A method for direction of arrival estimation based on angle differential compensation

Abstract

The application discloses a DOA estimation method based on angle differential compensation, which comprises the following steps: firstly, constructing an angle coupling covariance matrix; then deducing an error gradient projection operator and a manifold tangent space projection operator: calculating the angle derivative of the angle coupling covariance matrix, and constructing the error gradient projection operator according to the angle derivative; constructing the manifold tangent space projection operator, and projecting the correction vector into the tangent space orthogonal to the current guide vector through the manifold tangent space projection operator; further constructing an angle differential compensation matrix, and correcting the actual guide vector by using the angle differential compensation matrix, and normalizing the corrected guide vector; finally, applying the angle differential compensation matrix to DOA estimation. The method is used for improving the direction finding precision and robustness of the MUSIC subspace DOA estimation algorithm in the actual array environment, and is suitable for the array system with non-ideal factors such as amplitude and phase errors, array element position errors, channel inconsistencies and array element mutual coupling.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, specifically a direction-of-arrival estimation method based on angle differential compensation. Background Technology

[0002] Direction of Arrival (DOA) estimation is one of the core technologies in the field of array signal processing, widely used in radar target tracking, wireless communication smart antennas, sonar detection, radio monitoring, and seismic signal analysis. Subspace-based high-resolution DOA estimation algorithms, such as MUSIC (Multiple Signal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques), have become mainstream methods in DOA estimation because they overcome the Rayleigh diffraction limit and achieve super-resolution direction finding. The core assumption of these algorithms is that the array manifold matrix is ​​precisely known, meaning that the spatial positions of the array elements, the amplitude and phase responses of each channel, the element radiation patterns, and the mutual coupling relationships between elements are all strictly consistent with the theoretical model.

[0003] However, real-world array systems inevitably deviate from the aforementioned ideal assumptions. On one hand, due to inconsistencies in receiver hardware, the amplitude gain and phase delay of each array element channel differ, resulting in channel amplitude and phase errors. On the other hand, influenced by factors such as mechanical installation tolerances, temperature deformation, and structural vibrations, the actual spatial positions of the array elements deviate from their nominal design values, resulting in array element position errors. Furthermore, the mutual coupling phenomenon between array elements due to electromagnetic coupling effects causes the actual receiving response of each element to be affected by the induced current of neighboring elements. More importantly, these non-ideal factors mostly vary with the signal incident angle—the inconsistencies in the channel amplitude and phase frequency responses cause different disturbances to the steering vector at different incident angles, and position errors naturally manifest as angle-dependent phase errors. The mutual coupling effect is also closely related to the array geometry and incident angle.

[0004] The objective existence of the aforementioned array errors leads to a mismatch between the actual array manifold and the ideal array manifold. For the MUSIC algorithm, this mismatch directly disrupts the theoretical orthogonality between the signal subspace and the noise subspace, causing phenomena such as peak shift, peak broadening, and even spurious peaks in the conventional MUSIC spatial spectrum, ultimately resulting in a significant decrease in DOA estimation accuracy. Literature research shows that the MUSIC algorithm is particularly sensitive to array position errors and channel phase errors; even small errors can cause the root mean square error of direction finding to deteriorate from orders of magnitude to several or even tens of degrees.

[0005] Extensive research has been conducted by scholars both domestically and internationally on the problem of array error compensation. Existing methods can be broadly categorized as follows: blind calibration methods utilize the Toeplitz structure of the covariance matrix or the rotation invariance of the subspace for self-calibration; however, these methods are highly sensitive to initial estimates and signal-to-noise ratio (SNR) conditions, and their performance degrades drastically at low SNR. Auxiliary source calibration methods perform offline array calibration by deploying calibration sources with known azimuth angles; however, the deployment cost of calibration sources is high, and the generalization ability of calibration parameters at non-calibrated angles is insufficient. Iterative self-calibration methods alternately optimize by jointly estimating signal parameters and array error parameters; however, these methods are highly dependent on initial values, and are prone to getting trapped in local optima when the cost function is non-convex. In recent years, the first-order differential perturbation method has been attempted to describe the local variation characteristics of the array manifold; however, when the error form is complex or the error is strongly correlated with the angle, the approximate accuracy of a single-order differential expansion is limited, and its compensation capability is insufficient to meet the requirements of high-precision ranging.

[0006] In summary, existing array error compensation methods lack an effective means to systematically describe the variation of error angles and stably compensate the steering vector across the entire angle range when dealing with array mismatch problems that vary complexly with the incident angle. Therefore, there is an urgent need to develop a DOA estimation method that can accurately characterize the array manifold distortion characteristics and effectively restore the orthogonality of the signal and noise subspaces under complex array error conditions, thereby significantly improving the direction-finding accuracy and robustness in practical array environments. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a direction-of-arrival (DOA) estimation method based on angle differential compensation. This method aims to improve the direction-finding accuracy and robustness of the MUSIC subspace DOA estimation algorithm in practical array environments. The method is applicable to array systems with non-ideal factors such as amplitude and phase errors, element position errors, channel inconsistencies, and element mutual coupling.

[0008] To achieve the above objectives, the technical solution specifically adopted by the present invention is as follows: A direction-of-arrival estimation method based on angle differential compensation includes the following steps: Step 1: Construct the angle coupling covariance matrix: Obtain the sample covariance matrix of the array received data, calculate the Jacobian vector of the array manifold steering vector with respect to the angle, and perform the Hadamard product operation on the autocorrelation matrix of the sample covariance matrix and the Jacobian vector to obtain the angle coupling covariance matrix. Step 2: Derive the error gradient projection operator and the manifold tangent space projection operator: Calculate the angular derivative of the angular coupling covariance matrix, and construct the error gradient projection operator based on the angular derivative; construct the manifold tangent space projection operator, which is used to project the correction vector into the tangent space orthogonal to the current guiding vector to filter out the normal component along the direction of the guiding vector; Step 3: Construct the angle differential compensation matrix: Based on the error gradient projection operator and the manifold tangent space projection operator, construct the angle differential compensation matrix, use the angle differential compensation matrix to correct the actual steering vector, and normalize the corrected steering vector. Step 4: Apply the angle differential compensation matrix for DOA estimation: Perform eigenvalue decomposition on the covariance matrix of the array received data to obtain the signal subspace and noise subspace. Construct a modified MUSIC space spectrum using the steering vector compensated in Step 3. Obtain the direction of arrival estimation result by performing peak search on the modified MUSIC space spectrum.

[0009] Preferably, in step 1, for a uniform linear array with M elements, the incident angle is... Ideal steering vector Represented as: in, For the spacing between array elements, The wavelength of the signal; manifold Jacobian vector Represented as: The angle coupling covariance matrix Represented as: in, This is the sample covariance matrix of the data received by the array.

[0010] Preferably, in step 2, the angle coupling covariance matrix is... Taking the derivative of the angle, we get Define the error gradient projection operator for: The manifold tangent space projection operator Represented as: in, It is the identity matrix. It is the ideal guiding vector.

[0011] Preferably, in step 3, the angle differential compensation matrix Represented as: in, This is the compensation intensity factor, used to control the correction magnitude.

[0012] Preferably, the actual guidance vector is corrected using the angle differential compensation matrix: in It is the ideal guiding vector.

[0013] Normalize the magnitude of the corrected steering vector: And reference element phase normalization: Preferably, in step 4, the covariance matrix of the array received data is decomposed into eigenvalues: in, For the signal subspace, For the noise subspace, and These are the diagonal matrices of eigenvalues ​​corresponding to the signal and noise, respectively; The modified MUSIC spatial spectrum representation is as follows: By finding the spectral peak positions within the search angle range of the spatial spectrum, the DOA estimation results are obtained: .

[0014] As a preferred option, for those that exist K In a multi-source scenario with multiple information sources, the most significant signal is found within a search angle range using the modified MUSIC spatial spectrum. K The positions of each spectral peak are used, and the corresponding angles are used as the DOA estimation results for multiple sources: .

[0015] Preferably, the method is applicable to uniform linear array or planar array systems that have amplitude and phase errors, array element position errors, or mutual coupling effects.

[0016] Preferably, the compensation intensity factor The value of is adaptively adjusted based on the norm of the corrected residual matrix; the corrected residual matrix is ​​expressed as: in, This is the equivalent disturbance caused by limited snapshots and noise.

[0017] Preferably, the sample covariance matrix R of the array received data is calculated from the array multi-channel received data with a finite number of snapshots: .

[0018] This invention has the following characteristics and beneficial effects: This invention effectively amplifies the angle-related array error characteristics by coupling the sample covariance matrix with the autocorrelation matrix of the manifold Jacobian vector through the Hadamard product. Furthermore, through the dual action of the error gradient projection operator and the manifold tangent space projection operator, the correction amount is strictly constrained within the tangent space of the array manifold, filtering out the normal component that does not contain angle information, thus achieving precise compensation for the steering vector. Substituting the compensated steering vector into the MUSIC spatial spectrum effectively restores the orthogonality between the signal subspace and the noise subspace. Simulation results show that under complex mismatch conditions with coexisting amplitude and phase errors, position errors, and mutual coupling effects, the root mean square error (RMSE) of the conventional MUSIC algorithm is 8.653°, with all three targets deviating from the true incident direction. However, using the method of this invention, the RMSE is reduced to 0.0103°, a 99.8% reduction compared to conventional MUSIC, and the absolute errors of each signal source are controlled within 0.03°, with sharp spectral peaks accurately aligned with the true incident direction. This improvement in accuracy stems from the effective extraction of error gradient information and the strict constraint on the correction direction in this invention, which is a direct manifestation of the innovation in algorithm mechanism.

[0019] The angle differential compensation matrix constructed in this invention expresses the error compensation process as a unified matrix transformation, driven by both the error leakage term and the noise propagation term. Theoretical analysis shows that when the array error gradient is significant, the error gradient projection operator can effectively suppress the influence of the noise propagation term, significantly reducing the corrected residual compared to the uncorrected one. Even when the equivalent disturbance caused by finite snapshots and low signal-to-noise ratio is large, the compensation operator still has a good noise suppression effect. Simulation results verify this theoretical inference: the RMSE of the conventional MUSIC algorithm is basically stable at around 25° under different signal-to-noise ratios, hardly decreasing with the improvement of the signal-to-noise ratio; while after adopting the method of this invention, the RMSE shows a significant decreasing trend with the increase of the signal-to-noise ratio. Even under the low signal-to-noise ratio condition of -10 dB, the RMSE is only about 2.57°, far lower than that of the conventional MUSIC algorithm. This shows that this invention, through manifold differential constraint compensation, can still maintain effective recovery of the array manifold structure under extreme conditions where the noise power is much greater than the signal power, and has excellent low signal-to-noise ratio robustness.

[0020] Under actual array error conditions, the spatial spectrum estimation performance of the conventional MUSIC algorithm fluctuates with the incident angle, especially near the array end-fire direction (i.e., when the incident angle is close to ±90°). Due to the large rate of change of the manifold vector, the amplification effect on position and phase errors is more significant, leading to frequent spectral peak shifts and splits. This invention constructs an angle-coupled covariance matrix and calculates its angular derivative, enabling the error gradient projection operator to adaptively respond to local manifold changes at each scanning angle. Simultaneously, the compensation operator maintains continuous and smooth correction of the steering vector across the entire angle range. Simulation results show that, using the method of this invention, near the edge incident angle, the spectral peak shifts and splits caused by manifold mismatch in the conventional method are effectively suppressed, and the consistency of direction finding performance across the entire scanning angle range is significantly improved, thereby expanding the effective direction finding coverage of the MUSIC algorithm.

[0021] To address the common problem of magnitude drift or reference phase change after steering vector correction in conventional compensation methods, this invention performs two-step processing on the compensated steering vector after correction: magnitude normalization and reference element phase normalization. This normalization operation, combined with the manifold tangent space projection operator to filter out the normal component, ensures from the algorithm's structure that the compensated steering vector retains the error information of the measured array manifold while avoiding non-physical drift in the amplitude and common phase directions. This guarantees that no additional errors will be introduced during the subsequent MUSIC spectral peak search due to non-physical changes in the steering vector, which is beneficial to the convergence stability of the iterative process and makes the algorithm compatible with other array calibration preprocessing methods.

[0022] The method of this invention has clear steps, and each operator is a matrix operation and a Hadamard product operation. It can be directly implemented based on array-received data without iterative optimization or numerical search, ensuring computational efficiency. In particular, it corrects the norm of the residual matrix. The introduction of the compensation intensity factor The adaptive adjustment provides clear optimization criteria: users can adjust according to... Real-time value dynamic adjustment Furthermore, the method can be pre-calibrated under typical error scenarios through simulation experiments, thereby achieving optimal compensation results under different error severity levels. This controllability of compensation intensity based on analytical expression makes the method applicable to both fixed scenarios with known prior error information and online adaptive scenarios with unknown error characteristics, exhibiting good flexibility in engineering deployment.

[0023] This invention introduces the concept of manifold tangent space from differential geometry into the field of array error compensation. By constructing the manifold Jacobian vector and its autocorrelation matrix, a mathematical connection is established between the local geometric properties of the array manifold and the statistical information of the received signal. Through the cascaded design of the error gradient projection operator and the tangent space projection operator, precise control of the steering vector correction direction is achieved. The analytical derivation of the correction residual matrix shows that the method of this invention can be uniformly expressed as a framework of "error leakage term + noise propagation term." This expression provides a theoretical tool for analyzing compensation performance under different error scenarios and also provides a scalable mathematical foundation for the design of subsequent improved algorithms. Compared with existing blind calibration methods' dependence on initial conditions, the failure of auxiliary source methods for uncalibrated angles, and the convergence risk of iterative methods for non-convex cost functions, the analytical closed-loop compensation framework of this invention has significant advantages in both theoretical completeness and engineering applicability. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the method flow of a direction-of-arrival estimation method based on angle differential compensation according to an embodiment of the present invention; Figure 2 This is a simulation comparison of the spatial spectrum of uniform linear array DOA estimation before and after applying the angle manifold constraint compensation algorithm in an embodiment of the present invention. Figure 3 The graph shows the comparison curves of the root mean square error of the direction finding under different signal-to-noise ratios before and after applying the angle manifold constraint compensation algorithm in an embodiment of the present invention. Detailed Implementation

[0025] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0026] A direction-of-arrival estimation method based on angle differential compensation, such as Figure 1 As shown, it includes the following steps: Step 1: Construct the angle coupling covariance matrix: Obtain the sample covariance matrix of the array received data, calculate the Jacobian vector of the array manifold steering vector with respect to the angle, and perform the Hadamard product operation on the autocorrelation matrix of the sample covariance matrix and the Jacobian vector to obtain the angle coupling covariance matrix. Specifically, let the array be having A uniform linear array with n elements and n sources. The spacing between array elements is The signal wavelength is The angle of incidence is For a uniform linear array, its ideal steering vector can be expressed as: (1) It should be noted that a uniform linear array refers to the arrangement of the receiving matrix. It is a uniform linear array in a one-dimensional matrix, in which the array elements are arranged at equal intervals in a straight line.

[0027] To describe the local geometry of the arrayed manifold as a function of angle, the derivative of the steering vector with respect to angle is calculated to obtain the manifold Jacobian vector: (2) Define the covariance matrix of the array received data as: (3) The Hadamard product is performed between the covariance matrix and the autocorrelation matrix of the manifold Jacobian vector. The angular coupling covariance matrix is ​​defined as follows: (4) in, This represents the Hadamard product (element-wise multiplication). Let be the autocorrelation matrix of the Jacobian vectors of the manifold.

[0028] Consider an additive error model, let the error vector be... The actual steering vector can then be expressed as: (5) Therefore, when array errors exist, the covariance matrix of the received signal can be decomposed into the sum of the ideal signal covariance matrix, the noise covariance matrix, and the error perturbation matrix: (6) in, For the first The signal power of each signal source For noise power, It is an identity matrix.

[0029] Understandable, the covariance matrix of an ideal signal The signal covariance matrix represents the signal covariance under ideal, error-free conditions; the noise covariance matrix represents the noise covariance matrix. Caused by receiver thermal noise; error perturbation matrix This is caused by non-ideal factors such as channel amplitude and phase error, array element position error, and mutual coupling effect.

[0030] Step 2. Derive the error gradient projection operator and the manifold tangent space projection operator: Calculate the angular derivative of the angular coupling covariance matrix, and construct the error gradient projection operator based on the angular derivative; construct the manifold tangent space projection operator, which is used to project the correction vector into a tangent space orthogonal to the current guiding vector to filter out the normal component along the guiding vector direction.

[0031] Specifically, the angle coupling covariance matrix It simultaneously contains both received signal statistics and local geometric information of the array manifold. The angular coupling covariance matrix can also be decomposed into an ideal part, a noise part, and a perturbation term containing the error. By performing a Hadamard product between the error perturbation matrix and the manifold Jacobian autocorrelation matrix, the perturbation term of the angular coupling covariance matrix can be obtained. m Line number n The column elements are: (7) in, For the error perturbation matrix The ( m , n The ideal part of the angular coupling covariance matrix is ​​determined by both the array manifold and the ideal signal model, and is a function of the signal incident direction, independent of the scan angle. The signal changes abruptly; since the manifold derivative is smoothly differentiable, when differentiating the ideal part, its derivative appears as a smooth baseline that does not change abruptly near the signal direction. The noise error matrix is ​​independent of the signal incident angle, and no additional processing is required for the noise part in conventional array performance analysis and derivative derivation. However, the perturbation term of the angle-coupled covariance matrix carries array error information. When the scanning angle is close to a certain real signal direction, the error term coherently superimposes with the manifold derivative, forming structural fluctuations. When performing derivative analysis on the perturbation term, local peaks or rapid fluctuations will appear.

[0032] When the array error changes with the angle The derivative with respect to angle can characterize the direction and intensity of error variation. The angular derivative of the angular coupling covariance matrix is ​​defined as: (8) because This is the result of a weighted coupling between the received signal statistics and the manifold derivative. To convert it into a correction method for the steering vector, an error gradient projection operator is defined: (9) It can be divided into a smooth, ideal portion and a localized anomaly caused by errors. Multiplied by Afterwards, the ideal part remains flat, while the perturbation part shows a significant response near the signal direction.

[0033] The error gradient projection operator can be approximately expanded as follows: (10) in, This is an ideal part of the angular coupling covariance matrix. This perturbs the component. The error gradient projection operator can find the main direction of error variation with angle in the error weighted space of the angle-coupled covariance matrix and map it to the steering vector correction space. By applying the error gradient projection operator to the actual steering vector, a preliminary correction amount can be obtained: (11) However, this correction vector exists in a complete complex vector space and contains both tangent space components and normal components. The tangent space components are along the tangent plane of the array manifold and are directly related to changes in angular information; while the normal components only change the overall amplitude or common phase of the guide vector and do not contain angular information.

[0034] If used directly Compensating for the steering vector can lead to a shift in its magnitude or a change in the reference phase, potentially affecting the convergence and stability of the iterative process. Therefore, the compensation amount needs to be restricted to the local tangent space of the array manifold, leading to the introduction of the manifold tangent space projection operator: (12) The manifold tangent space projection operator can project any modified vector into a subspace orthogonal to the current steering vector, thereby filtering out the normal component along the steering vector direction.

[0035] To more directly assess the impact of the correction on the steering vector itself, the correction residual matrix is ​​defined as follows: (13) This matrix directly measures the vector difference between the corrected steering vector and the true physical response. This is a compensation intensity factor used to control the correction magnitude. Let... , in This represents the equivalent disturbance caused by finite snapshots and noise. Substituting into the above equation and simplifying, we get: (14) in, As a higher-order small quantity, it is ignored. Therefore, the corrected residual matrix is ​​driven by two terms: the error leakage term. and noise transmission terms When the error changes slowly and the gradient information is weak, ,but The residual is determined only by noise; when the error gradient is significant, Effective suppression The influence of Compared to the uncorrected version Significantly reduced. Therefore, It directly measures the actual compensation effect of the correction algorithm and can be used as a basis for subsequent adaptive adjustment of constraint strength. The optimization criteria.

[0036] Step 3. Construct the angle differential compensation matrix based on the error analysis results: Construct the angle differential compensation matrix based on the error gradient projection operator and the manifold tangent space projection operator, use the angle differential compensation matrix to correct the actual steering vector, and normalize the corrected steering vector.

[0037] Specifically, the deviation between the corrected steering vector and the true steering vector consists of two terms: an error leakage term and a noise propagation term. This indicates that the entire correction process can be expressed as a unified matrix transformation, thus organically integrating error gradient information, tangent space constraints, and the original observation data. Based on this, the angle differential compensation matrix is ​​defined as follows: (15) when If the time is too small, the compensation will be insufficient; when If the value is too large, it may lead to overcompensation or numerical oscillation. In practical applications, The value of can be determined based on the norm of the modified residual matrix. Adaptive adjustments can be made, or the calibration can be performed in advance under typical error scenarios through simulation experiments.

[0038] The steering vector is corrected using this compensation operator to obtain the compensated steering vector: (16) To prevent changes in the magnitude of the guide vector after compensation, it is normalized: (17) Meanwhile, to maintain phase reference consistency, the reference array elements can be further subjected to phase normalization processing: (18) Through the above processing, the compensated guide vector retains the error information of the measured array manifold while avoiding non-physical drift in the amplitude and common phase directions.

[0039] Step 4: Apply the angle differential compensation matrix to perform DOA estimation: Perform eigenvalue decomposition on the covariance matrix of the array received data to obtain the signal subspace and noise subspace. Construct a corrected MUSIC space spectrum using the steering vector compensated in Step 3. Obtain the direction of arrival estimation result by performing peak search on the corrected MUSIC space spectrum.

[0040] Specifically, eigenvalue decomposition is performed on the covariance matrix of the array received data: (19) in, For the signal subspace, For the noise subspace, and These are the corresponding eigenvalue diagonal matrices.

[0041] Using the compensated guide vector Constructing a modified MUSIC spatial spectrum: (20) The DOA estimation result can be obtained by finding the spatial spectral peak within the search angle range: (twenty one) For multi-source scenarios, the most significant source is searched in the spatial spectrum. K The position of each spectral peak is used as the estimated angle. (twenty two) Since this method uses a guide vector compensated by the differential constraint of the angle manifold, it can effectively reduce the mismatch between the actual array manifold and the search guide vector, thereby restoring the orthogonality between the signal subspace and the noise subspace and improving the direction finding accuracy of the MUSIC algorithm under complex array error environment.

[0042] After correction using the angle differential compensation matrix, theoretical analysis based on differential constraints and tangent space projection shows that, under typical array error conditions, the compensated MUSIC spatial spectral peaks are significantly sharpened, with peak positions closely matching the true incident direction, and sidelobe levels are reduced by more than 3 dB overall. Simultaneously, the norm bound of the corrected residual vector indicates that the root mean square error of the direction finding is reduced from the order of magnitude before compensation to the sub-order of magnitude, representing a performance improvement of more than an order of magnitude. Within the full scanning angle range, especially near the edge incident angles, the peak shift and splitting phenomena caused by manifold mismatch in conventional methods are effectively suppressed. Furthermore, based on the analytical relationship between error leakage and noise propagation, under different signal-to-noise ratios, the RMSE curve after applying the compensation matrix has a lower steady-state value, and the upward trend with decreasing signal-to-noise ratio is significantly smoother, indicating that this method can still maintain good direction finding accuracy and robustness at low signal-to-noise ratios.

[0043] This embodiment is applicable to uniform linear or planar array systems with array amplitude and phase errors, position errors, or mutual coupling effects, and is particularly suitable for single-channel or multi-channel receiving systems with high direction-finding accuracy requirements. Specifically, firstly, by constructing the array manifold Jacobian vector, the sample covariance matrix is ​​coupled with the manifold derivative autocorrelation matrix through a Hadamard product, thereby amplifying and extracting angle-related array error information. Secondly, based on this coupling, an error gradient projection operator is constructed, and combined with manifold tangent space projection, the normal component along the steering vector direction is strictly filtered out. Finally, an adjustable manifold differential constraint compensation operator is formed, and the compensated steering vector is normalized. This method can retain angle-related error information while avoiding non-physical drift of the steering vector amplitude and common phase. Under complex mismatch conditions such as amplitude and phase errors, array element position errors, and mutual coupling effects, it effectively restores the orthogonality of the signal subspace and noise subspace, thereby significantly improving the generalization ability and direction-finding accuracy of MUSIC-type DOA estimation algorithms.

[0044] pass Figure 2 As can be seen, the spectral peaks of the conventional MUSIC algorithm are significantly broadened and deviate from the true incident direction, with a root mean square error (RMSE) of 8.653° for the three targets. However, after correction using the method of this invention, the spatial spectral peaks become sharper and accurately aligned with the true incident direction, reducing the RMSE to 0.0103°, a 99.8% reduction compared to the conventional MUSIC algorithm. The absolute errors of each signal source are all controlled within 0.03°. These results demonstrate that the compensation method proposed in this invention can significantly improve the direction-finding accuracy and robustness of the MUSIC algorithm even when multiple non-ideal factors coexist.

[0045] pass Figure 3 It can be seen that the RMSE of the conventional MUSIC algorithm does not change significantly with the signal-to-noise ratio (SNR), remaining relatively stable at around 25°. However, after adopting the angle differential compensation method of this invention, the RMSE shows a significant decreasing trend with increasing SNR. Even under a low SNR condition of -10dB, the RMSE is only about 2.57°, far lower than that of the conventional method. This result verifies that the compensation strategy proposed in this invention can effectively recover the array manifold structure and maintain good direction-finding accuracy and robustness even at low SNR conditions.

[0046] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A direction-of-arrival estimation method based on angle differential compensation, characterized in that, Includes the following steps: Step 1: Construct the angle coupling covariance matrix: Obtain the sample covariance matrix of the array received data, calculate the Jacobian vector of the array manifold steering vector with respect to the angle, and perform the Hadamard product operation on the autocorrelation matrix of the sample covariance matrix and the Jacobian vector to obtain the angle coupling covariance matrix. Step 2: Derive the error gradient projection operator and the manifold tangent space projection operator: Calculate the angular derivative of the angular coupling covariance matrix, and construct the error gradient projection operator based on the angular derivative; construct the manifold tangent space projection operator, which is used to project the correction vector into the tangent space orthogonal to the current guiding vector to filter out the normal component along the direction of the guiding vector; Step 3: Construct the angle differential compensation matrix: Based on the error gradient projection operator and the manifold tangent space projection operator, construct the angle differential compensation matrix, use the angle differential compensation matrix to correct the actual steering vector, and normalize the corrected steering vector. Step 4: Apply the angle differential compensation matrix for DOA estimation: Perform eigenvalue decomposition on the covariance matrix of the array received data to obtain the signal subspace and noise subspace. Construct a modified MUSIC space spectrum using the steering vector compensated in Step 3. Obtain the direction of arrival estimation result by performing peak search on the modified MUSIC space spectrum.

2. The method according to claim 1, characterized in that, In step 1, for a uniform linear array with M elements, the incident angle is... The ideal steering vector is represented as: in, For the spacing between array elements, The wavelength of the signal; The Jacobian vector of a manifold is represented as: The angle coupling covariance matrix is ​​expressed as: Where R is the sample covariance matrix of the array received data, It represents the Hadamaji.

3. The method according to claim 1, characterized in that, In step 2, the angle coupling covariance matrix is... Taking the derivative of the angle, we get Define the error gradient projection operator for: The manifold tangent space projection operator Represented as: in, It is the identity matrix. It is the ideal guiding vector.

4. The method according to claim 1, characterized in that, In step 3, the angle differential compensation matrix Represented as: in, This is the compensation intensity factor, used to control the correction magnitude.

5. The method according to claim 4, characterized in that, The actual guidance vector is corrected using the aforementioned angle differential compensation matrix: Normalize the magnitude of the corrected steering vector: And reference element phase normalization: 。 6. The method according to claim 1, characterized in that, In step 4, the covariance matrix of the array received data is decomposed into eigenvalues: in, For the signal subspace, For the noise subspace, and These are the diagonal matrices of eigenvalues ​​corresponding to the signal and noise, respectively; The modified MUSIC spatial spectrum representation is as follows: By finding the spectral peak positions within the search angle range of the spatial spectrum, the DOA estimation results are obtained: 。 7. The method according to claim 1, characterized in that, For existence K In a multi-source scenario with multiple information sources, the most significant signal is found within a search angle range using the modified MUSIC spatial spectrum. K The positions of each spectral peak are used, and the corresponding angles are used as the DOA estimation results for multiple sources: 。 8. The method according to claim 1, characterized in that, The method is applicable to uniform linear or planar array systems that have amplitude and phase errors, element position errors, or mutual coupling effects.

9. The method according to claim 4, characterized in that, The compensation intensity factor The value of is adaptively adjusted based on the norm of the modified residual matrix; The corrected residual matrix is ​​expressed as follows: in, This is the equivalent disturbance caused by limited snapshots and noise.

10. The method according to claim 1, characterized in that, The sample covariance matrix R of the array received data is calculated from the array multi-channel received data with a finite number of snapshots: 。

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