A method and system for deconvolutional MVDR azimuth spectrum estimation based on PM regularization
By constructing an array-received signal model and introducing a PM-regularized deconvolution iterative algorithm, the problem of insufficient azimuth estimation accuracy of passive sonar under low signal-to-noise ratio conditions is solved, achieving higher resolution and robustness.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SUN YAT SEN UNIV
- Filing Date
- 2026-03-31
- Publication Date
- 2026-06-30
AI Technical Summary
Existing passive sonars suffer from decreased azimuth estimation accuracy under low signal-to-noise ratio conditions, high algorithm complexity, and insufficient stability and robustness, especially in complex environments where they struggle to effectively distinguish multiple close-range targets.
A PM-regularized deconvolution MVDR azimuth spectrum estimation method is adopted. By constructing an array received signal model, calculating the covariance matrix and point spread function, and combining the PM-regularized deconvolution iterative algorithm, the estimation error is reduced and the robustness is enhanced.
It improves the accuracy and resolution of azimuth estimation under low signal-to-noise ratio conditions, suppresses noise amplification and spurious peak problems, and enhances target resolution in complex environments.
Smart Images
Figure CN122306961A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of array signal processing technology, and in particular to a method and system for deconvolutional MVDR azimuth spectrum estimation based on PM regularization. Background Technology
[0002] Passive sonar detects, identifies, and locates underwater targets by receiving and analyzing the radiated noise. It is widely used in various underwater acoustic monitoring systems, including submarine sonar, shore-based sonar, moorings, and buoys. These systems offer advantages such as low power consumption and high stealth capabilities. Array signal processing is one of the core technologies of passive sonar. By processing the signals received by the array, the system can develop spatial directivity, increase gain, thereby enhancing detection capabilities, extending the effective range, and estimating the target's azimuth and distance. Direction of Arrival (DOA) estimation, as an important component of array signal processing, has wide applications in radar, sonar, wireless communication, and seismic exploration.
[0003] In related technologies, passive sonar direction finding methods include, for example, a fast high-resolution azimuth estimation method for underwater broadband noise targets. This method constructs a DOA model and a sparse representation model of the broadband array signal, uses the expectation-maximization sparse Bayesian learning algorithm for frame loop processing, and outputs the squared absolute value of the posterior mean of each direction to achieve target azimuth estimation. Alternatively, there is a low-complexity azimuth estimation method based on noise eigenvalue reconstruction. This method constructs a covariance matrix through joint processing of sound pressure and vibration velocity, constructs a pseudo-data covariance matrix with non-divergent noise power, introduces symmetrical target angles and scanning sources to form an extended matrix, and designs a spatial spectrum function using eigenvalue relationships to search and filter the true target angles within the half-spectrum.
[0004] For a fast, high-resolution orientation estimation method for underwater broadband noisy targets, the improved noise variance update model, designed to enhance processing speed under low signal-to-noise ratio conditions, introduces a significant uncertainty penalty, leading to decreased estimation accuracy. Its root mean square error is greater than that of traditional algorithms. Furthermore, the algorithm involves multi-layered nested loops of frames, frequency points, and sparse iterations, and includes several sensitive parameters such as state transition matrix, process noise, and convergence criteria. In practical applications, these parameters need to be carefully adjusted according to different marine environments and target states, increasing the complexity of engineering adaptation and debugging.
[0005] A low-complexity orientation estimation method based on noise eigenvalue reconstruction suffers from a complex algorithm involving multiple steps, including eigenvalue decomposition of the initial covariance matrix, noise eigenvalue reconstruction, complex conjugate operation to construct a pseudo-data matrix, symmetric matrix construction, and the introduction of an extended matrix. This increases the complexity of engineering implementation and the risk of numerical error accumulation. Furthermore, the construction of the spectral function heavily relies on the accurate estimation of the number of sources K (requiring the selection of the 2K+1 eigenvalue). However, in practical applications, K is often unknown and requires estimation using other criteria. Any estimation error will lead to incorrect eigenvalue indexing, causing the spatial spectral function to fail or generate spurious peaks. This combination of multi-step matrix reconstruction and prior dependence on K makes the overall stability of the algorithm susceptible to interference, posing a challenge to its robustness in complex environments. Summary of the Invention
[0006] To address the aforementioned technical problems, the present invention aims to provide a deconvolutional MVDR azimuth spectrum estimation method and system based on PM regularization, thereby reducing the estimation error of the minimum variance distortionless response beamforming azimuth spectrum.
[0007] The first technical solution adopted in this invention is: a deconvolution MVDR azimuth spectrum estimation method based on PM regularization, comprising the following steps:
[0008] Set the array parameters and sound source parameters, and construct the array signal receiving model;
[0009] Calculate the covariance matrix of the array received data based on the array received signal model, and determine the output power of the MVDR beamformer and the point spread function of the MVDR beamformer.
[0010] The azimuth spectrum of the MVDR beamformer and the point spread function of the MVDR beamformer are substituted into the deconvolution iterative algorithm for deconvolution to obtain the deconvolutioned azimuth spectrum, and the azimuth of the target is determined.
[0011] Furthermore, the step of setting array parameters and sound source parameters to construct the array received signal model specifically includes:
[0012] Construct a uniform linear array, the uniform linear array comprising a plurality of array elements, and set array parameters, the array parameters including the array element spacing;
[0013] The sound source parameters are set, which are several unrelated far-field narrowband plane wave signals, and incident at a preset angle relative to the transverse direction of the uniform linear array. Based on the signals received by the uniform linear array, an array received signal model is constructed.
[0014] Furthermore, the specific expression for the array received signal model is as follows:
[0015]
[0016] In the above formula, This represents the array receiving signal model. Represents an array manifold matrix. This represents received noise that is uncorrelated with the incident signal. This represents several uncorrelated far-field narrowband plane wave signals. Indicates the time.
[0017] Furthermore, the step of calculating the covariance matrix of the array received data based on the array received signal model, and determining the output power of the MVDR beamformer and the point spread function of the MVDR beamformer, specifically includes:
[0018] Calculate the covariance matrix of the array received data based on the array received signal model;
[0019] Obtain the steering vector of the array manifold matrix in the array received signal model, and multiply it with the result of the inversion operation of the covariance matrix of the array received data to construct the weighting vector of the MVDR beamformer;
[0020] The output power of the MVDR beamformer is obtained by performing a quadratic operation on the weighting vector of the MVDR beamformer and the covariance matrix of the array received data.
[0021] The output power of the MVDR beamformer is converted into a point convolution form and combined with the weighted vector of the MVDR beamformer to construct the point spread function of the MVDR beamformer.
[0022] Furthermore, the expression for the output power of the MVDR beamformer is as follows:
[0023]
[0024] In the above formula, This indicates the output power of the MVDR beamformer. express The power of the directional signal, This represents the weighting vector of the MVDR beamformer. This represents the covariance matrix of the received data. The power representing the noise. express Directional guidance vector, This represents the conjugate transpose operator. express An uncorrelated far-field narrowband plane wave signal.
[0025] Furthermore, the specific expression for the point spread function of the MVDR beamformer is as follows:
[0026]
[0027] In the above formula, This represents the point spread function of the MVDR beamformer. This represents the weighting vector of the MVDR beamformer. This represents the conjugate transpose operator. express The directional guide vector.
[0028] Furthermore, the step of substituting the azimuth spectrum of the MVDR beamformer and the point spread function of the MVDR beamformer into the deconvolution iterative algorithm for deconvolution to obtain the deconvolutioned azimuth spectrum and determining the azimuth of the target specifically includes:
[0029] Define the regularization term of the PM likelihood function and construct the cost function with regularization constraints;
[0030] Based on the cost function with PM regularization constraints, the derivative of the cost function with respect to the estimated sound source power distribution is obtained, and an extremum problem is constructed.
[0031] Based on the extremum problem, the complete extremum problem is obtained by introducing Lagrange multipliers to constrain the estimated sound source power distribution;
[0032] Obtain the gradient zero-point equation of the complete extremum problem and substitute it into the complete extremum problem to construct the Lagrange multiplier equation;
[0033] The Lagrange multipliers are determined by multiplying both sides of the Lagrange multiplier equation by the estimated source power distribution and integrating.
[0034] Substituting the Lagrange multipliers into the Lagrange multiplier equation, we obtain the iterative equation of the RL algorithm based on PM regularization;
[0035] The azimuth spectrum and point spread function of the MVDR beamformer are substituted into the iterative equation of the RL algorithm based on PM regularization for deconvolution to obtain the deconvolutioned azimuth spectrum.
[0036] Furthermore, the expression for the Lagrange multiplier is as follows:
[0037]
[0038] In the above formula, Represents the Lagrange multipliers. Represents the regularization parameter. Indicates the diffusion coefficient. This represents the estimated power distribution of the sound source. This represents a differential operator.
[0039] Furthermore, the expression for the iterative equation of the RL algorithm based on PM regularization is as follows:
[0040]
[0041] In the above formula, This indicates the output power of the MVDR beamformer. This represents the point spread function of the MVDR beamformer. Represents the regularization parameter. Indicates the diffusion coefficient. This represents a differential operator.
[0042] The second technical solution adopted in this invention is: a deconvolutional MVDR azimuth spectrum estimation system based on PM regularization, comprising:
[0043] The first module is used to set array parameters and sound source parameters, and to build an array signal receiving model.
[0044] The second module is used to calculate the covariance matrix of the array received data based on the array received signal model, and to determine the output power of the MVDR beamformer and the point spread function of the MVDR beamformer.
[0045] The third module is used to substitute the azimuth spectrum of the MVDR beamformer and the point spread function of the MVDR beamformer into the deconvolution iterative algorithm to deconvolve them, obtain the deconvolutioned azimuth spectrum, and determine the azimuth of the target.
[0046] The beneficial effects of the method and system of this invention are as follows: This invention constructs an array receiving signal model by setting array parameters and sound source parameters; further, it calculates the covariance matrix of the array receiving data based on the array receiving signal model to determine the output power of the MVDR beamformer and the point spread function of the MVDR beamformer; finally, it substitutes the azimuth spectrum of the MVDR beamformer and the point spread function of the MVDR beamformer into the deconvolution iterative algorithm for deconvolution to obtain the deconvolutioned azimuth spectrum, thereby determining the azimuth of the target. Based on MVDR beamforming, it introduces deconvolution post-processing and Perona-Malik nonlinear diffusion regularization, which effectively reduces the spectral broadening caused by the point spread function, improves the spectral peak focusing and near-space target resolution, suppresses noise amplification and spurious peak problems in the later stage of standard RL algorithm iteration, enhances deconvolution robustness, and reduces the estimation error of the azimuth spectrum of minimum variance distortionless response beamforming. Attached Figure Description
[0047] Figure 1This is a flowchart of the steps of the deconvolution MVDR azimuth spectrum estimation method based on PM regularization of the present invention;
[0048] Figure 2 This is a block diagram of a deconvolutional MVDR orientation spectrum estimation system based on PM regularization according to the present invention.
[0049] Figure 3 This is a schematic diagram of a uniform linear array provided in a specific embodiment of the present invention;
[0050] Figure 4 These are schematic diagrams illustrating the orientation estimation results of two methods provided in specific embodiments of the present invention;
[0051] Figure 5 This is a convolution diagram provided in a specific embodiment of the present invention;
[0052] Figure 6 This is a schematic diagram of the deconvolution MVDR orientation estimation process based on PM regularization provided in a specific embodiment of the present invention;
[0053] Figure 7 This is a schematic diagram comparing the azimuth spectra of five methods when the signal-to-noise ratio is -5dB, provided in a specific embodiment of the present invention.
[0054] Figure 8 This is a schematic diagram comparing the azimuth spectra of five methods when the signal-to-noise ratio is -10dB, provided in a specific embodiment of the present invention.
[0055] Figure 9 This is a schematic diagram comparing the azimuth spectra of five methods when the signal-to-noise ratio is -15dB, provided in a specific embodiment of the present invention.
[0056] Figure 10 This is a schematic diagram comparing the azimuth spectra of five methods for multi-target scenarios with different signal-to-noise ratios, provided in a specific embodiment of the present invention.
[0057] Figure 11 This is a schematic diagram comparing the azimuth spectra of five methods for multiple targets with the same signal-to-noise ratio, provided in a specific embodiment of the present invention.
[0058] Figure 12 This is a comparative diagram of five methods for handling multiple moving targets provided in a specific embodiment of the present invention;
[0059] Figure 13 This is a schematic diagram comparing the root error of the five methods provided in a specific embodiment of the present invention;
[0060] Figure 14 This is a schematic diagram comparing the target resolution probabilities of five methods provided in a specific embodiment of the present invention. Detailed Implementation
[0061] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.
[0062] First, the technical terms in this embodiment will be explained:
[0063] 1) CBF: Conventional beamforming.
[0064] 2) MVDR: Minimum variance distortionless response beamforming.
[0065] 3) DOA: Direction of arrival.
[0066] 4) BTR: Time-location history graph.
[0067] 5) RL: A method for deconvolution.
[0068] 6) RL-CBF: Deconvolution conventional beamforming.
[0069] 7) RL-MVDR: Deconvolution MVDR formation.
[0070] 8) PM-RL-MVDR: Deconvolutional MVDR based on PM regularization.
[0071] 9) PSF: Point spread function.
[0072] Reference Figure 1 This invention provides a deconvolutional MVDR azimuth spectrum estimation method based on PM regularization, which includes the following steps:
[0073] S100: Set array parameters and sound source parameters to construct an array received signal model;
[0074] S110. Construct a uniform linear array, the uniform linear array comprising several array elements, and set array parameters, the array parameters including the array element spacing;
[0075] In this embodiment, as Figure 3 As shown, suppose a... A uniform linear array composed of n array elements, with an element spacing of [missing information]. .
[0076] S120. Set the sound source parameters, which are several unrelated far-field narrowband plane wave signals, and incident them at a preset angle relative to the transverse direction of the uniform linear array. Based on the signals received by the uniform linear array, construct an array received signal model.
[0077] In this embodiment, Unrelated far-field narrowband plane wave signals The angle between the two arrays in the horizontal direction is respectively... Incidence direction, superscript It is the transpose operator. Signal received by the time array It can be written as a matrix expression:
[0078]
[0079] In the above formula, This represents the array receiving signal model. Represents an array manifold matrix. This represents received noise that is uncorrelated with the incident signal. This represents several uncorrelated far-field narrowband plane wave signals. Indicates the time.
[0080] exist In the matrix expression received by the time array, For received noise that is independent of the incident signal, Let be an array manifold matrix, where for Directional guidance vector:
[0081]
[0082] exist In the directional guidance vector, At the current speed of sound, The incident signal frequency is denoted as .
[0083] S200. Calculate the covariance matrix of the array received data based on the array received signal model, and determine the output power of the MVDR beamformer and the point spread function of the MVDR beamformer.
[0084] S210. Calculate the covariance matrix of the array received data based on the array received signal model;
[0085] S220. Obtain the steering vector of the array manifold matrix in the array received signal model, and multiply it with the result of the inversion operation of the covariance matrix of the array received data to construct the weighting vector of the MVDR beamformer.
[0086] In this embodiment, the weighting vector of the MVDR beamformer for:
[0087]
[0088] Weighting vector in MVDR beamformer middle, Represents the received data covariance matrix, with superscript indicating the superscript. For the inverse operator, superscript This is the conjugate transpose operator.
[0089] S230. Combine the weighting vector of the MVDR beamformer with the covariance matrix of the array received data to perform a quadratic operation to obtain the output power of the MVDR beamformer;
[0090] In this embodiment, the output power of the MVDR beamformer for:
[0091]
[0092] Output power of MVDR beamformer middle, The MVDR algorithm is for the direction of arrival. The location estimation results of a unit power sound source. express The power of the directional signal, The power representing the noise. This represents the weighting vector of the MVDR beamformer.
[0093] S240. Convert the output power of the MVDR beamformer into a point convolution form and combine it with the weighted vector of the MVDR beamformer to construct the point spread function of the MVDR beamformer.
[0094] In this embodiment, we now assume the following simulation scenario: Suppose a 10-element uniform linear array with an element spacing of half a wavelength is used to simulate waves with a direction of arrival of... For single-target azimuth estimation, the direction of arrival is compared. The azimuth spectrum of the target is respectively in Translation on axis The azimuth spectrum images of the two azimuth estimation results are superimposed and displayed as follows: Figure 4 As shown. MVDR beamformers can target waves with arbitrary directions of arrival in space. The azimuth estimation result of a single target is shifted from the azimuth spectrum estimation result of a single target in the 0° direction by the MVDR beamformer. The results are similar, with the two orientation spectra basically overlapping. This is because MVDR is a high-resolution algorithm, and MVDR's resolution capability at each angle is basically consistent.
[0095] Therefore, the following approximate equation exists:
[0096]
[0097] The guide vector representing the 0° direction.
[0098] Substitute into the output power of the MVDR beamformer The output power of the MVDR beamformer can be obtained from this. convolutional form
[0099]
[0100] In the above formula, This refers to the PSF of the MVDR beamformer.
[0101] The physical meaning of PSF (Point Spread Function) is the image diffused after a point light source in space is convolved with the impulse response function of an imaging system, such as... Figure 5 As shown, the point light source forms a ripple-like diffusion ring image after being convolved by the sampling function.
[0102] Based on the physical meaning of PSF, a feasible method for determining... The method is as follows: assuming there is a point target at the center of the region of interest, the target's power is the average value of the MVDR azimuth spectrum peaks, i.e., according to the formula... calculate ,in , It is the average power of the sound source estimated by MVDR. This represents the normalization operation. We can obtain... The calculation formula is:
[0103]
[0104] In the above formula, This represents the point spread function of the MVDR beamformer. This represents the weighting vector of the MVDR beamformer. This represents the conjugate transpose operator. express The directional guide vector.
[0105] S300. Substitute the azimuth spectrum of the MVDR beamformer and the point spread function of the MVDR beamformer into the deconvolution iterative algorithm to deconvolve them, and obtain the deconvolutioned azimuth spectrum to determine the azimuth of the target.
[0106] S310. Define the regularization term of the PM likelihood function and construct the cost function with regularization constraints.
[0107] In this embodiment, the PM model is a two-dimensional constraint model for image blurring. This method aims to improve the directional smoothness of noisy backgrounds, reduce false peaks caused by noise, obtain lower sidelobes, and maintain rapid decay near the target peak, thereby improving the resolution of the deconvolution method. The PM regularization term is widely used to solve partial differential equations in noisy image restoration. This method adjusts the diffusion coefficient by the gradient magnitude of the image, making the smoothed region isotropic and causing the image edges to diffuse along the gradient direction. The model in image restoration is given by the following equation:
[0108]
[0109] The model in image restoration Images representing evolution, and These represent the normal and tangential directions of the outline lines of equal grayscale lines in the image, respectively. and They represent The derivatives along the normal and tangential directions in the local coordinate system. Indicates the diffusion coefficient. This is a differential operator. Inspired by the PM model described above, the method in this embodiment designs a one-dimensional regularization term for direction estimation.
[0110] The regularization term of the likelihood function is defined as follows:
[0111]
[0112] In the definition of regular terms For regularization parameters, Where is the diffusion coefficient. Let be the estimated sound source power distribution. Then the cost function with regularization constraints is:
[0113]
[0114] In the above formula, For regularization parameters, Where is the diffusion coefficient. This represents the estimated power distribution of the sound source.
[0115] S320. Based on the cost function with PM regularization constraints, find the derivative of the cost function with respect to the estimated sound source power distribution and construct an extremum problem.
[0116] In this embodiment, the goal is to find right The derivative of is obtained as follows:
[0117]
[0118] In the above formula, For regularization parameters, is the diffusion coefficient.
[0119] S330. Based on the extremum problem, by introducing Lagrange multipliers to constrain the estimated sound source power distribution, the complete extremum problem is obtained.
[0120] In this embodiment, the Lagrange multiplier method is used to solve this extremum problem. This is achieved by introducing Lagrange multipliers. To constrain The value of gives the complete extremum problem as follows:
[0121]
[0122] S340. Obtain the gradient zero-point equation of the complete extremum problem and substitute it into the complete extremum problem to construct the Lagrange multiplier equation;
[0123] In this embodiment, finding the maximum value is equivalent to finding the gradient zero of the complete extremum problem, and its expression is:
[0124]
[0125] Substituting the complete extremum problem into the gradient zero-point equation yields the Lagrange multiplier equation:
[0126]
[0127] S350. Multiply both sides of the Lagrange multiplier equation by the estimated source power distribution and integrate to determine the Lagrange multipliers;
[0128] In this embodiment, both sides of the Lagrange multiplier equation are multiplied by And on Integrating, we obtain the Lagrange multipliers:
[0129]
[0130] In the above formula, Represents the Lagrange multipliers. Represents the regularization parameter. Indicates the diffusion coefficient. This represents the estimated power distribution of the sound source. This represents a differential operator.
[0131] S360. Substitute the Lagrange multipliers into the Lagrange multiplier equation to obtain the iterative equation of the RL algorithm based on PM regularization;
[0132] In this embodiment, substituting the Lagrange multipliers into the Lagrange multiplier equation yields:
[0133]
[0134] use Multiplying by this and substituting it into both sides of the equation, we obtain the iterative equation for the RL algorithm based on PM regularization:
[0135]
[0136] In the above formula, This indicates the output power of the MVDR beamformer. This represents the point spread function of the MVDR beamformer. Represents the regularization parameter. Indicates the diffusion coefficient. This represents a differential operator.
[0137] S370. Substitute the azimuth spectrum and point spread function of the MVDR beamformer into the iterative equation of the RL algorithm based on PM regularization to deconvolve and obtain the deconvolved azimuth spectrum.
[0138] Finally, as Figure 6 As shown, this embodiment first sets the array parameters and sound source parameters; constructs an array received signal model based on the set array parameters and sound source parameters; calculates the array received data covariance matrix based on the array received signal model; calculates the azimuth spectrum of the MVDR beamformer based on the calculated received data covariance matrix; calculates the PSF of the MVDR beamformer; substitutes the azimuth spectrum and PSF of the MVDR beamformer into the deconvolution iterative algorithm for deconvolution, and finally obtains the deconvolutioned azimuth spectrum.
[0139] from Figure 7 , Figure 8 ,and Figure 9The single-target azimuth spectra of different algorithms under different signal-to-noise ratios (SNRs) show that, under all three SNR conditions, each algorithm can form a main peak near the true target azimuth, but there are significant differences in main lobe width and background noise level. The CBF algorithm has the widest main lobe, but the background noise level in the non-target region is relatively high, indicating lower resolution and weaker noise resistance. The MVDR algorithm forms a narrower main lobe than the CBF algorithm, demonstrating higher spatial resolution, but its background noise level can even be higher than CBF under low SNR conditions. After introducing RL deconvolution, the main lobe width in the target direction of both RL-CBF and RL-MVDR is significantly compressed, and the background noise level is reduced, indicating that post-deconvolution processing can effectively reduce the array point diffusion effect and improve the target energy focusing ability. PM-RL-MVDR exhibits the sharpest main peak and the lowest background noise level under all three SNR conditions, indicating that PM regularization can effectively suppress noise and spurious peak amplification while enhancing main lobe focusing, thus obtaining better azimuth spectrum estimation results. The PM-RL-MVDR method maintains a narrower main lobe width and stronger background noise suppression capability under different signal-to-noise ratio conditions, demonstrating superior overall orientation estimation performance.
[0140] from Figure 10 and Figure 11 In multi-target scenarios, the azimuth spectrum shows that the difference between the two peaks and valleys of CBF in this region is too small, making it difficult to effectively distinguish between two adjacent targets. Although MVDR narrows the main lobe compared to CBF, its resolution for closely spaced targets remains limited. RL-CBF compresses the main lobe width of CBF, thus improving its resolution. RL-MVDR forms a more obvious bimodal structure at 10° and 14°, demonstrating higher resolution. PM-RL-MVDR forms sharper spectral peaks in all three target directions, especially exhibiting the clearest bimodal structure and more obvious inter-peak valleys in the region of closely spaced targets, while also having the lowest background noise level, indicating that this method has the best resolution performance in multi-target scenarios.
[0141] from Figure 12 As can be seen from the temporal and positional history diagrams of multi-target motion scenarios, all five algorithms can reflect the general motion trend of the targets, but there are significant differences in trajectory width, background suppression, and intersection region resolution. For example, Figure 12 As shown in (a), the target trajectory of CBF is the widest, with a strong background noise level. Especially when two moving targets approach and intersect, the trajectories overlap significantly, making it difficult to accurately distinguish the targets. Figure 12 As shown in (b) above, MVDR significantly improves the main lobe width of the target trajectory compared to CBF, and the background noise is significantly reduced. Figure 12As shown in (c), RL-CBF compresses the main lobe width of the target trajectory to some extent by deconvolving the CBF azimuth spectrum, but it is still limited by the resolution of the original CBF. Figure 12 As shown in (d), RL-MVDR combines the high-resolution characteristics of MVDR with the spectral sharpening capability of deconvolution, further refining the three target trajectories and maintaining good trajectory separation even during target approach and intersection phases. Figure 12 As shown in (e), PM-RL-MVDR exhibits the clearest target trajectory and the lowest background noise level throughout the entire observation period.
[0142] from Figure 13 and Figure 14 As can be seen from the root mean square error curve and the target detection probability curve shown, by Figure 13 It can be seen that as the input signal-to-noise ratio increases, the RMSE of each algorithm generally shows a downward trend. Figure 14 As the input signal-to-noise ratio (SNR) increases, the target resolution probability of all algorithms except CBF gradually increases, indicating that improving the SNR can effectively improve the target azimuth estimation performance. However, significant differences still exist among the different algorithms. CBF consistently exhibits the highest RMSE and the lowest target resolution probability under high SNR conditions, indicating its weakest ability to resolve close-range targets, limited by the Rayleigh limit. MVDR shows significant improvement over CBF in both metrics, demonstrating the effectiveness of adaptive beamforming in improving spatial resolution. RL-CBF and RL-MVDR further compress the target spectral peaks through deconvolution. RL-MVDR exhibits higher estimation accuracy and resolution probability in the low SNR region, indicating that deconvolution recovery based on the high-resolution MVDR azimuth spectrum is more advantageous. In contrast, PM-RL-MVDR has the lowest RMSE and the highest target resolution probability across the entire SNR range, with its advantage being most pronounced under low SNR conditions.
[0143] In summary, this embodiment introduces deconvolution post-processing and Perona-Malik nonlinear diffusion regularization on the basis of MVDR beamforming. This effectively reduces spectral broadening caused by the point spread function, improves spectral peak focusing and near-space target resolution, and suppresses noise amplification and spurious peak problems in the later stages of standard RL algorithm iteration, thus enhancing deconvolution robustness. This method performs well in both static single / multi-target and dynamic multi-target scenarios. Even in low signal-to-noise ratio environments, it still has the narrowest main lobe, the lowest background spectrum, and the best target separation and trajectory preservation effects. Moreover, it has the smallest estimation error and the highest resolution probability. Its overall azimuth estimation performance is significantly better than traditional methods such as CBF, MVDR, RL-CBF, and RL-MVDR.
[0144] Reference Figure 2A deconvolutional MVDR azimuth spectrum estimation system based on PM regularization includes:
[0145] The first module 201 is used to set array parameters and sound source parameters, and to construct an array receiving signal model.
[0146] The second module 202 is used to calculate the covariance matrix of the array received data based on the array received signal model, and to determine the output power of the MVDR beamformer and the point spread function of the MVDR beamformer.
[0147] The third module 203 is used to substitute the azimuth spectrum of the MVDR beamformer and the point spread function of the MVDR beamformer into the deconvolution iterative algorithm to deconvolve them, obtain the deconvolutioned azimuth spectrum, and determine the azimuth of the target.
[0148] The content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.
[0149] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.
Claims
1. A method for estimating the MVDR azimuth spectrum based on PM regularization deconvolution, characterized in that, Includes the following steps: Set the array parameters and sound source parameters, and construct the array signal receiving model; Calculate the covariance matrix of the array received data based on the array received signal model, and determine the output power of the MVDR beamformer and the point spread function of the MVDR beamformer. The azimuth spectrum of the MVDR beamformer and the point spread function of the MVDR beamformer are substituted into the deconvolution iterative algorithm for deconvolution to obtain the deconvolutioned azimuth spectrum, and the azimuth of the target is determined.
2. The method for estimating the MVDR azimuth spectrum based on PM regularization according to claim 1, characterized in that, The step of setting array parameters and sound source parameters to construct an array received signal model specifically includes: Construct a uniform linear array, the uniform linear array comprising a plurality of array elements, and set array parameters, the array parameters including the array element spacing; The sound source parameters are set, which are several unrelated far-field narrowband plane wave signals, and incident at a preset angle relative to the transverse direction of the uniform linear array. Based on the signals received by the uniform linear array, an array received signal model is constructed.
3. The method for estimating the MVDR azimuth spectrum based on PM regularization according to claim 2, characterized in that, The specific expression for the array received signal model is as follows: In the above formula, This represents the array receiving signal model. Represents an array manifold matrix. This represents received noise that is uncorrelated with the incident signal. This represents several uncorrelated far-field narrowband plane wave signals. Indicates the time.
4. The method for estimating the MVDR azimuth spectrum based on PM regularization deconvolution according to claim 1, characterized in that, The step of calculating the covariance matrix of the array received data based on the array received signal model, and determining the output power of the MVDR beamformer and the dot spread function of the MVDR beamformer, specifically includes: Calculate the covariance matrix of the array received data based on the array received signal model; Obtain the steering vector of the array manifold matrix in the array received signal model, and multiply it with the result of the inversion operation of the covariance matrix of the array received data to construct the weighting vector of the MVDR beamformer; The output power of the MVDR beamformer is obtained by performing a quadratic operation on the weighting vector of the MVDR beamformer and the covariance matrix of the array received data. The output power of the MVDR beamformer is converted into a point convolution form and combined with the weighted vector of the MVDR beamformer to construct the point spread function of the MVDR beamformer.
5. The deconvolution MVDR azimuth spectrum estimation method based on PM regularization according to claim 4, characterized in that, The specific expression for the output power of the MVDR beamformer is as follows: In the above formula, This indicates the output power of the MVDR beamformer. express The power of the directional signal, This represents the weighting vector of the MVDR beamformer. This represents the covariance matrix of the received data. The power representing the noise. express Directional guidance vector, This represents the conjugate transpose operator. express An uncorrelated far-field narrowband plane wave signal.
6. The method for estimating the MVDR azimuth spectrum based on PM regularization according to claim 4, characterized in that, The specific expression for the point spread function of the MVDR beamformer is as follows: In the above formula, This represents the point spread function of the MVDR beamformer. This represents the weighting vector of the MVDR beamformer. This represents the conjugate transpose operator. express The directional guide vector.
7. The method for estimating the MVDR azimuth spectrum based on PM regularization deconvolution according to claim 1, characterized in that, The step of substituting the azimuth spectrum of the MVDR beamformer and the point spread function of the MVDR beamformer into a deconvolution iterative algorithm for deconvolution to obtain the deconvolutioned azimuth spectrum and determining the azimuth of the target specifically includes: Define the regularization term of the PM likelihood function and construct the cost function with regularization constraints; Based on the cost function with PM regularization constraints, the derivative of the cost function with respect to the estimated sound source power distribution is obtained, and an extremum problem is constructed. Based on the extremum problem, the complete extremum problem is obtained by introducing Lagrange multipliers to constrain the estimated sound source power distribution; Obtain the gradient zero-point equation of the complete extremum problem and substitute it into the complete extremum problem to construct the Lagrange multiplier equation; The Lagrange multipliers are determined by multiplying both sides of the Lagrange multiplier equation by the estimated source power distribution and integrating. Substituting the Lagrange multipliers into the Lagrange multiplier equation, we obtain the iterative equation of the RL algorithm based on PM regularization; The azimuth spectrum and point spread function of the MVDR beamformer are substituted into the iterative equation of the RL algorithm based on PM regularization for deconvolution to obtain the deconvolutioned azimuth spectrum.
8. The deconvolution MVDR azimuth spectrum estimation method based on PM regularization according to claim 7, characterized in that, The expression for the Lagrange multipliers is as follows: In the above formula, Represents the Lagrange multipliers. Represents the regularization parameter. Indicates the diffusion coefficient. This represents the estimated power distribution of the sound source. This represents a differential operator.
9. The method for estimating the MVDR azimuth spectrum based on PM regularization deconvolution according to claim 7, characterized in that, The specific expression of the iterative equation of the RL algorithm based on PM regularization is as follows: In the above formula, This indicates the output power of the MVDR beamformer. This represents the point spread function of the MVDR beamformer. Represents the regularization parameter. Indicates the diffusion coefficient. This represents a differential operator.
10. A deconvolutional MVDR azimuth spectrum estimation system based on PM regularization, characterized in that, Includes the following modules: The first module is used to set array parameters and sound source parameters, and to build an array signal receiving model. The second module is used to calculate the covariance matrix of the array received data based on the array received signal model, and to determine the output power of the MVDR beamformer and the point spread function of the MVDR beamformer. The third module is used to substitute the azimuth spectrum of the MVDR beamformer and the point spread function of the MVDR beamformer into the deconvolution iterative algorithm to deconvolve them, obtain the deconvolutioned azimuth spectrum, and determine the azimuth of the target.