A passive synthetic aperture sonar direction finding method based on variational message passing

Abstract

The application specifically relates to a passive synthetic aperture sonar direction finding method based on variational message passing, and belongs to the technical field of signal processing. The application adopts a broken line model to fit a distorted array shape, and establishes an array receiving data model containing array shape disturbance, in view of the problems that a traditional algorithm can only process space-time coherent signals, is sensitive to array shape distortion, and has high operation complexity; a spatial domain super-complete dictionary is constructed to convert a direction finding problem into a sparse reconstruction problem, a layered probability model is established by using a Gaussian scale mixed model and is expressed as a factor graph; each parameter posterior probability is solved by using variational message passing iteration, high-dimensional matrix inversion is avoided, and angle fine estimation is realized by combining Laplace interpolation. The application can jointly estimate a signal source direction and array shape distortion parameters, keeps high precision in a random signal and distorted array shape environment, significantly reduces operation complexity, and is suitable for underwater passive synthetic aperture high-resolution direction finding engineering application.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and specifically to a passive synthetic aperture sonar direction finding method based on variational message passing. Background Technology

[0002] The spatial angular resolution of a linear array is determined by the Rayleigh limit (the ratio of the incident signal wavelength to the array aperture). To improve weak target detection capabilities and angle estimation accuracy, the array aperture needs to be increased, which undoubtedly increases the hardware implementation cost of the array direction-finding system. Passive synthetic aperture array processing technology can convert the time gain of a towed small-aperture array into spatial gain, achieving the same direction-finding accuracy as an equivalent large-aperture array, and thus has been widely used in the field of underwater acoustic signal processing.

[0003] Traditional passive synthetic aperture direction finding algorithms can be divided into two categories: beam-domain algorithms and element-domain algorithms. Beam-domain algorithms include the Yen-Carey algorithm (NC Yen and W. Carey, “Application of synthetic-aperture processing to towed-array data,” J. Acoust. Soc. Amer., vol. 86, no.2, pp. 754-765, 1989) and the FFTSA algorithm (S. Stergiopoulos and H. Urban, “A new passive synthetic aperture technique for towed arrays,” IEEE J. Oceanic Eng., vol. 17, no. 1, pp. 16-25, 1992). These algorithms coherently superimpose the beam outputs of a small-aperture physical array at each sampling time to obtain beam-domain direction finding results for a virtual long array.Array element domain algorithms include ETAM algorithm (S. Stergiopoulos and EJ Sullivan, "Extended towered array processing by overlapped correlator," J. Acoust. Soc. Amer., vol. 86, no. 1, pp. 158-171, 1989), METAM algorithm (R. Rajagopal and P. Ramakrishna Rao, "A modified extended tower method (METAM) for passive synthetic aperture beamforming," International Symposium on Signal Processing and its Applications, ISSPA, Gold Coast, Australia, 1996), TD-ETAM algorithm (S. Kim, DH Youn, and C. Lee, "Temporal domain processing for a synthetic aperture array," IEEE J. OceanicEng., vol. 27, no. 2, pp. 322-327, 2002) and Jin-Li algorithm (S. Jin, Y. Li, and H. Huang, “An improved passive synthetic aperture algorithm based on curvilinear maneuverability of autonomous underwater vehicles,” J. Electron. Inf. Technol., vol. 40, no. 9, pp. 2265-2272, 2018, etc. These algorithms utilize overlapping correlators to compensate for the phase deviation of the received data from the towed array at each sampling time, thereby synthesizing the received data of a virtual long array and improving angular resolution. However, the aforementioned passive synthetic aperture direction finding algorithms are only applicable when the array has no array distortion during towing. In practical applications, due to the influence of ocean currents and non-uniform tugboat speeds, the towed array is difficult to maintain an ideal horizontal straight line state, which makes the above algorithms unable to effectively synthesize a virtual long array and obtain high angular resolution.Furthermore, when the incident source is an empty random source, the signals received by the overlapping subarrays at adjacent sampling times are no longer correlated, making it impossible to estimate the phase compensation factor and thus preventing the virtual aperture synthesis process of the aforementioned algorithm from proceeding. Although the maximum likelihood passive synthetic aperture direction finding algorithm proposed by Nuttall et al. (AH Nuttall, “The maximum likelihood estimator for acoustic synthetic aperture processing,” IEEE J. Oceanic Eng., vol. 17, no.1, pp. 26-29, 1992) can partially solve the problem of not being able to detect random sources, this algorithm involves multidimensional search, has an extremely high computational load, and cannot be applied to practical engineering. In recent years, sparse Bayesian learning techniques have achieved parameter estimation accuracy comparable to maximum likelihood algorithms, but with significantly reduced computational complexity. Traditional sparse Bayesian learning algorithms use the expectation-maximization (EM) technique to iteratively maximize the posterior probability of unknown parameters in a hierarchical probability model. This probability estimation process involves matrix inversion operations, and its real-time performance cannot be guaranteed in high-dimensional data models. To overcome this shortcoming, Ziniel et al. introduced approximate message passing techniques into the sparse Bayesian learning framework (J. Ziniel and P. Schniter, “Efficient high-dimensional inference in the multiple measurementvector problem,” IEEE Trans. Signal Process., vol. 61, no. 2, pp. 340-354, 2012). By constructing a factor graph model and employing a sum-product message passing algorithm, they avoided the matrix inversion operation required when estimating the posterior probability of unknown parameters. However, this algorithm can only handle Gaussian prior probabilities. When the sparse prior probability model does not satisfy this distribution, the message passing process of this algorithm cannot proceed. Therefore, a more universal and low-complexity passive synthetic aperture high-resolution direction finding method needs to be designed.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] This invention provides a passive synthetic aperture sonar direction finding method based on variational message passing, aiming to solve the problems of traditional passive synthetic aperture sonar direction finding methods that can only process spatiotemporal coherent signals, are sensitive to distorted array configurations, and have high computational complexity.

[0006] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0007] According to a first aspect of the present invention, a passive synthetic aperture sonar direction finding method based on variational message passing is provided, the method comprising: Step 1: Establish the received data model of the towed array at any sampling time, use a piecewise linear model to approximate the actual distorted array shape, and construct the array observation data expression corresponding to the sampling time; Step 2: Define a spatial overcomplete array manifold dictionary, convert the array received data into an equivalent sparse observation model, and transform the direction of arrival estimation problem into the problem of determining the coordinates of non-zero elements in the sparse vector; Step 3: Establish a hierarchical probability model corresponding to the sparse observation model, and represent the hierarchical probability model equivalently using a factor graph; Step 4: Based on the factor graph, the variational message passing algorithm is used to iteratively calculate the maximum a posteriori probability estimate of each unknown variable to obtain the spatial reconstruction result of the incident source azimuth. Then, the Laplace interpolation technique is used to achieve the precise estimation of the direction of arrival angle.

[0008] In some exemplary embodiments, step 1, which uses a piecewise linear model to approximate the actual distorted array shape and constructs the array observation data expression corresponding to the sampling time, specifically involves: by Drag uniform linear array receiver The incident signal from an underwater sound source, wherein the element spacing is... The actual distorted array formation is approximated by a piecewise linear model, that is, the line connecting the first element and its adjacent elements is used as the reference line, and vectors are used to represent the distorted array formation. Describe the angle between the lines connecting the remaining array elements and the reference line; then the sampling time... Corresponding array observation data Represented as:

[0009] in, Indicates the sampling time The corresponding array manifold matrix, Indicates the first One incident source direction and sampling time The corresponding guide vector, It is by A waveform vector composed of the complex amplitudes of the incident signals. and They represent the first Each information source at the sampling time The amplitude and phase, Indicates the sampling time The noise received by each array element.

[0010] In some exemplary embodiments, step 2, which involves converting the array-received data into a sparse observation model, specifically includes: Define a dictionary of spatially overcomplete array manifolds ,in The array receives data based on the preset number of spatial discrete grids. The equivalent representation is the following sparse observation model:

[0011] in, It is a sparse vector, constructed as follows: Given a predefined spatial grid... If it does not correspond to the actual incident signal DOA, then let ,otherwise The element value at the corresponding position in the vector is the true waveform of the signal incident from this direction.

[0012] In some exemplary embodiments, the hierarchical probability model described in step 3 is used to characterize the prior distribution of each latent variable in the array received data, specifically: The incident signal waveform vector follows a complex Gaussian distribution, and its accuracy parameter follows a gamma distribution; The array distortion vector follows a Gaussian distribution, and its precision parameter follows a gamma distribution. The array receives noise accuracy according to a gamma distribution.

[0013] In some exemplary embodiments, the variational message passing algorithm described in step 4 is specifically as follows: The posterior probability of a variable node in the factor graph is calculated as the product of messages from all factor nodes flowing into that node; the message sent by a factor node is calculated as the integral of the posterior probability of the variable nodes connected to that factor node; the posterior distribution of each latent variable is updated iteratively until convergence.

[0014] In some exemplary embodiments, the Laplace interpolation technique described in step 4 specifically includes: By selecting sampling points near the spectral peak in the spatial reconstruction results to construct an interpolation function, taking the derivative of the interpolation function and setting the derivative to 0, the accurate estimation result of the true direction of arrival of the source is obtained.

[0015] According to a second aspect of the present invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the passive synthetic aperture sonar direction finding method based on variational message passing as described in the first aspect.

[0016] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, it implements the passive synthetic aperture sonar direction finding method based on variational message passing described in the first aspect.

[0017] According to a fourth aspect of the present invention, an electronic device is provided, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to implement the passive synthetic aperture sonar direction finding method based on variational message passing as described in the first aspect by executing the executable instructions.

[0018] The passive synthetic aperture sonar direction finding method based on variational message passing provided by the embodiments of the present invention has the following advantages compared with the prior art: (1) To address the issue of decreased accuracy in traditional passive synthetic aperture direction-finding algorithms under array distortion scenarios, this invention proposes a direction-finding method based on Bayesian sparse reconstruction theory to enhance the robustness of existing algorithms in non-ideal signal environments. This method fully characterizes the spatial sparsity of the incident signal using a Gaussian scale mixture model, characterizes the prior distribution of array distortion parameters and array received noise using a Gaussian probability density function, and characterizes the prior distribution of array disturbance, signal, and noise accuracy using a gamma probability density function. The established hierarchical probability model can adaptively adjust its sparsity according to the actual signal environment, exhibiting strong scalability.

[0019] (2) To address the problem that traditional sparse Bayesian learning algorithms have high computational complexity and cannot be applied to high-dimensional array direction finding scenarios, this invention designs a low-complexity probabilistic inference method based on variational message passing theory. This method first represents the hierarchical probability model equivalently in the form of a factor graph. Then, the inference process of the posterior probability of each factor node is transformed into a computation process of the information flow flowing into that node. This computation process decouples the elements in the latent variables, allowing for accurate estimation of the posterior probability of each latent variable without the need for time-consuming matrix inversion operations. After the algorithm converges, this invention also uses the spatial domain reconstruction results and the Laplace interpolation principle to obtain a low-complexity angle estimation method. This method does not require the time-consuming joint estimation operations of grid point errors and sparse azimuth sets found in traditional sparse direction finding algorithms.

[0020] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0021] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0022] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 A schematic diagram of the broken-line approximation model of the distorted array; Figure 3 This is a schematic diagram of a factor graph model; Figure 4 This is a schematic diagram illustrating the transmission of variable message flow in a factor graph. Figure 5 This is a schematic diagram of the transmission of factor message flow in a factor graph; Figure 6 A schematic diagram of Laplace interpolation; Figure 7 Spatial spectrum comparison of the method designed in this invention with ETAM, FFTSA, and Yang's algorithm (J. Yang, YX Yang, and B. Liao, “Sparse Bayesian synthetic aperture processing based DOA estimation with deformed towed arrays,” IEEE Int. Conf. Acoust. Speech Signal Process., Seoul, Korea, 2024, pp. 13161-13165.) in a random signal environment; Figure 8 The RMSE of the direction finding results of the method designed in this invention and the traditional passive synthetic aperture direction finding algorithm changes with SNR (the incident source is a random source, and the number of sources is 3). Detailed Implementation

[0023] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0024] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0025] To address the shortcomings and deficiencies of existing technologies, this example embodiment provides a passive synthetic aperture sparse high-resolution direction finding method with lower computational complexity. This method utilizes variational message passing technology to iteratively maximize the posterior probability of each unknown parameter in a Bayesian network, achieving direction finding accuracy comparable to maximum likelihood methods, but with significantly reduced computational complexity. The specific design process is as follows: First, probabilistic modeling is performed on the received data of the towed array with distorted array shape, using a Gaussian-scale mixture probability model as the spatial sparse prior model of the incident signal. Second, for the factor graph of the established hierarchical probability model, the variational message passing algorithm is iteratively used to complete probability inference, i.e., maximizing the log-likelihood function of the array observation data. Finally, Laplace interpolation technology is used to achieve precise angle estimation. The algorithm designed in this invention can jointly estimate the incident azimuth of an unknown signal source and array distortion parameters, and can achieve effective aperture synthesis in random signal environments.

[0026] refer to Figure 1 As shown, the specific steps may include: Step 1: Establish the received data model of the towed array at any sampling time, use a piecewise linear model to approximate the actual distorted array shape, and construct the array observation data expression corresponding to the sampling time; Step 2: Define a spatial overcomplete array manifold dictionary, convert the array received data into an equivalent sparse observation model, and transform the direction of arrival estimation problem into the problem of determining the coordinates of non-zero elements in the sparse vector; Step 3: Establish a hierarchical probability model corresponding to the sparse observation model, and represent the hierarchical probability model equivalently using a factor graph; Step 4: Based on the factor graph, the variational message passing algorithm is used to iteratively calculate the maximum a posteriori probability estimate of each unknown variable to obtain the spatial reconstruction result of the incident source azimuth. Then, the Laplace interpolation technique is used to achieve the precise estimation of the direction of arrival angle.

[0027] The steps in this exemplary embodiment will now be described in more detail with reference to the accompanying drawings and embodiments.

[0028] In step S1, a model of the received data of the towed array at any sampling time is established.

[0029] Assuming underwater There are one sound source, and the receiving array is... N A uniform linear array of hydrophones with an element spacing of [missing information]. ,but Time of the first The signal received by the hydrophone can be represented as:

[0030] in, , Indicates the first Each sampling time, Indicates the time sampling interval; and They represent the first The waveforms of noise received by each signal source and array, and , , and They represent the first Each information source at the sampling time The amplitude, phase, and angular frequency; When the first element is used as the reference element, the first... The hydrophone received the first The relative propagation time delay of information from each source.

[0031] A broken-line model is used to approximate the distorted dragged formation, that is, the line connecting the first element (located at the drag point) and its adjacent elements is used as the reference line, and vectors are used to represent the distorted dragged formation. Describe the angles between the lines connecting the remaining array elements and the reference line, such as Figure 2 As shown. If the first array element is located at the starting timing point... Then the first The spatial coordinates of each array element at this moment are:

[0032]

[0033] Based on the method of establishing the broken line model, At this time, the first The time delay of each array element relative to the first array element can be expressed as:

[0034] in, The first calculated based on the piecewise linear model Each array element and the reference array element in the... The incident direction of the signal source The spatial distance is calculated as follows: ; It indicates the speed of sound.

[0035] When the drag speed of the hydrophone array is At that time, each array element was at the specified time. The spatial coordinates are: ;

[0036] At this time, the The element received the first The waveform information of each signal source is as follows:

[0037] in, and These represent the received number of... The time angular frequency and spatial angular frequency of each signal source are calculated as follows:

[0038]

[0039] by Represents an array manifold matrix. Represents the guide vector, its first... Each element can be represented as After defining the above parameters, the sampling time... Corresponding array observation data It can be represented as:

[0040] in, It is by K A waveform vector composed of the complex amplitudes of the incident signals. Includes sampling time The noise received by each array element, where each element of the vector follows a mean of 0 and a precision (i.e., the reciprocal of the variance) of . The Gaussian distribution.

[0041] In step S2, an array sparse observation model is established.

[0042] Define a dictionary of spatially overcomplete array manifolds ,in The array receives data based on the preset number of spatial discrete grids. This can be equivalently represented by the following sparse observation model:

[0043] in, A sparse vector can be constructed as follows: given a predefined spatial grid... If it does not correspond to the actual incident signal DOA, then let ,otherwise The element value at the corresponding position in the vector represents the true waveform of the signal incident from this direction. After obtaining the sparse observation model, the DOA estimation problem can be equivalently transformed into... The problem of determining the coordinates of non-zero elements. Furthermore, using the mean as... The covariance matrix is Gaussian distribution represents the array distortion vector The prior probability model, without loss of generality, can be assumed to be... The array steering vector can be approximated by the following Taylor expansion:

[0044] in, , Let be a triangular matrix. Under the above sparse observation model, the likelihood function of the array's received data can be expressed as:

[0045] in, This represents a spatially complete signal waveform matrix.

[0046] In step S3, a Bayesian hierarchical probability model is established and represented by a factor graph, which facilitates the derivation of a low-complexity probability inference algorithm.

[0047] A hierarchical probability model is established to finely characterize the prior distribution of each latent variable in the array-received data. Specifically: First, assume the signal waveform vector at any sampling time... Each element in the equation is independent, and any element... Follows the mean of 0 and the precision is If the complex Gaussian distribution is followed, then The prior distribution can be expressed as the following complex Gaussian distribution:

[0048] in, express The One element, Represents the precision vector. express .

[0049] By applying a second layer of conjugate priors to the aforementioned Gaussian priors, a sparse prior can be synthesized. This conjugate prior conforms to the following gamma distribution:

[0050] in, and These represent shape parameters and scale parameters, respectively.

[0051] Secondly, assume the array distortion vector The elements in the array follow a mean of 0 and a precision of 1. The Gaussian prior, then The prior distribution can be expressed as:

[0052] in, express A zero vector of dimension 1 express An identity matrix of dimension 1.

[0053] Finally, regarding noise accuracy and the precision of distorted variables Perform probabilistic modeling. Assume... and They all follow the following gamma distribution:

[0054]

[0055] in, , Indicates shape parameters, , Indicates the scale parameter.

[0056] To facilitate probabilistic inference using message passing algorithms, the established hierarchical probability model needs to be represented in the form of a factor graph, such as... Figure 3 As shown in the diagram, in this factor graph, a rectangle represents a factor node, and a short line represents a variable node. Each factor node represents a specific conditional probability distribution, and the variable on which this distribution depends is determined by the variable referred to by the short line connected to this factor node. Figure 3 The correspondence between the factor nodes included in the model and the prior distributions in the hierarchical probability model is as follows: , , , , , , , , , . express The prior probability, express The prior probability, which is a conditional probability, is... Prior probability density function and variables and related, The prior probability is represented by , which is a conditional probability. Prior probability density function and variables related.

[0057] In step S4, the maximum a posteriori probability estimation results of each unknown variable in the factor graph are obtained by using the variational message passing algorithm, and then the spatial reconstruction result of the incident source azimuth is obtained. Based on this result, the angle estimation result is obtained by using the Laplace interpolation technique.

[0058] The design concept of the variational message passing algorithm is as follows: the message received on each "edge" (i.e., the short line where the variable node is located) in the factor graph (i.e., the posterior distribution of the variable corresponding to that edge) is obtained by multiplying the messages flowing into each factor node connected to it. Figure 4 For example, Let represent the posterior probability of any variable in the factor graph. It can be calculated using the following formula:

[0059] in, and This indicates messages flowing into this side. Estimated... Then, it can also serve as the message flow input for the node connected to that edge, calculating the message flow emitted by each factor node (such as...). Figure 5 As shown, where (Representing any factor node in the factor graph), the specific calculation formula is:

[0060] Using the message passing algorithm described above, the iterative update formula for the posterior distribution of each latent variable in the factor graph is obtained as follows: posterior distribution This can be represented by the product of the message streams flowing into the node. The specific calculation formula is as follows, and the calculation result conforms to the Gaussian distribution:

[0061] in, This indicates taking the first element of the matrix within the parentheses. Line 1 Operations on column elements This indicates the operation of obtaining the mathematical expectation. These two symbols represent the message flow that is passed upwards and the message flow that is passed downwards, respectively.

[0062] Based on the above calculation method, we can obtain The posterior distribution is a gamma distribution:

[0063] Similarly, The posterior distribution of is a Gaussian distribution, and the specific calculation formula is as follows:

[0064] The posterior distribution of is a gamma distribution, and the specific calculation formula is as follows:

[0065] The posterior distribution of is a gamma distribution, and the specific calculation formula is as follows:

[0066] When constructing a sparse observation model, the quantization error introduced by the spatial discretization operation limits the direction-finding accuracy to the smallest grid resolution unit. To address this issue, this invention employs the Laplace interpolation algorithm to "purify" the coarse angle estimation results, further reducing the direction-finding error. The specific steps are as follows: After the probabilistic inference process converges, the following steps can be used... estimator This describes the spatial distribution of incident signal power over a predefined grid point set. Assume... The sparse reconstruction results include There are 10 spectral peaks, each containing multiple spectral lines. Without loss of generality, let the 10th peak be considered as the first peak. Taking the first spectral peak as an example, we will introduce the position of the target true spectral line within that peak (corresponding to the first peak). The method for estimating the true angle of each target, and assuming that the coordinates of the position of the highest energy spectral line within the spectral peak are... Construct the following interpolation function:

[0067] in, , , Represents the polynomial coefficients. The interpolation process is as follows: Figure 6 As shown in the figure, the spectral lines of the three actual sampling points can be described by the following system of equations:

[0068] The above system of equations has a unique solution because its coefficient matrix is ​​a Vandermonde matrix. Let the true location of the source be... Then the following relationship holds:

[0069] The above equation regarding Taking the derivative and setting the result to 0, we get:

[0070] For the rest in turn By applying the above interpolation method to each spectral peak, the angle estimation results of all information sources can be obtained.

[0071] The following simulation further illustrates the effects of the invention: 1. Simulation conditions: The uniform linear hydrophone array has 36 elements, the narrowband incident sound source has a frequency of 100 Hz, the element spacing is half a wavelength, the tugboat's speed is 12 knots, and the signal sampling frequency is 200 Hz.

[0072] 2. Simulation content and results: Simulation 1: Figure 7 The image shows a spatial spectrum comparison between the method designed in this invention and the ETAM, FFTSA, and Yang algorithms. Three equal-power random sound sources were respectively introduced from... , and The direction is incident on the array, and the signal-to-noise ratio is set to dB. The array perturbation follows a mean of 0 and a standard deviation of . The data follows a Gaussian distribution. The number of snapshots is set to 9000.

[0073] from Figure 7 Simulation results show that the ETAM and FFTSA algorithms cannot accurately estimate the location of all signal sources, while the Yang algorithm and the algorithm designed in this invention can effectively distinguish three signal sources. However, the spectral peaks of the algorithm proposed in this invention are sharper, thus resulting in higher angular resolution. Simulation results demonstrate the disadvantage of traditional passive synthetic aperture direction finding algorithms based on phase correction factor estimation in distinguishing random signal sources.

[0074] Simulation 2: The direction-finding accuracy of the algorithm designed in this invention is compared with other existing algorithms through 100 Monte Carlo trials. The evaluation criterion is the root mean square error (RMSE), which is defined as follows: ,in and The first The Monte Carlo trial The true and estimated values ​​of the source azimuth. The spatial discretization grid resolution unit is... The incident directions of the three random sources are respectively , and The number of snapshots is set to Other simulation parameters remain the same as in Simulation 1.

[0075] Figure 8 The RMSE curves for each test algorithm are shown as a function of SNR. Additionally, the Cramer-Rao Lower Bound (CRLB) for direction-finding accuracy is also presented in the figure. Figure 8 The results show that the ETAM, METAM, TD-ETAM, and Yen-Carey algorithms all fail to achieve high direction-finding accuracy because the coherence between the received signals is disrupted, preventing the synthesis of virtual apertures. The DOA estimation accuracy of FFTSA and the Yang algorithm is also low, indicating that these two algorithms are not robust to array position errors. Figure 8 The results shown further verify the superior direction-finding performance of the method designed in this invention, indicating that this method is a practical high-precision passive synthetic aperture direction-finding algorithm under distorted array and random source environments.

[0076] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0077] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0078] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is defined only by the appended claims.

Claims

1. A passive synthetic aperture sonar direction finding method based on variational message passing, characterized in that, The method includes: Step 1: Establish the received data model of the towed array at any sampling time, use a piecewise linear model to approximate the actual distorted array shape, and construct the array observation data expression corresponding to the sampling time; Step 2: Define a spatial overcomplete array manifold dictionary, convert the array received data into an equivalent sparse observation model, and transform the direction of arrival estimation problem into the problem of determining the coordinates of non-zero elements in the sparse vector; Step 3: Establish a hierarchical probability model corresponding to the sparse observation model, and represent the hierarchical probability model equivalently using a factor graph; Step 4: Based on the factor graph, the variational message passing algorithm is used to iteratively calculate the maximum a posteriori probability estimate of each unknown variable to obtain the spatial reconstruction result of the incident source azimuth. Then, the Laplace interpolation technique is used to achieve the precise estimation of the direction of arrival angle.

2. The method according to claim 1, characterized in that, Step 1 describes using a piecewise linear model to approximate the actual distorted array shape and constructing the array observation data expression corresponding to the sampling time, specifically as follows: by Drag uniform linear array receiver The incident signal from an underwater sound source, wherein the element spacing is... The actual distorted array formation is approximated by a piecewise linear model, that is, the line connecting the first element and its adjacent elements is used as the reference line, and vectors are used to represent the distorted array formation. Describe the angle between the lines connecting the remaining array elements and the reference line; then the sampling time... Corresponding array observation data Represented as: in, Indicates the sampling time The corresponding array manifold matrix, Indicates the first One incident source direction and sampling time The corresponding guide vector, It is by A waveform vector composed of the complex amplitudes of the incident signals. and They represent the first Each information source at the sampling time The amplitude and phase, Indicates the sampling time The noise received by each array element.

3. The method according to claim 2, characterized in that, Step 2, which involves converting the array-received data into an equivalent sparse observation model, specifically includes: Define a dictionary of spatially overcomplete array manifolds ,in The array receives data based on the preset number of spatial discrete grids. The equivalent representation is the following sparse observation model: in, It is a sparse vector, constructed as follows: Given a predefined spatial grid... If it does not correspond to the actual incident signal DOA, then let ,otherwise The element value at the corresponding position in the vector is the true waveform of the signal incident from this direction.

4. The method according to claim 1, characterized in that, The hierarchical probability model described in step 3 is used to characterize the prior distribution of each latent variable in the array received data, specifically: The incident signal waveform vector follows a complex Gaussian distribution, and its accuracy parameter follows a gamma distribution; The array distortion vector follows a Gaussian distribution, and its precision parameter follows a gamma distribution. The array receives noise accuracy according to a gamma distribution.

5. The method according to claim 4, characterized in that, The variational message passing algorithm described in step 4 is as follows: The posterior probability of a variable node in the factor graph is calculated as the product of messages from all factor nodes flowing into that node; the message sent by a factor node is calculated as the integral of the posterior probability of the variable nodes connected to that factor node; the posterior distribution of each latent variable is updated iteratively until convergence.

6. The method according to claim 1, characterized in that, The Laplace interpolation technique described in step 4 is specifically as follows: By selecting sampling points near the spectral peak in the spatial reconstruction results to construct an interpolation function, taking the derivative of the interpolation function and setting the derivative to 0, the accurate estimation result of the true direction of arrival of the source is obtained.

7. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the passive synthetic aperture sonar direction finding method based on variational message passing as described in any one of claims 1 to 6.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the passive synthetic aperture sonar direction finding method based on variational message passing as described in any one of claims 1 to 6.

9. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute the passive synthetic aperture sonar direction finding method based on variational message passing according to any one of claims 1 to 6 by executing the executable instructions.

Images