the noise subspace Un. The spectral function is calculated within the angular search range, and the DOA estimate is obtained through peak detection.

[0115] 2. Performance Analysis

[0116] (1) Improved Efficiency in Practical Tests: Under the same computer and MATLAB R2021a environment, eigenvalue decomposition was performed on the same 256×256 matrix. Experimental data fully demonstrates that, for large-scale matrices, the present invention (18992 iterations) is on par with the classical large-value method (18992 iterations) in terms of the number of iterations. In addition, by solving the overhead problem of maximum element selection in the classical large-value method, the total computation time of the present invention (23.13 seconds) is reduced by 16% compared with the classical large-value method (27.58 seconds). The larger the matrix dimension, the more significant the technical effect.

[0117] (2) Accuracy consistency: Under large-scale matrices, the classical large value method and the present invention are used for feature decomposition. The extracted noise subspace is completely consistent with the DOA estimation result, which proves that the present invention maintains the numerical accuracy of the algorithm while improving the speed.

[0118] Example 2: Modular Hardware Device

[0119] This embodiment provides an example of a fast MUSIC direction finding hardware device for implementing the method, to illustrate that the fast MUSIC direction finding method can be efficiently implemented using dedicated hardware.

[0120] The device adopts a modular design, with each module operating sequentially under the coordination of the system control unit, forming a complete data processing pipeline. The device mainly includes the following modules:

[0121] (1) Signal acquisition and preprocessing module: realizes signal digitization.

[0122] (2) Covariance matrix calculation and realization module: Calculate and output the real symmetric matrix A.

[0123] (3) Fast Feature Decomposition Module: During the initialization phase, this hardware module stores the current maximum value and its column index of each row of matrix A into a register pair. The iterative process quickly outputs the position of the global maximum value (p, q) through a comparison network. After the rotation is completed, the intelligent update logic performs a local update, specifically: for rows p and q, a rescan is triggered, and for other rows, a rescan is determined by comparing the stored column indices or by reading only two new elements for fast comparison and replacement.

[0124] (4) Complex feature pair recovery module: Based on the inverse transformation relationship of the real number transformation step, select or calculate the eigenvalues ​​and eigenvectors corresponding to the original complex covariance matrix from the eigenvalues ​​and eigenvectors obtained from the eigenvalues ​​and eigenvectors of the real symmetric matrix eigenvalue decomposition.

[0125] (5) Noise subspace extraction module: Completes subspace extraction.

[0126] (6) Spatial spectrum calculation and DOA estimation module: complete the final direction finding.

[0127] (7) System control unit: coordinates the assembly line operation of each module.

[0128] This device achieves orders-of-magnitude improvements in processing speed and energy efficiency by embedding innovative algorithms in dedicated hardware, making it particularly suitable for high-performance real-time direction finding systems.

[0129] This embodiment fully demonstrates that the method and apparatus proposed in this invention are particularly suitable for real-time MUSIC direction finding systems with large-scale arrays, and can provide significantly higher real-time processing capabilities than traditional solutions while maintaining high accuracy.

Claims

1. A fast MUSIC direction finding method based on maximum value tracking Jacobi eigendecomposition, characterized in that, Specifically, the process includes the following: Step 1: Receive spatial signals through an N-element sensor array to obtain an array output data matrix X of K snapshots; and perform preprocessing on the data matrix X, including down-conversion, filtering, and digitization. Step 2, according to the formula in(·) H The conjugate transpose is used to calculate the sampling covariance matrix R, and the correlation between the received signals of each array element is obtained. Through the real-valued method based on the real part-imaginary part solution, a 2N×2N real symmetric matrix A corresponding to R is obtained. Matrix A contains all the information of the original complex covariance matrix R. Step 3: Using the real symmetric matrix A as input, perform Jacobi eigenvalue decomposition based on maximum value tracking to obtain its eigenvalues ​​D_A and eigenvectors V_A; Step 4: Based on the correspondence used in the realization process, extract N effective eigenvalues ​​from D_A to form the eigenvalues ​​D_R corresponding to the covariance matrix R; at the same time, recover the complex eigenvector matrix V_R of the covariance matrix R from the column vectors of V_A through linear combination or selection. Step 5: Sort the recovered feature values ​​D_R, and select the feature vectors corresponding to the smallest MD feature values ​​to form the noise subspace Un based on the estimated number of sources D; Step 6: Construct a spatial spectrum function using the noise subspace Un, calculate the spectrum function within the angle search range, and obtain the DOA estimate through peak detection.

2. The fast MUSIC direction finding method based on maximum value tracking Jacobi eigendecomposition according to claim 1, characterized in that, The specific process of step 3 is as follows: Step 301: Initialize the eigenvector matrix V, where V is an M×M identity matrix, and M = 2N; Initialize a candidate set of maximum values; this set is used to store the information of the element with the largest absolute value among the off-diagonal elements of each row, specifically a one-dimensional array maxValues ​​of length M and a one-dimensional array maxIndices of length M; maxValues[i] stores the maximum value among the off-diagonal elements of the i-th row, and maxIndices[i] stores the column index corresponding to maxValues[i]. Step 302: Calculate the global maximum value in the candidate set of maximum values, globalMax = max(maxValues[i]). If globalMax is less than the preset tolerance ε, the algorithm converges, outputs the eigenvalues ​​and eigenvector matrix V, and proceeds to step 5; otherwise, execute step 303. Step 303: From the candidate set of maximum values, find the row index p corresponding to globalMax and obtain its corresponding column index q = maxIndices[p]; (p, q) is the optimal rotation pair for this iteration; Step 304: Based on the element A[p,q] at position (p,q) in the real symmetric matrix A and the corresponding diagonal elements A[p,p] and A[q,q], calculate the Givens rotation sine parameter s and cosine parameter c used to clear A[p,q]. Step 305: Update the p-th row, q-th row, p-th column, and q-th column of matrix A using parameters c and s; simultaneously, update the p-th column and q-th column of the eigenvector matrix V. Step 306: Update the candidate set of maximum values ​​using the following update strategy: Rescan all off-diagonal elements in rows p and q, and update their corresponding maxValues ​​and maxIndices in the maximum value candidate set; Determine if the historical maximum value is in column p or column q. If it is, the historical maximum value is invalid, and all off-diagonal elements in the row need to be rescanned, updating their corresponding maxValues ​​and maxIndices in the maximum value candidate set. If the historical maximum value is not in column p or column q, determine if the value in column p or column q is greater than the historical maximum value. If the updated element in column p or q is greater than the element in the maximum value candidate set for that row, then directly update the corresponding maxValues ​​in the maximum value candidate set for that row to the element in column p or q, and maxIndices to p or q. Then return to step 302 to perform the next judgment iteration until convergence.

3. A fast MUSIC direction finding system based on maximum value tracking Jacobi eigenvalue decomposition, used to implement the fast MUSIC direction finding method based on maximum value tracking Jacobi eigenvalue decomposition as described in claim 1 or claim 2, characterized in that, include: The signal acquisition and preprocessing module is used to convert the analog signals received by the array into digital signals and perform step 1. The covariance matrix calculation and realization module is connected to the signal acquisition and preprocessing module. It is used to calculate the sampling covariance matrix and output the corresponding real symmetric matrix, and to execute step 2. The fast feature decomposition module is used to implement Jacobi feature decomposition based on maximum value tracking and to execute step 3. The input of this module is a real symmetric matrix A, and this module contains a hardware-based candidate set management unit, which is responsible for implementing the maintenance and update logic of the dynamic maximum value candidate set, thereby efficiently completing feature decomposition. The feature pair recovery module selects or calculates the eigenvalues ​​and eigenvectors corresponding to the complex covariance matrix from the eigenvalues ​​and eigenvectors obtained from the eigenvalues ​​and eigenvectors of the real symmetric matrix eigenvalue decomposition, based on the inverse transformation relationship of the realization step. Then proceed to step 4. The noise subspace extraction module is used to perform step 5; The spatial spectrum calculation and DOA estimation module is used to perform step 6; The system control unit is used to schedule the orderly collaboration of various modules and control the entire data processing logic.

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