Multi-snapshot Newton orthogonal matching pursuit sound source localization method under related Gaussian noise

Abstract

The invention discloses a multi-snapshot Newton orthogonal matching pursuit sound source localization method under related Gaussian noise, and the method employs an autoregression model to estimate the inversion of a noise covariance matrix, carries out the pre-whitening processing of a received signal, and remarkably improves the robustness of a system under the background of related Gaussian noise. Secondly, obtaining initial incident angle estimation by utilizing coarse-grained search, and refining an angle estimation value through Newton iteration so as to improve estimation precision; and further eliminating the optimized angle and the corresponding signal component by using an orthogonal matching pursuit principle, and calculating a residual error. And the iteration stop opportunity is determined according to the self-adaptive termination criterion based on the overestimation probability threshold value, the finally detected angle number is the corresponding actual sound source number, and the limitation that the sound source number needs to be preset or the threshold value is set unreasonably in a traditional method is avoided. According to the method, the multi-source positioning precision under a complex noise background is remarkably improved on the premise of keeping relatively low calculation complexity, and the method has a wide engineering application prospect.

Description

Technical Field

[0001] The present invention belongs to the field of array signal processing and acoustic positioning, and particularly relates to a multi-snapshot Newton orthogonal matching pursuit sound source positioning method under correlated Gaussian noise. Background Art

[0002] In modern sound source localization systems, classic angle-of-arrival estimation algorithms such as Multiple Signal Classification (MUSIC) and Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) have been widely used in practical engineering due to their high resolution and theoretical solvability. However, these methods are generally based on a series of idealized assumptions, particularly regarding noise processing, which is often assumed to be independent and identically distributed, zero-mean, white noise. In reality, this assumption often fails in complex ocean acoustic environments, in the presence of significant electromagnetic interference, or in the presence of device non-idealities. Specifically, noise correlation caused by mutual coupling between array elements, spatially correlated background noise caused by variations in ocean temperature and salinity structure, non-whitening or non-stationary noise processes generated by the device itself, and aliasing caused by structural reflections or boundary multipath can all cause significant correlation in the actual received noise. In such situations, the covariance matrix constructed by traditional algorithms will be distorted by correlated Gaussian noise, destroying the orthogonality between the signal and noise subspaces. This ultimately leads to spectral peak splitting, loss of main path directions, and the appearance of false directions, severely impacting the system's localization accuracy and stability. In recent years, to address challenges such as signal coherence and insufficient snapshots, novel methods such as sparse reconstruction and compressed sensing have emerged, demonstrating robustness under low-sample conditions. However, these methods often rely on white noise or simplified noise models in their model assumptions, lacking the ability to model and suppress correlated Gaussian noise in real environments. Therefore, to improve the performance of sound source localization systems in complex correlated Gaussian noise scenarios, it is necessary to introduce a more universal and adaptive noise modeling mechanism, construct a noise covariance structure in realistic settings, integrate space-time spectral estimation techniques, and incorporate adaptive optimization strategies to structurally extend traditional subspace-based algorithms to enhance their applicability and robustness in non-ideal environments. Summary of the Invention

[0003] To address the performance degradation of existing direction estimation algorithms in the presence of correlated Gaussian noise, the present invention proposes a multi-snapshot Newtonized Orthogonal Matching Pursuit (W-MNOMP) sound source localization method under correlated Gaussian noise. This method is an improved multi-snapshot Newtonized Orthogonal Matching Pursuit (W-MNOMP) algorithm. This method uses an autoregressive (AR) model to characterize the correlation between noises, inverts the Yule-Walker equation to obtain the inverse noise covariance matrix, and pre-whitens the signal to suppress the impact of correlated Gaussian noise on estimation performance. At the same time, a Newton iterative refinement step is introduced to improve the accuracy of the initial angle estimate and avoid deviations caused by off-grid effects. Furthermore, an adaptive termination criterion based on a chi-square threshold and overestimation probability control is used, eliminating the need to pre-set the number of sources, thereby enhancing the universality and application flexibility of the present invention.

[0004] The purpose of the present invention is achieved through the following technical solutions:

[0005] A multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise, characterized by comprising the following steps:

[0006] S1: Establishing an array receiving signal model in a scenario where correlated Gaussian noise exists, wherein the correlated Gaussian noise is modeled using an autoregressive model;

[0007] S2: Calculate the inverse matrix of the noise covariance matrix using the model parameters of the correlated Gaussian noise and perform pre-whitening on the received signal;

[0008] S3: Set the overestimation probability and the number of grid search angles, and calculate the iteration stopping threshold;

[0009] S4: Based on the pre-whitened received signal, a coarse search of the incident angle of the sound source is performed by maximizing the objective function;

[0010] S5: Perform Newton iterative optimization on the angle obtained by the rough search to obtain a more accurate estimated angle;

[0011] S6: Use the orthogonal matching pursuit principle to remove the optimized angle and the corresponding signal component from the received signal, and calculate the residual energy; if the residual energy is less than the iteration stop threshold, stop the iteration and output the estimated angle; otherwise, return to step S4.

[0012] Furthermore, the correlated Gaussian noise in step S1 is modeled using a P-order autoregressive model. The noise component received by each array element is linearly composed of the noise components of the P adjacent array elements and superimposed with Gaussian white noise, thereby exhibiting noise correlation characteristics between array elements.

[0013] Furthermore, the calculation steps of the inverse matrix of the noise covariance matrix in step S2 are:

[0014] First, the coefficients in the autoregressive model are estimated using the Yule-Walker equation. Then, the estimated coefficients are combined into two Toeplitz matrices, and the two matrices are combined to obtain the inverse matrix of the covariance matrix. Finally, the inverse matrix is square rooted, and the square root of the inverse matrix is multiplied on both sides of the equation of the array received signal model to obtain a pre-whitened received signal.

[0015] Furthermore, in step S3, the iteration stopping threshold is calculated based on the overestimation probability as follows:

[0016] The projection energy of the pre-whitened received signal on the array steering vector is used as an indicator for calculating the iterative stopping threshold. The iterative stopping threshold that satisfies the overestimation probability is obtained by reverse deduction based on a preset overestimation probability and the inverse of the cumulative distribution function corresponding to the chi-square distribution obeyed by the projection energy.

[0017] Furthermore, the coarse search in step S4 is equivalent to defining angle grid points under a given search angle range and finding the angle value corresponding to the minimized cost function; wherein the cost function is to minimize the noise energy after pre-whitening.

[0018] Furthermore, the Newton iterative optimization in step S5 is specifically as follows: defining a function related to the current angle estimation, which function is composed of the relationship between the received signal and the noise covariance matrix; the new angle estimation value is equal to the current estimation value minus the correction term, and the correction term is the ratio of the first and second order derivatives of the function related to the current angle estimation to the angle; at this point, the new angle estimation value replaces the angle obtained in the coarse search step.

[0019] Furthermore, in step S6, each time optimization is performed on all angles detected in the previous round.

[0020] The invention discloses a multi-snapshot Newton orthogonal matching pursuit sound source localization device under correlated Gaussian noise, which is used to implement a multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise.

[0021] An electronic device, comprising:

[0022] one or more processors;

[0023] The storage device is used to store one or more programs. When the one or more programs are executed by the electronic device, the electronic device implements a multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise.

[0024] A computer-readable storage medium stores a program, which, when executed by a processor, implements a multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise.

[0025] The beneficial effects of the present invention are as follows:

[0026] (1) The present invention introduces an autoregressive model to estimate the noise covariance structure and performs pre-whitening, which effectively suppresses the interference of noise correlation on positioning performance and significantly enhances the adaptability of the positioning method in complex noise environments.

[0027] (2) The present invention combines coarse-grained search with Newton iterative optimization to achieve high-precision incident angle estimation with low computational complexity, overcoming the problem of insufficient accuracy of traditional matching pursuit methods.

[0028] (3) The present invention introduces an adaptive termination criterion based on the overestimation probability to achieve online discrimination of the estimated angle and thus obtain the number of sound sources, thus avoiding the situation in which the traditional method requires a preset number of sound sources or unreasonable threshold settings. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is a flow chart of a method according to one embodiment of the present invention.

[0030] Figure 2 Schematic diagram of the impact of correlated Gaussian noise of different orders on positioning.

[0031] Figure 3 The left figure is before pre-whitening, and the right figure is after pre-whitening.

[0032] Figure 4 1 is an iterative process diagram of a positioning method according to one embodiment of the present invention, wherein FIG (a) is the original spatial spectrum, FIG (b) is the first iteration, FIG (c) is the second iteration, and FIG (d) is the third iteration.

[0033] Figure 5 The figures are performance comparison diagrams of the method of one embodiment of the present invention and other positioning methods, wherein Figure (a) is MUSIC, Figure (b) is W-MUSIC, Figure (c) is MNOMP, and Figure (d) is W-MNOMP. DETAILED DESCRIPTION

[0034] The present invention is further described below with reference to the accompanying drawings and specific examples, but the implementation and protection scope of the present invention are not limited thereto.

[0035] The multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise proposed in the present invention aims to solve the problem that the performance of traditional array signal processing methods is significantly reduced when the noise is correlated. The method first models the noise at the receiving end through an autoregressive model and estimates its covariance structure, thereby providing a basis for whitening processing and realizing pre-whitening operation on the array received signal, thereby effectively suppressing the interference of correlated Gaussian noise on direction estimation. On the preprocessed signal, a coarse-grained direction search is used to obtain the initial incident angle estimate, and the angle parameters are further refined in combination with the Newton iterative algorithm to improve the estimation accuracy. The OMP criterion is further used to remove the optimized angle and the corresponding signal component from the received signal, and the residual energy is calculated for the next round of iteration. In order to overcome the limitation of the traditional method that the number of sound sources needs to be preset, the present invention combines an adaptive termination criterion based on an overestimation probability threshold, which can dynamically judge the number of sound sources and control the iterative process to ensure the accuracy and robustness of the estimation results.

[0036] On the one hand, the multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise of the present invention specifically includes the following steps:

[0037] S1: Establish an array receiving signal model in the presence of correlated Gaussian noise. The correlated Gaussian noise is modeled using an autoregressive model. The model is specifically expressed as:

[0038]

[0039] in, Indicates that the array receives the signal, express Segment incident signal, represents the steering matrix, is additive noise.

[0040] Each element in is represented as:

[0041]

[0042] in, is the array element spacing, For the Angle of incidence, is the number of array elements, is the signal wavelength.

[0043] Different from the general Gaussian white noise assumption, the correlation between array elements is considered here, and the noise term is modeled using the autoregressive model (AR). Each item in can be expressed as

[0044]

[0045] Among them, the subscript and Respectively represent array elements and time, represents the coefficient of the AR model, is the model order, The corresponding variance is Gaussian white noise.

[0046] That is, the noise component received by each array element is linearly composed of the noise components of the P adjacent array elements and superimposed with Gaussian white noise, thus showing the noise correlation characteristics between array elements.

[0047] S2: Calculate the inverse matrix of the noise covariance matrix using the model parameters of the correlated Gaussian noise and perform pre-whitening on the received signal. The inverse matrix of the noise covariance matrix can be expressed as:

[0048]

[0049] ,

[0050] in, Represents the coefficients in the AR model, which can be solved by combining the classic Yule-Walker equation. Therefore, when the AR model coefficients are known or estimated, the Toeplitz matrix can be used and The inverse of the noise covariance matrix is calculated and used to pre-whiten the received signal. Each algorithm iteration assumes that only a single angle exists. This angle is detected and removed before the next iteration. Therefore, in a single-angle scenario, the whitened array received signal model is expressed as:

[0051]

[0052] in, Represents the steering vector corresponding to a single angle, Represents a single incident signal.

[0053] S3: Set the overestimation probability and the number of grid search angles, and calculate the iteration stop threshold. The threshold calculation formula is as follows:

[0054]

[0055] in, To meet the degree of freedom The chi-square distribution of corresponds to the inverse of the cumulative distribution function, is the preset overestimation probability, The number of grid points is pre-determined.

[0056] S4: Based on the pre-whitened received signal, a coarse search is performed on the incident angle of the sound source by maximizing the objective function.

[0057] This step is equivalent to searching at a given angle. Under the premise of minimizing the cost function, find the angle estimation value corresponding to the minimum cost function. For the set angle interval, the cost function is expressed as:

[0058]

[0059] in represents the Frobenius norm, and the coefficient in the upper right corner represents the square operation.

[0060] The cost function can be further expressed as follows:

[0061]

[0062] Where T represents the total number of snapshots of the received signal, and the subscript Indicates the first A quick shot, represents the array received signal vector at the t-th snapshot, represents the signal of the t-th snapshot, Indicates the real part operation. Finally, the angle estimation value can be obtained

[0063]

[0064] S5: Perform Newton iterative optimization on the angles obtained by the rough search to obtain a more accurate estimated angle. Note:

[0065]

[0066] Its mathematical meaning represents the projected energy of the received signal component on the steering vector. Taking the partial derivative of the angle, we can get its rate of change with respect to the angle. Using the Newton iteration principle, we can get the updated angle estimate after iterative optimization:

[0067]

[0068]

[0069]

[0070] in, and They represent the first and second derivatives of the steering vector with respect to the incident angle.

[0071] S6: Use the orthogonal matching pursuit principle to remove the optimized angle and the corresponding signal component from the received signal, and calculate the residual energy; if the residual energy is less than the iteration stop threshold, stop the iteration and output the estimated angle; otherwise, return to step S4.

[0072] The algorithm stops iterating when the following equation is satisfied:

[0073]

[0074] in, Indicates the received signal after removing the detected arrival angle signal component The corresponding The formula is expressed as: for all pre-defined arrival angles, the projection energy of the signal residual at the arrival angle is less than the threshold.

[0075] Corresponding to the embodiment of the multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise, the present invention also provides an embodiment of a multi-snapshot Newton orthogonal matching pursuit sound source localization device under correlated Gaussian noise.

[0076] An embodiment of the present invention provides a multi-snapshot Newton orthogonal matching pursuit sound source localization device under correlated Gaussian noise, including one or more processors for implementing the multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise in the above embodiment.

[0077] The embodiment of the multi-snapshot Newton orthogonal matching pursuit sound source localization device under correlated Gaussian noise of the present invention can be applied to any device with data processing capabilities, and the any device with data processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented by software, or by hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capabilities in which it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for execution. From the hardware level, in addition to the processor, memory, network interface, and non-volatile memory, the any device with data processing capabilities in which the device in the embodiment is located can also include other hardware according to the actual function of the any device with data processing capabilities, which will not be described in detail.

[0078] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0079] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the partial description of the method embodiments. The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present invention. A person of ordinary skill in the art can understand and implement the present invention without inventive work.

[0080] An embodiment of the present invention further provides a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, the multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise in the above embodiment is implemented.

[0081] The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the aforementioned embodiments, such as a hard disk or memory. The computer-readable storage medium may also be an external storage device, such as a plug-in hard disk, a smart memory card (SmartMedia card, SMC), an SD card, a flash card, etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit of any device with data processing capabilities and an external storage device. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or is to be output.

[0082] The present invention is tested by simulation and compared with other positioning algorithms such as MUSIC, W-MUSIC and MNOMP. Figure 2 The figure below shows the impact of correlated Gaussian noise of different orders on positioning. It can be seen that white noise has a nearly flat spatial spectrum, indicating no specific directionality. However, when the noise is correlated, such as in third-order or fourth-order AR noise scenarios, the spatial spectrum exhibits directionality within a specific angular range, which is not conducive to sound source arrival angle estimation.

[0083] Figure 3 Figure 2 is the noise covariance coefficient diagram before and after pre-whitening. It can be seen from the figure that before pre-whitening, due to the presence of correlated noise, the covariance coefficients between array elements are centered on the diagonal line and widen to both sides, indicating that there is correlation between array elements.

[0084] Figure 4It is an algorithm iteration process, from the most original spatial spectrum to the third iteration, the correct three sound source arrival angles are detected, and the final signal residual is lower than the pre-calculated threshold, at which time the algorithm automatically stops iterating.

[0085] Figure 5 The following figure compares the performance of the present invention and other positioning algorithms. As can be seen, the MUSIC algorithm's positioning results are all concentrated near 0°. While the W-MUSIC algorithm mitigates the effects of correlated Gaussian noise, the angular error near 0° is significant. The MNOMP algorithm also exhibits numerous false peaks. In contrast, the present invention accurately estimates the true three angles of arrival, resulting in very sharp spectral peaks.

[0086] By incorporating autoregressive noise modeling, Newton iterative optimization, and an adaptive sound source number determination mechanism, this method suppresses the effects of noise correlation and improves positioning accuracy while maintaining low computational complexity. This significantly enhances the robustness and practicality of multi-source sound localization in complex environments. Simulation results demonstrate that this method achieves higher positioning accuracy and greater adaptability to correlated Gaussian noise.

[0087] Those skilled in the art will understand that the foregoing descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art will still be able to modify the technical solutions described in the foregoing examples or substitute equivalents for some of the technical features therein. Any modifications, equivalent substitutions, etc. made within the spirit and principles of the invention shall be included within the scope of protection of the invention.

Claims

1. A multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise, characterized in that: The following steps are involved: S1: Establishing an array receiving signal model in a scenario where correlated Gaussian noise exists, wherein the correlated Gaussian noise is modeled using an autoregressive model; S2: Calculate the inverse matrix of the noise covariance matrix using the model parameters of the correlated Gaussian noise and perform pre-whitening on the received signal; S3: Set the overestimation probability and the number of grid search angles, and calculate the iteration stopping threshold; S4: Based on the pre-whitened received signal, a coarse search of the incident angle of the sound source is performed by maximizing the objective function; S5: Perform Newton iterative optimization on the angle obtained by the rough search to obtain a more accurate estimated angle; S6: Use the orthogonal matching pursuit principle to remove the optimized angle and the corresponding signal component from the received signal, and calculate the residual energy; if the residual energy is less than the iteration stop threshold, stop the iteration and output the estimated angle; otherwise, return to step S4.

2. The multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise according to claim 1, characterized in that: The correlated Gaussian noise in step S1 is modeled using a P-order autoregressive model. The noise component received by each array element is linearly composed of the noise components of the P adjacent array elements and superimposed with Gaussian white noise, thereby exhibiting noise correlation characteristics between array elements.

3. The multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise according to claim 1, characterized in that: The calculation steps of the inverse matrix of the noise covariance matrix in step S2 are: First, the coefficients in the autoregressive model are estimated using the Yule-Walker equation. Then, the estimated coefficients are combined into two Toeplitz matrices, and the two matrices are combined to obtain the inverse matrix of the covariance matrix. Finally, the inverse matrix is square rooted, and the square root of the inverse matrix is multiplied on both sides of the equation of the array received signal model to obtain a pre-whitened received signal.

4. The multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise according to claim 1, characterized in that: In step S3, the iteration stopping threshold is calculated based on the overestimation probability as follows: The projection energy of the pre-whitened received signal on the array steering vector is used as an indicator for calculating the iterative stopping threshold. The iterative stopping threshold that satisfies the overestimation probability is obtained by reverse deduction based on a preset overestimation probability and the inverse of the cumulative distribution function corresponding to the chi-square distribution obeyed by the projection energy.

5. The multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise according to claim 1, characterized in that: The coarse search in step S4 is equivalent to defining angle grid points under a given search angle range and finding the angle value corresponding to the minimized cost function; wherein the cost function is to minimize the noise energy after pre-whitening.

6. The multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise according to claim 1, characterized in that: The Newton iterative optimization in step S5 is specifically as follows: defining a function related to the current angle estimate, which is composed of the relationship between the received signal and the noise covariance matrix; the new angle estimate is equal to the current estimate minus a correction term, and the correction term is the ratio of the first and second order derivatives of the function related to the current angle estimate to the angle; at this point, the new angle estimate replaces the angle obtained in the coarse search step.

7. The multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise according to claim 1, characterized in that: In step S6, each time, optimization is performed on all angles detected in the previous round.

8. A multi-snapshot Newton orthogonal matching pursuit sound source localization device under correlated Gaussian noise, characterized in that: The device is used to implement the multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise as described in any one of claims 1 to 7.

9. An electronic device, characterized in that: include: one or more processors; A storage device for storing one or more programs, which, when executed by the electronic device, enables the electronic device to implement the multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that A program is stored thereon, and when the program is executed by a processor, the multi-snapshot Newton orthogonal matching pursuit sound source localization method under correlated Gaussian noise as claimed in any one of claims 1 to 7 is implemented.

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