Blind sparsity subspace backtracking homogeneous multi-source positioning method for residual divergence decision

Abstract

The embodiment of the invention discloses a blind sparsity subspace backtracking homogeneous multi-source positioning method for residual divergence decision, which comprises the following steps of: rasterizing a monitored area containing an unknown signal source node and a known sensing node, and acquiring actual received signal strength as an observation vector (also as a residual vector); and a sparse observation model is constructed based on the grid position and the observation vector. And calculating the normalized inner product of the residual vector and each column of the sensing matrix in the model to obtain a correlation numerical value sequence, determining an adaptive threshold value through the absolute deviation of the digits and the mean value, screening candidate elements to form a candidate support set, screening through a received signal strength estimation value to generate an iteration position support set, and updating the residual vector. And after each iteration, comparing theoretical and empirical probability distributions of the residual vector to obtain a difference metric value, stopping iteration when a termination condition is met, and taking the grid position corresponding to the current position support set as a positioning result. The method only depends on the received signal strength, and the deployment cost of sensor hardware is reduced.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and signal processing technology, and in particular to a blind sparseness subspace backtracking homogeneous multi-source localization method based on residual divergence decision. Background Technology

[0002] With the widespread application of unmanned systems and other wireless devices, the electromagnetic environment is becoming increasingly complex. In many application scenarios, it is necessary to locate non-cooperative wireless signal sources. When multiple non-cooperative signal sources transmit signals at the same time and frequency, it leads to severe signal aliasing in both the spatial and frequency domains, posing a threat to the normal operation and security of wireless systems. Traditional passive positioning techniques, such as those based on parameters like angle of arrival and time difference of arrival, are primarily designed for single signal sources. When dealing with such simultaneous, multi-source aliasing signals at the same frequency, they struggle to effectively separate and locate individual signal sources, resulting in poor positioning performance.

[0003] In recent years, sparse multi-source localization technology based on compressed sensing theory has provided a new approach to solving this problem. This technology divides the passively monitored physical area into a grid, leveraging the prior knowledge that signal sources typically occupy only a few grid cells in spatial distribution, transforming the complex localization problem into a mathematical problem of sparse signal recovery. However, existing compressed sensing-based localization methods still have significant drawbacks. On the one hand, most of their iterative solution algorithms directly adopt traditional greedy algorithms, such as the orthogonal matching pursuit algorithm, selecting only the position most relevant to the residual in each iteration. This mechanism is prone to misjudgment in scenarios with mutual interference from multiple signal sources, leading to insufficient localization accuracy. On the other hand, and more critically, the iteration stopping conditions of these algorithms heavily rely on prior information, typically requiring prior knowledge of the exact number of signal sources (i.e., sparsity) or the precise power level of background noise. In real-world non-cooperative localization scenarios, the number of signal sources and noise levels are unknown and dynamically changing. This strong dependence on prior information greatly limits the practicality and robustness of existing technologies. Summary of the Invention

[0004] Based on this, it is necessary to propose a blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making to address the above problems.

[0005] A blind sparse subspace backtracking homogeneous multi-source localization method based on residual divergence decision, the method comprising: The monitored area is divided into grids, which include signal source nodes at unknown locations and sensor nodes at known locations. The signal source nodes emit electromagnetic signals, and the sensor nodes collect the electromagnetic signals. The actual received signal strength of the electromagnetic signals collected by the sensor nodes is obtained, and the actual received signal strength is used as the observation vector. A sparse observation model is constructed based on the grid position of the signal source nodes and the observation vector.

[0006] The observation vector is used as the residual vector.

[0007] Calculate the normalized inner product of the residual vector with each column of the sensing matrix in the sparse observation model to obtain a correlation numerical sequence. Determine an adaptive threshold based on the median absolute deviation and mean of the correlation numerical sequence. Determine candidate elements based on the comparison between the adaptive threshold and each element in the correlation numerical sequence. Form a candidate support set based on the grid position of the candidate elements.

[0008] Based on the estimated received signal strength at grid positions within the candidate support set, the candidate support set is filtered to generate a position support set for this iteration.

[0009] The residual vector is updated based on the position support set used for this iteration.

[0010] After each iteration of updating the residual vector, the theoretical probability distribution and the empirical probability distribution of the residual vector are determined. The theoretical probability distribution and the empirical probability distribution are compared to obtain a difference metric. When the difference metric meets the preset termination condition, the iteration process is stopped. The grid position corresponding to the position support set of the current iteration is the final positioning result of the signal source.

[0011] The construction of the sparse observation model based on the grid position of the signal source node and the observation vector specifically includes: The existence of signal source nodes at the grid location is taken as a sparse vector to be solved.

[0012] A measurement matrix is ​​constructed using the sensor nodes as rows and the grid positions as columns.

[0013] The Euclidean distance between the sensor node and the grid location is determined based on the spatial coordinates of the sensor node and the grid location.

[0014] The path energy loss is determined based on the Euclidean distance, and the path loss matrix is ​​obtained.

[0015] The sensing matrix is ​​determined by multiplying the measurement matrix and the path loss matrix. Each row vector of the sensing matrix corresponds to a sensing node, and each column vector corresponds to a grid position.

[0016] Based on the sensing matrix and the sparse vector to be solved, and combined with the observation vectors collected by the sensing nodes, a sparse observation model is constructed.

[0017] Specifically, the process of determining an adaptive threshold based on the median absolute deviation and mean of the correlation numerical sequence, determining candidate elements based on the comparison between the adaptive threshold and each element in the correlation numerical sequence, and forming a candidate support set through the grid positions of the candidate elements includes: The elements in the correlation sequence are sorted in ascending order to obtain the first sorted sequence.

[0018] Determine the median of the first sorted sequence, calculate the absolute difference between each element in the sorted sequence and the median, and construct an absolute deviation sequence.

[0019] The absolute deviation sequence is sorted in ascending order to obtain the second sorted sequence.

[0020] Determine the median of the second sorted sequence, where the median of the second sorted sequence is the absolute deviation of the median.

[0021] Determine the mean of the correlation sequence.

[0022] The adaptive threshold is determined based on the absolute deviation of the median and the mean.

[0023] If an element in the correlation numerical sequence is greater than an adaptive threshold, then that element is the most relevant element, and a candidate support set is formed by the grid position corresponding to the most relevant element.

[0024] Specifically, the step of filtering the candidate support set based on the estimated received signal strength values ​​corresponding to the grid positions within the candidate support set to generate a location support set for this iteration includes: Extract column vectors corresponding to the grid positions within the candidate support set from the sensing matrix to form a sub-sensing matrix.

[0025] Based on the sub-sensing matrix and the residual vector, the estimated value of the received signal strength corresponding to the grid position in the sub-sensing matrix is ​​determined, and the received signal strength estimation matrix is ​​formed.

[0026] The received signal strength estimates in the received signal strength estimation matrix are sorted in descending order, and a preset number of grid positions corresponding to the received signal strength estimates are selected as the position support set for this iteration.

[0027] Specifically, determining the received signal strength estimate corresponding to the grid position within the sub-sensing matrix based on the sub-sensing matrix and the residual vector, thereby constructing the received signal strength estimation matrix of the sub-sensing matrix, includes: Replace the sensing matrix in the sparse observation model with the sub-sensing matrix.

[0028] Based on the mapping relationship between the sub-sensing matrix and the observation vector in the sparse observation model, the estimated value of the received signal strength at each grid position in the sub-sensing matrix is ​​determined, and the estimated value of the received signal strength of the sub-sensing matrix is ​​obtained.

[0029] Specifically, updating the residual vector based on the position support set used for this iteration includes: The column vectors corresponding to the grid positions within the position support set are extracted from the sensing matrix to form the support set sensing matrix.

[0030] The sensing matrix in the sparse observation model is replaced with the support set sensing matrix. Based on the mapping relationship between the support set sensing matrix and the observation vector in the sparse observation model, the received signal strength estimate of each grid position in the support set sensing matrix is ​​determined, thus obtaining the received signal strength estimate matrix of the support set sensing matrix.

[0031] The sparse vector to be solved is replaced with the received signal strength estimation matrix of the support set sensing matrix to obtain the updated sparse observation model.

[0032] The updated residual vector is determined based on the observation vector in the updated sparse observation model, the received signal strength estimation matrix of the support set sensing matrix, and the support set sensing matrix.

[0033] Specifically, after updating the residual vector in each iteration, the theoretical probability distribution and empirical probability distribution of the residual vector are determined. The theoretical probability distribution and empirical probability distribution are compared to obtain a difference metric. When the difference metric meets a preset termination condition, the iteration process stops. The grid position corresponding to the position support set of this iteration is the final localization result of the signal source. After each iteration of updating the residual vector, the mean and variance of the residual vector are determined.

[0034] The theoretical probability distribution is determined based on the mean and variance of the residual vector.

[0035] The empirical probability distribution of the residual vector is determined by kernel density estimation.

[0036] The difference measure is determined based on the theoretical probability distribution and the empirical probability distribution.

[0037] When the difference metric is greater than a preset threshold, update the iteration count and return to the step of calculating the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model.

[0038] When the difference metric is greater than or equal to a preset threshold, the iteration process stops, and the grid position corresponding to the position support set of this iteration is the final positioning result of the signal source.

[0039] Specifically, determining the difference metric based on the theoretical probability distribution and the empirical probability distribution includes: according to Determine the difference measure, where, This is a measure of difference. Let the empirical probability distribution of the residual vector be... This represents the theoretical probability distribution of the reference noise.

[0040] A blind sparse subspace backtracking homogeneous multi-source localization system based on residual divergence decision, the system comprising: A sparse observation model construction module is used to divide the monitored area into grids. The monitored area includes signal source nodes at unknown locations and sensor nodes at known locations. The signal source nodes emit electromagnetic signals, and the sensor nodes collect these electromagnetic signals. The module obtains the actual received signal strength of the collected electromagnetic signals, uses this actual received signal strength as an observation vector, and constructs a sparse observation model based on the grid positions of the signal source nodes and the observation vector. The candidate support set determination module is used to take the observation vector as a residual vector, calculate the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model to obtain a correlation numerical sequence, determine an adaptive threshold based on the median absolute deviation and mean of the correlation numerical sequence, determine candidate elements based on the comparison between the adaptive threshold and each element in the correlation numerical sequence, and form a candidate support set through the grid position of the candidate elements.

[0041] The location support set determination module is used to filter the candidate support set based on the estimated received signal strength of the grid positions within the candidate support set, and generate a location support set for this iteration.

[0042] The signal source location determination module is used to update the residual vector according to the location support set used for this iteration. After updating the residual vector in each iteration, the module determines the theoretical probability distribution and the empirical probability distribution of the residual vector, compares the theoretical probability distribution and the empirical probability distribution to obtain a difference metric value, and stops the iteration process when the difference metric value meets the preset termination condition. The grid position corresponding to the location support set of the current iteration is the final location result of the signal source.

[0043] A computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method described above.

[0044] The embodiments of the present invention have the following beneficial effects: This invention adaptively selects multiple candidate grid positions based on the median absolute deviation and mean of the correlation sequence during iteration to obtain a candidate support set. The candidate support set is then corrected based on the estimated received signal strength at the grid positions within the set. This effectively combats multi-source signal aliasing interference and significantly improves positioning accuracy. Furthermore, this invention determines whether the iteration terminates by comparing the difference between the theoretical probability distribution and the empirical probability distribution of the residual vector. This eliminates the need for prior information such as the number of signal sources or background noise power, allowing the positioning method to adaptively operate in unknown and changing complex electromagnetic environments, enhancing the practicality and robustness of the technology. Moreover, the positioning method of this application can rely solely on received signal strength, resulting in lower hardware deployment costs for the required sensors compared to solutions requiring high-precision time synchronization modules or complex array antennas. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] in: Figure 1 A flowchart illustrating an embodiment of a blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making provided by the present invention; Figure 2 A schematic diagram of the spatial discrete model provided by this invention; Figure 3 This is a flowchart illustrating another embodiment of the blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making provided by the present invention. Figure 4 This is a flowchart illustrating another embodiment of the blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making provided by the present invention. Figure 5 The curves show a performance comparison between the present invention and current multi-source sparse localization schemes. Figure 6 Comparison curves of positioning performance under different numbers of signal sources; Figure 7 Comparison curves of positioning performance under different numbers of sensor nodes; Figure 8 Comparison curves of positioning performance in scenarios where the number of sensor nodes is reduced. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] like Figure 1 As shown, Figure 1 This is a flowchart illustrating an embodiment of a blind sparse subspace backtracking homogeneous multi-source localization method based on residual divergence decision-making provided by the present invention. The method includes: S101: The monitored area is divided into grids, which include signal source nodes at unknown locations and sensor nodes at known locations. The signal source nodes emit electromagnetic signals, and the sensor nodes collect electromagnetic signals. The actual received signal strength of the electromagnetic signals collected by the sensor nodes is obtained. The actual received signal strength is used as the observation vector, and a sparse observation model is constructed based on the grid position of the signal source nodes and the observation vector.

[0049] For example, the monitored area is configured with x signal source nodes at unknown locations and y sensor nodes at known locations, with both types of nodes spatially distributed. All signal source nodes continuously emit electromagnetic signals of the same frequency band within the same time window. The sensor nodes are deployed spatially discretely within the monitored area, forming a collaborative sensing network of electromagnetic signals from the signal sources. Each node is equipped with a broadband signal receiving device, capable of simultaneously capturing electromagnetic signals emitted by multiple signal sources. The signals emitted by the signal sources form a superimposed electromagnetic field in space, and its wavefront propagation characteristics are synchronously acquired by the sensor node array. When multiple signal sources emit electromagnetic signals at the same time and frequency, the mixed signal received by the sensor nodes contains spatial interference characteristics. These characteristics manifest as physical parameters such as signal intensity variations.

[0050] Furthermore, such as Figure 2 As shown, Figure 2 This is a schematic diagram of the spatial discrete model provided by the present invention. The monitored area is divided into grids, constructing N square grid arrays of equal size to form a spatial discrete model. In this spatial discrete model, K signal sources are randomly distributed inside the grids, and M sensing nodes are randomly distributed at the grid intersections. The number of grids must be greater than the number of signal sources, i.e., satisfying... The configuration relationship leads to the formation of a spatially sparse distribution of signal sources within the monitored area.

[0051] Based on the above spatial discrete model, the spatial distribution information of the M sensing nodes constitutes a set of position coordinates. The two-dimensional coordinate data of each node is For the signal source distribution within N grid cells, a sparse location set is used. The set contains N elements whose position indices correspond to the position indices of each raster cell, with only K non-zero elements. This represents the grid position where the signal source actually exists, with the remaining grid positions corresponding to zero-value elements. The signal source coordinate data associated with each non-zero element forms a radiation source location information set.

[0052] refer to Figure 2 The spatial discrete model shown uses the presence of signal source nodes at grid locations as a sparse solution vector characterizing the spatial distribution of the signal. This vector is a column vector structure with N elements, whose dimensions strictly correspond to the total number of grid cells. The index number of each element maps to the spatial location identifier of a specific grid, while the element value represents the signal transmission strength at the corresponding grid location, as shown in the following formula: ; At the physical level, this vector inherently possesses spatial sparsity. The vast majority of elements in the vector are zero, indicating that there is no valid signal source within the grid region corresponding to their index. Only K non-zero elements are distributed in the vector; the index numbers of these non-zero elements point to the grid positions where actual signal sources exist, and their specific values ​​quantify the signal emission intensity of the electromagnetic signal from the corresponding location.

[0053] Furthermore, in compressed sensing algorithms, the sensing matrix... Defined as a measurement matrix With sparse basis matrix The product form of the sensing matrix. The mathematical expression represents the linear combination relationship between two key matrices. The specific formula is as follows: ; Among them, the measurement matrix This represents the sensor deployment scheme in a rasterized scene; sparse basis matrix. This represents the energy measurement coefficient for each grid cell.

[0054] Specifically, a measurement matrix is ​​constructed with sensor nodes as rows and grid positions as columns. The dimensions of this matrix are determined by the number of sensor nodes (M) and the total number of grid cells (N), and its mathematical form is a combination of M N-dimensional row vectors. Each row vector uniquely corresponds to the spatial location characteristics of a specific sensor node. Measurement Matrix The specific formula is expressed as follows: ; Each row vector uses sparse coding to represent sensor location information. Only one element in the vector has a value of 1, while the other n elements are all 0. The index number of this non-zero element precisely maps to the spatial location identifier of the sensor node in the grid coordinate system. When a sensor node is located at a grid intersection, its index corresponds to the unique coordinate number of the grid node. The formula for this row vector is as follows: .

[0055] Sparse basis matrix This represents the energy measurement coefficient between each grid and every other grid. Based on the current electromagnetic environment and the established mathematical model, a corresponding path loss matrix is ​​constructed. This model assumes that the electromagnetic signal propagates in a straight line in uniform free space, and its energy decreases in a square-proportional manner with increasing propagation distance.

[0056] First, the Euclidean distance between the sensor node and the grid location is determined based on the spatial coordinates of the sensor node and the grid location, thus constructing an accurate distance matrix. , used to characterize the Euclidean distance between any two grid cells: .

[0057] Subsequently, combining system parameters such as signal frequency and antenna gain, the path energy loss is determined based on the Euclidean distance using the path loss formula, as shown below: ; in, Indicates the first Energy loss between sensor node j and grid position j Indicates the first The number of sensor nodes and the first The physical straight-line distance between grid positions, assuming no obstacles within the scene and that signals propagate in a straight line. Indicates the frequency of the electromagnetic signal. This represents the propagation speed of electromagnetic signals.

[0058] Convert it to a decay factor on a linear scale: ; Therefore, the path loss matrix is ​​constructed. Each element Indicates from the first The sensor node and the first Gain attenuation ratio at grid number 1.

[0059] Ultimately, the complete sensor matrix The combined measurement structure and propagation characteristics are expressed as follows: ; That is, each element of the sensing matrix Indicates the first Signal sensing nodes and The signal energy loss coefficient between grid positions already includes the attenuation effect caused by geometric distance.

[0060] In summary, the sparse observation model The structure is as follows: ; in, A sparse signal vector represents the presence or absence of a signal source and its signal strength in N grid cells, and satisfies the sparsity property. . For the first Electromagnetic signal strength at grid number 1; The sensing matrix, which integrates sensor deployment topology and free-space path loss characteristics, characterizes the linear mapping relationship from the signal source to the observed value. For the first Number grid and Signal energy loss coefficient between grid cells; The observation vector consists of the signal energy collected by M sensors. For the first Signal strength received at sensor node. For noise, For the first The sensor node receives signal noise.

[0061] This sparse observation model fully utilizes the spatial sparsity of signal sources, the distribution characteristics of sensors, and the laws of electromagnetic propagation to construct an efficient mathematical framework suitable for compressed sensing localization, transforming the multi-source localization problem into the following L1 norm minimization problem: ; To address this problem, a sparse reconstruction algorithm is used to reconstruct data from a small number of observation vectors. Recover the sparse vector to be solved from the middle This enables high-precision, low-sampling-cost multi-radiation-source localization.

[0062] S102: Use the observation vector as the residual vector.

[0063] For example, the key parameters are first initialized, including the location information support set. Setting it to an empty set indicates that, initially, no location is identified as the signal source. Residual vector Initialized to the observation vector actually received by the sensor array This represents all observational information that has not yet been interpreted by the model. An iteration counter is also set. Set the value to 1, and define a preliminary support set for temporarily storing candidate positions. Its initial capacity is set to empty, and the modulation size is adaptively adjusted in subsequent calculations to avoid relying on prior knowledge of the number of signal sources.

[0064] S103: Calculate the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model to obtain the correlation numerical sequence. Determine the adaptive threshold based on the median absolute deviation and mean of the correlation numerical sequence. Determine the candidate elements based on the comparison between the adaptive threshold and each element in the correlation numerical sequence. Form a candidate support set based on the grid position of the candidate elements.

[0065] For example, in each iteration of the sparse reconstruction algorithm, the system first calls the residual vector of the current iteration. With pre-built sensing matrix Where M is the number of sensor nodes, N is the total number of grid cells, and the sensor matrix is... Each column The atomic feature corresponding to a grid position integrates key information such as the propagation path loss from that grid to all sensing nodes and the sensor deployment topology. The correlation between the current residual vector and each column of the sensing matrix is ​​calculated. The magnitude of the correlation value determines whether the grid position corresponding to that column contains a real signal component; the higher the correlation value, the greater the probability of the presence of a real signal source.

[0066] To avoid interference from energy attenuation due to differences in propagation paths on correlation assessment and thus improve the accuracy of potential signal source location selection, this invention employs a normalized inner product as the method for calculating correlation. The initial normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model is calculated as follows: ; However, due to differences in propagation distance from different grids to the sensing node and variations in obstacle occlusion, the energy amplitude of each column vector in the sensing matrix is ​​affected. Grids closer to the sensing node have larger L2 norms for their column vectors, while grids farther away have smaller L2 norms. Directly using the unnormalized inner product might result in grids that are close to the node but lack a real signal source exhibiting high correlation due to their large column vector amplitudes, or grids that are far away but have a real signal source exhibiting low correlation due to their small column vector amplitudes, thus affecting the accuracy of the selection results. Therefore, the calculation of the normalized inner product introduces the L2 norm of the sensing matrix column vectors: ; Furthermore, the initial normalized inner product is standardized using the following formula: ; in, Let L be the L2 norm of the column vectors of the sensing matrix.

[0067] Through the above normalized inner product calculation, the correlation value corresponding to each grid position is obtained, forming a complete correlation value sequence: ; Each element The normalized inner product correlation value of the j-th grid after the rasterization of the monitoring area is accurately represented, and N represents the total number of grids formed after the uniform discretization of the monitoring area.

[0068] Furthermore, the elements in the correlation sequence are first sorted in ascending order of their values ​​to obtain the first sorted sequence: Then, the median of the first sorted sequence is calculated based on the parity of the total number of grid cells N. If N is odd, then If N is even, then The median effectively reflects the intermediate level of the correlation numerical sequence and possesses robustness, providing initial resistance to outliers. Based on this, the median... Calculate the sequence one by one Each element and The absolute difference is used to construct an absolute deviation sequence: .

[0069] Furthermore, the absolute deviation sequence is sorted in ascending order to obtain a second sorted sequence, and then calculated... The same rules are used to calculate the median of the sorted sequence, and the median of the second sorted sequence is the absolute deviation of the median; After obtaining the median absolute deviation (MAD), the correlation numerical sequence is further calculated. mean The calculation method is as follows: ; The mean It can reflect the overall average correlation level of the correlation numerical sequence, serving as a basic reference benchmark for threshold construction. (The last part, "mean," appears to be incomplete and lacks context.) Absolute deviation from the median Based on this, the present invention constructs an adaptive threshold: ; The threshold can be dynamically adjusted adaptively according to the actual distribution of the correlation sequence in each iteration, effectively avoiding the problem of low screening accuracy under different interference intensities and different numbers of signal sources with a fixed threshold.

[0070] Complete adaptive threshold After construction, traverse the correlation numerical sequence. Each element in All satisfied The elements are the most relevant set of atoms, and the raster position indices corresponding to the most relevant set of atoms are included in the candidate support set. ,Right now: ; S104: Based on the estimated received signal strength of the grid positions within the candidate support set, the candidate support set is filtered to generate a position support set for this iteration.

[0071] For example, from a pre-built sensing matrix Extract the corresponding column vectors, and then construct a sub-sensing matrix that matches the current most relevant set of atoms. Among them, the sensing matrix It is an M x N matrix; while the sub-sensing matrix The dimension is M rows and S columns, where S represents the candidate support set. The number of grid positions contained is strictly corresponding to the number of column vectors. Each grid position in the sensing matrix The original column vectors in the array. This construction method makes... It can focus on highly correlated raster regions, and while removing low-correlation column vectors to reduce the dimensionality of data processing, it fully preserves the signal propagation characteristics of highly correlated raster regions, providing structured and accurate input data for subsequent signal strength estimation, and avoiding the influence of irrelevant information on the calculation results.

[0072] In the signal strength estimation stage, it is necessary to base it on the sub-sensor matrix. Received signal With multi-source signal strength mapping relationship The sub-sensing matrix was calculated using the least squares method. Corresponding estimated signal strength Specifically, the sensing matrix in the sparse observation model is replaced with a sub-sensing matrix; based on the mapping relationship between the sub-sensing matrix and the observation vector in the sparse observation model, the estimated received signal strength at each grid position in the sub-sensing matrix is ​​determined, resulting in the estimated received signal strength matrix of the sub-sensing matrix. The core objective of the least squares method is to minimize the squared Euclidean norm between the residual vector and the product of the sub-sensing matrix and the signal strength vector, i.e., to minimize the objective function: ; To obtain the optimal The least squares criterion function is defined as follows: ; in, Denotes the L2 norm, for about Find the partial derivative and set it equal to zero, that is: ; After sorting, the candidate support set can be obtained. The estimated signal strength at the corresponding location is: .

[0073] signal strength After estimation, all elements in the received signal strength estimation matrix are sorted in descending order, and the corresponding position sequence is as follows: Select the largest value among them. The position constitutes the first Location support set of the next iteration ,Right now .

[0074] S105: Update the residual vector based on the position support set used for this iteration.

[0075] For example, from a pre-built M-row N-column sensing matrix Selected from The column vectors corresponding to the grid positions are used to construct the support set sensing matrix. Where M is the total number of sensor nodes, and N is the total number of grid cells in the monitored area after gridding. The dimension is M rows List, That is The number of grid positions contained therein, and Each column corresponds strictly The middle grid position is in the original sensing matrix The column vectors in the data fully preserve the signal propagation loss characteristics and sensor deployment topology information from the grid location to all sensor nodes.

[0076] Complete the support set sensor matrix After construction, the sensing matrix in the sparse observation model is replaced with the support set sensing matrix, and the sparse vector to be solved is replaced with the received signal strength estimation matrix of the support set sensing matrix, resulting in the updated sparse observation model: ; in, Let M be the received signal vector. for 3D signal intensity vector Given an M-dimensional background noise vector, similar to the previous steps, this invention uses the least squares method to calculate... Estimated received signal strength at corresponding grid positions : ; Obtain the received signal strength estimate Then, based on the observation vector in the updated sparse observation model, the received signal strength estimation matrix of the support set sensing matrix, and the support set sensing matrix, the residual vector required for the next iteration is determined. The calculation formula is: ; in, Given an M-dimensional vector, its i-th element The uninterpreted component in the signal received by the i-th sensing node includes valid signals from unidentified signal sources and background noise.

[0077] S106: After updating the residual vector in each iteration, determine the theoretical probability distribution and the empirical probability distribution of the residual vector, compare the theoretical probability distribution and the empirical probability distribution to obtain the difference metric value, and stop the iteration process when the difference metric value meets the preset termination condition. The grid position corresponding to the position support set of the current iteration is the final positioning result of the signal source.

[0078] For example, complete the residual vector After acquisition, the process enters the iterative control phase to determine whether to terminate the iteration process. This occurs when all signal source locations are included in the support set. After that, the residual vector The residual vector no longer contains any effective signal components, only background noise. Common background noise in electronic systems, such as thermal noise and electromagnetic interference, generally follows a Gaussian distribution. Iterative control is achieved by quantizing the difference between the empirical distribution and the Gaussian distribution of the residual vector, specifically: To fit the Gaussian distribution of the reference noise, the residual vector must first be calculated. The mean and variance are used to quantify the overall level and dispersion of the residuals, and the residual vector is used for this purpose. mean With variance The calculation is as follows: ; .

[0079] The mean calculated above and variance As a distribution parameter, a theoretical probability distribution is constructed, which simulates the ideal statistical properties of the residuals containing only background noise, and the corresponding probability density function is... for: ; Where z represents the possible values ​​of the noise, and the probability density function is... The physical meaning is: if the current residual has no residual signal and is pure noise, its distribution should be similar to... Highly consistent; however, if unrecovered signals remain in the residuals, the distribution will deviate significantly. .

[0080] To measure the degree of difference between the residuals and the Gaussian distribution, this invention calculates the KL divergence, or relative entropy, between the empirical probability distribution and the theoretical probability distribution. The physical meaning of KL divergence is a measure of the asymmetry between two probability distributions; a smaller value indicates greater similarity between the two distributions. KL divergence is used as a measure of difference. KL divergence is denoted as: ; in, For residuals The empirical probability distribution; The theoretical probability distribution of the reference noise. That is, obey the above .

[0081] For residuals empirical probability distribution This invention uses the residual values ​​obtained through iteration The calculation is performed using a kernel density estimation method, with a Gaussian kernel chosen as the kernel function. The calculation formula is as follows: ; Where M is the number of samples; h is the kernel function bandwidth, which is selected using the Silverman empirical formula to ensure that the estimated empirical probability density has both low bias and low variance. The calculation formula is as follows: ; In the formula, 1.06 is an empirical coefficient. For sample size adjustment, the larger the sample size M, the smaller the bandwidth h, and the higher the resolution of the empirical probability density.

[0082] Since the residuals are discrete observations, the discrete form of the KL divergence formula is used: ; This indicates that the empirical probability distribution and the theoretical probability distribution are completely consistent; the larger the value of H, the greater the difference between the two. A preset threshold for the KL divergence is set to c=1. This indicates that the residual still contains unidentified signal source components, so the iteration continues, and the iteration count counter is updated. Updated to Returning to the steps of calculating the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model, recalculating the most relevant set of atoms, and proceeding to the next round of support set optimization; if This indicates that there is no residual signal in the residual, the iteration stops, and the current support set... The corresponding grid position is the final location result of the signal source.

[0083] As described above, this invention adaptively selects multiple candidate grid positions based on the median absolute deviation and mean of the correlation sequence during iteration to obtain a candidate support set. The candidate support set is then corrected based on the estimated received signal strength of the grid positions within it. This effectively combats multi-source signal aliasing interference and significantly improves positioning accuracy. Furthermore, this invention determines whether the iteration terminates by comparing the difference between the theoretical probability distribution and the empirical probability distribution of the residual vector. This eliminates the need for prior information such as the number of signal sources or background noise power, allowing the positioning method to adaptively operate in unknown and changing complex electromagnetic environments, enhancing the practicality and robustness of the technology. Moreover, the positioning method of this application can rely solely on received signal strength, resulting in lower hardware deployment costs for the required sensors compared to solutions requiring high-precision time synchronization modules or complex array antennas.

[0084] like Figure 3 As shown, Figure 3 This is a flowchart illustrating another embodiment of the blind sparse subspace backtracking homogeneous multi-source localization method based on residual divergence decision-making provided by the present invention. The method includes: S201: The monitored area is divided into grids, which include signal source nodes at unknown locations and sensor nodes at known locations. The signal source nodes emit electromagnetic signals, and the sensor nodes collect electromagnetic signals. The actual received signal strength of the electromagnetic signals collected by the sensor nodes is obtained, and the actual received signal strength is used as the observation vector.

[0085] For example, in conjunction with reference Figure 2 The monitored area is divided into grids, constructing N equal-sized square grid arrays to form a spatial discrete model. In this spatial discrete model, K signal sources are randomly distributed within the grids, and M sensing nodes are randomly distributed at the grid intersections. The number of grids must be greater than the number of signal sources, i.e., satisfying... The configuration relationship is determined, thus forming a spatially sparse distribution characteristic of signal sources within the monitored area. Signal source nodes emit electromagnetic signals, and sensor nodes collect electromagnetic signals, obtaining the actual received signal strength of the electromagnetic signals collected by the sensor nodes, and using the actual received signal strength as the observation vector.

[0086] S202: The existence of signal source nodes at the grid location is taken as a sparse vector to be solved.

[0087] For example, the presence of signal source nodes at grid locations is used as a sparse vector to be solved to characterize the spatial distribution of the signal. This vector is a column vector structure with N elements, whose dimensions strictly correspond to the total number of grid cells. The index number of each element maps to the spatial location identifier of a specific grid, while the element value represents the signal transmission strength at the corresponding grid location, as shown in the following formula: .

[0088] S203: Construct a measurement matrix with sensor nodes as rows and grid positions as columns.

[0089] For example, a measurement matrix is ​​constructed with sensor nodes as rows and grid positions as columns. The dimensions of this matrix are determined by the number of sensor nodes M and the total number of grids N, and its mathematical form is a combination of M N-dimensional row vectors. Each row vector uniquely corresponds to the spatial location characteristics of a specific sensor node. Measurement Matrix The specific formula is expressed as follows: .

[0090] S204: Determine the Euclidean distance between the sensor node and the grid position of the signal source node based on the spatial coordinates of the sensor node and the grid position.

[0091] For example, the Euclidean distance between the sensor node and the grid location is determined based on the spatial coordinates of the sensor node and the grid location, and an accurate distance matrix is ​​constructed to characterize the Euclidean distance between any two grids.

[0092] S205: Determine the path energy loss based on the Euclidean distance to obtain the path loss matrix.

[0093] For example, the path energy loss is determined based on the Euclidean distance using the path loss formula, as shown below: ; in, Indicates the first Energy loss between sensor node j and grid position j Indicates the first The number of sensor nodes and the first The physical straight-line distance between grid positions, assuming no obstacles within the scene and that signals propagate in a straight line. Indicates the frequency of the electromagnetic signal. This represents the propagation speed of electromagnetic signals.

[0094] Convert it to a decay factor on a linear scale: ; Therefore, the path loss matrix is ​​constructed. Each element Indicates from the first The sensor node and the first Gain attenuation ratio at grid number 1.

[0095] S206: Determine the sensing matrix based on the product of the measurement matrix and the path loss matrix. Each row vector of the sensing matrix corresponds to a sensing node, and each column vector corresponds to a grid position.

[0096] For example, the sensing matrix is ​​determined by the product of the measurement matrix and the path loss matrix, as follows: ; That is, each element of the sensing matrix Indicates the first Signal sensing nodes and The signal energy loss coefficient between grid positions already includes the attenuation effect caused by geometric distance.

[0097] S207: Construct a sparse observation model based on the sensing matrix and the sparse vector to be solved, combined with the observation vectors collected by the sensing nodes.

[0098] For example, based on the sensing matrix and the sparse vector to be solved, combined with the observation vectors collected by the sensing nodes, a sparse observation model is constructed. The structure is as follows: ; in, A sparse signal vector represents the presence or absence of a signal source and its signal strength in N grid cells, and satisfies the sparsity property. . For the first Electromagnetic signal strength at grid number 1; The sensing matrix, which integrates sensor deployment topology and free-space path loss characteristics, characterizes the linear mapping relationship from the signal source to the observed value. For the first Number grid and Signal energy loss coefficient between grid cells; The observation vector consists of the signal energy collected by M sensors. For the first Signal strength received at sensor node. For noise, For the first The sensor node receives signal noise.

[0099] S208: Use the observation vector as the residual vector.

[0100] S209: Calculate the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model to obtain the correlation numerical sequence.

[0101] For example, the observation vector is used as the residual vector. In each iteration of the sparse reconstruction algorithm, the system first calls the residual vector of the current iteration and the pre-constructed sensing matrix to calculate the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model, as shown in the following formula: ; Through the above normalized inner product calculation, the correlation value corresponding to each grid position is obtained, forming a complete correlation value sequence: .

[0102] S210: Sort the elements in the correlation sequence in ascending order to obtain the first sorted sequence.

[0103] S211: Determine the median of the first sorted sequence, calculate the absolute difference between each element in the sorted sequence and the median, and construct the absolute deviation sequence.

[0104] S212: Sort the absolute deviation sequence in ascending order to obtain the second sorted sequence.

[0105] S213: Determine the median of the second sorted sequence, where the median of the second sorted sequence is the absolute deviation of the median.

[0106] S214: Determine the mean of the correlated sequence.

[0107] S215: Determine the adaptive threshold based on the absolute deviation of the median and the mean.

[0108] For example, the elements in the correlation sequence are first sorted in ascending order of their values ​​to obtain the first sorted sequence: Then, the median of the first sorted sequence is calculated based on the parity of the total number of grid cells N. If N is odd, then If N is even, then The median effectively reflects the intermediate level of the correlation numerical sequence and possesses robustness, providing initial resistance to outliers. Based on this, the median... Calculate the sequence one by one Each element and The absolute difference is used to construct an absolute deviation sequence: .

[0109] Furthermore, the absolute deviation sequence is sorted in ascending order to obtain a second sorted sequence, and then calculated... The same rules are used to calculate the median of the sorted sequence, and the median of the second sorted sequence is the absolute deviation of the median; After obtaining the median absolute deviation (MAD), the correlation numerical sequence is further calculated. mean The calculation method is as follows: ; The mean It can reflect the overall average correlation level of the correlation numerical sequence, serving as a basic reference benchmark for threshold construction. (The last part, "mean," appears to be incomplete and lacks context.) Absolute deviation from the median Based on this, the present invention constructs an adaptive threshold: ; The threshold can be dynamically adjusted adaptively according to the actual distribution of the correlation sequence in each iteration, effectively avoiding the problem of low screening accuracy under different interference intensities and different numbers of signal sources with a fixed threshold.

[0110] S216: If an element in the correlation numerical sequence is greater than the adaptive threshold, then the element is the most relevant element, and a candidate support set is formed by the grid position corresponding to the most relevant element.

[0111] For example, adaptive thresholding is performed. After construction, traverse the correlation numerical sequence. Each element in All satisfied The elements are the most relevant set of atoms, and the raster position indices corresponding to the most relevant set of atoms are included in the candidate support set. ,Right now: .

[0112] S217: Based on the estimated received signal strength of the grid positions within the candidate support set, the candidate support set is filtered to generate a position support set for this iteration.

[0113] S218: Update the residual vector based on the position support set used for this iteration.

[0114] S219: After updating the residual vector in each iteration, determine the theoretical probability distribution and the empirical probability distribution of the residual vector, compare the theoretical probability distribution and the empirical probability distribution to obtain the difference metric value, and stop the iteration process when the difference metric value meets the preset termination condition. The grid position corresponding to the position support set of the current iteration is the final positioning result of the signal source.

[0115] It should be noted that steps S217-S219 are... Figure 1 The implementation scenarios shown have been discussed in detail and will not be repeated here.

[0116] like Figure 4 As shown, Figure 4 This is a flowchart illustrating another embodiment of the blind sparse subspace backtracking homogeneous multi-source localization method based on residual divergence decision-making provided by the present invention. The method includes: S301: The monitored area is divided into grids, which include signal source nodes at unknown locations and sensor nodes at known locations. The signal source nodes emit electromagnetic signals, and the sensor nodes collect electromagnetic signals. The actual received signal strength of the electromagnetic signals collected by the sensor nodes is obtained. The actual received signal strength is used as the observation vector, and a sparse observation model is constructed based on the grid position of the signal source nodes and the observation vector.

[0117] S302: Use the observation vector as the residual vector.

[0118] S303: Calculate the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model to obtain the correlation numerical sequence. Determine the adaptive threshold based on the median absolute deviation and mean of the correlation numerical sequence. Determine candidate elements based on the comparison between the adaptive threshold and each element in the correlation numerical sequence. Form a candidate support set based on the grid position of the candidate elements.

[0119] It should be noted that steps S301-S303 are in Figure 1 The implementation scenarios shown have been discussed in detail and will not be repeated here.

[0120] S304: Extract column vectors corresponding to the grid positions within the candidate support set from the sensing matrix to form a sub-sensing matrix.

[0121] For example, from a pre-built sensing matrix Extract the corresponding column vectors, and then construct a sub-sensing matrix that matches the current most relevant set of atoms. Among them, the sensing matrix It is an M x N matrix; while the sub-sensing matrix The dimension is M rows and S columns, where S represents the candidate support set. The number of grid positions contained is strictly corresponding to the number of column vectors. Each grid position in the sensing matrix The original column vector in.

[0122] S305: Determine the received signal strength estimate corresponding to the grid position within the sub-sensing matrix based on the sub-sensing matrix and the residual vector, and construct the received signal strength estimation matrix.

[0123] For example, it needs to be based on the sub-sensing matrix Received signal With multi-source signal strength mapping relationship The sub-sensing matrix was calculated using the least squares method. Corresponding estimated signal strength Specifically, the sensing matrix in the sparse observation model is replaced with a sub-sensing matrix; based on the mapping relationship between the sub-sensing matrix and the observation vector in the sparse observation model, the estimated received signal strength at each grid position in the sub-sensing matrix is ​​determined, resulting in the estimated received signal strength matrix of the sub-sensing matrix. The core objective of the least squares method is to minimize the squared Euclidean norm between the residual vector and the product of the sub-sensing matrix and the signal strength vector, i.e., to minimize the objective function: ; To obtain the optimal The least squares criterion function is defined as follows: ; in, Denotes the L2 norm, for about Find the partial derivative and set it equal to zero, that is: ; After sorting, the candidate support set can be obtained. The estimated signal strength at the corresponding location is: .

[0124] This forms the received signal strength estimation matrix.

[0125] S306: Sort the received signal strength estimates in the received signal strength estimation matrix in descending order, and select a preset number of grid positions corresponding to the received signal strength estimates as the position support set for this iteration.

[0126] For example, if all elements in the received signal strength estimation matrix are arranged in descending order, the corresponding position sequence is: Select the largest value among them. The position constitutes the first Location support set of the next iteration ,Right now .

[0127] S307: Update the residual vector based on the position support set used for this iteration.

[0128] It should be noted that step S307 is in Figure 1 The implementation scenarios shown have been discussed in detail and will not be repeated here.

[0129] S308: After updating the residual vector in each iteration, determine the mean and variance of the residual vector.

[0130] S309: Determine the theoretical probability distribution based on the mean and variance of the residual vector.

[0131] For example, residual vector mean With variance The calculation is as follows: ; .

[0132] The mean calculated above and variance As a distribution parameter, a theoretical probability distribution is constructed, which simulates the ideal statistical properties of the residuals containing only background noise, and the corresponding probability density function is... for: ; Where z represents the possible values ​​of the noise, and the probability density function is... The physical meaning is: if the current residual has no residual signal and is pure noise, its distribution should be similar to... Highly consistent; however, if unrecovered signals remain in the residuals, the distribution will deviate significantly. .

[0133] S310: Determine the empirical probability distribution of the residual vector through kernel density estimation.

[0134] For example, by analyzing the residual values ​​obtained through iteration The calculation is performed using a kernel density estimation method, with a Gaussian kernel chosen as the kernel function. The calculation formula is as follows: ; Where M is the number of samples; h is the kernel function bandwidth, which is selected using the Silverman empirical formula to ensure that the estimated empirical probability density has both low bias and low variance. The calculation formula is as follows: ; In the formula, 1.06 is an empirical coefficient. For sample size adjustment, the larger the sample size M, the smaller the bandwidth h, and the higher the resolution of the empirical probability density.

[0135] S311: Determine the difference measure value based on the theoretical probability distribution and the empirical probability distribution.

[0136] For example, the difference measure is determined according to the following formula: ; in, This is a measure of difference. Let the empirical probability distribution of the residual vector be... This represents the theoretical probability distribution of the reference noise.

[0137] S312: When the difference metric is greater than a preset threshold, update the iteration count and return to the step of calculating the normalized inner product of the residual vector with each column of the sensing matrix in the sparse observation model.

[0138] S313: When the difference metric is greater than or equal to the preset threshold, stop the iteration process. The grid position corresponding to the position support set of this iteration is the final positioning result of the signal source.

[0139] For example, a preset threshold c=1 is set for the KL divergence. This indicates that the residual still contains unidentified signal source components, so the iteration continues, and the iteration count counter is updated. Updated to Returning to the steps of calculating the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model, recalculating the most relevant set of atoms, and proceeding to the next round of support set optimization; if This indicates that there is no residual signal in the residual, the iteration stops, and the current support set... The corresponding grid position is the final location result of the signal source.

[0140] The superiority of this invention is demonstrated through simulation experiments. The specific simulation scenarios and parameters are shown below.

[0141] Construct a two-dimensional multi-source localization scenario, assuming the target area is 100m. A 100m square area was divided into a grid, with each grid cell measuring 10m. 10m, 10 10 grids and 11 There are 11 grid nodes, of which The sensor nodes are randomly distributed across 121 grid nodes. Several signal sources are randomly distributed across 100 grids. All signal sources are configured to simultaneously use a common frequency signal at a frequency of [frequency value missing]. The signal source is an omnidirectional radiated signal with a radiated power of m. In the simulation, the signal-to-noise ratio (SNR) is defined as... The simulation results are as follows: Figure 5 As shown, Figure 5To compare the performance of this invention with existing multi-source sparse localization schemes, the number of sensor nodes was set to 40 and the number of signal sources to 3. When the number of signal sources (i.e., sparsity) is unknown, this invention compares its proposed method with existing sparse localization methods.

[0142] In blind sparsity algorithms, the most basic existing implementation is the Orthogonal Matching Pursuit (OMP) algorithm, which uses threshold decision-making for iterative control. This approach, serving as the initial comparison benchmark for blind sparsity localization, exhibits the worst localization performance, achieving only 60% accuracy at a signal-to-noise ratio of 10dB. To address this deficiency, this invention first replaces the threshold decision-making in the iterative control stage with a residual divergence decision-making mechanism designed in this invention. This mechanism is based on the core assumption that the residual after complete signal recovery contains only background noise and follows a Gaussian distribution. It achieves iterative control by quantifying the difference between the empirical residual distribution and the benchmark Gaussian distribution using the KL divergence (relative entropy), without relying on prior information such as background noise power. Simulation results show that this improvement enhances localization performance by 4dB compared to the original threshold-decision OMP algorithm. This directly demonstrates that the residual divergence decision-making mechanism of this invention can adapt to harsher noise environments, significantly enhancing the anti-interference robustness of the localization method.

[0143] Based on the aforementioned residual divergence decision mechanism, the core framework of the original OMP algorithm is further replaced with an existing subspace-based method (i.e., the Compressed Sample Matching Pursuit (CoSaMP) method) to verify the effectiveness of subspace technology in multi-source sparse localization. Simulation results show that the combined scheme achieves stable localization performance with an accuracy of 80% at a signal-to-noise ratio of 9dB. This data not only confirms the fundamental value of the subspace method in multi-source signal separation and localization but also provides a comparative reference for subsequent optimization and improvement of the subspace mechanism in this invention.

[0144] To address the limitations of existing subspace methods (such as CoSaMP) that rely on a fixed sparsity for candidate support set selection and are ill-suited for multi-source aliasing scenarios, this invention innovatively optimizes the subspace backtracking mechanism. This mechanism abandons the traditional fixed-size backtracking subspace approach and instead dynamically adjusts the size and composition of the candidate support set in each iteration based on the numerical distribution characteristics of the signal projection inner product vector (an adaptive threshold is constructed through sorting, median, and absolute median deviation), thus more accurately capturing the location of the true signal source. Based on the residual divergence decision and existing subspace methods, simulations were conducted using the optimized subspace backtracking mechanism of this invention. The results show that even with a signal-to-noise ratio of only 8dB, the positioning accuracy can reach over 95%, significantly higher than the 80% of existing subspace methods. This fully demonstrates that the improved subspace backtracking mechanism of this invention effectively overcomes the accuracy bottleneck of existing technologies and significantly improves the accuracy of multi-source localization.

[0145] To further verify the advantages of the residual divergence decision-making mechanism, comparative tests were conducted using threshold decision-making and residual divergence decision-making, respectively, based on the optimized subspace backtracking mechanism of this invention. Simulation results show that the positioning performance using residual divergence decision-making is improved by approximately 3 dB compared to the threshold decision-making scheme. This secondary verification further confirms that the residual divergence decision-making method of this invention can more effectively handle complex noisy environments. Its characteristics of not requiring a preset threshold and relying on prior information make its applicability in real complex electromagnetic environments far superior to existing threshold decision-making schemes. In addition, this invention also conducted positioning simulation experiments under known sparsity. As shown in the simulation curves, under known sparsity, the performance of this invention is closer to the positioning performance under known sparsity than that of threshold decision-making, further confirming that the residual divergence decision-making method of this invention can more effectively handle complex noisy environments.

[0146] To further investigate the impact of key parameters on the positioning performance of this invention, a comparative simulation experiment was conducted based on the above-mentioned two-dimensional multi-source positioning simulation scenario, focusing on the number of signal sources and the number of sensors. The experimental results are as follows: Figure 6 and Figure 7 As shown, Figure 6 The curves show the comparison of positioning performance under different numbers of signal sources. Figure 7 The curves show the comparison of positioning performance under different numbers of sensor nodes. Under the premise of keeping other experimental parameters fixed, the positioning accuracy achieved by the present invention shows a gradual improvement trend as the number of signal sources decreases. At the same time, under the condition of fixed number of signal sources, the positioning accuracy also shows a significant improvement effect as the number of sensors increases.

[0147] In real-world applications, there are scenarios with a limited number of sensors. To evaluate the positioning performance in such scenarios, this invention conducts corresponding experimental simulations, and the results are as follows: Figure 8 As shown, Figure 8The simulation results show a comparison of positioning performance under scenarios with a reduced number of sensor nodes. Sensor nodes were evenly distributed within a grid area, with the number of nodes set to 15, 20, 25, and 30, while other simulation conditions remained unchanged. As the simulation curves show, with 30 sensor nodes and unknown sparsity (i.e., the number of signal sources), the positioning accuracy decreased by 1 dB compared to the known sparsity, but at a signal-to-noise ratio (SNR) of 20 dB, the performance reached over 95%. With 25 sensor nodes and a SNR of 20 dB, the positioning accuracy reached over 90% with known sparsity and approximately 85% with unknown sparsity. With 20 sensor nodes and a SNR of 25 dB, the positioning accuracy reached approximately 80% with known sparsity and approximately 65% ​​with unknown sparsity. With 15 sensor nodes and a signal-to-noise ratio of 25 dB, the positioning accuracy can reach approximately 60% when the sparsity is known, and approximately 40% when the sparsity is unknown. This demonstrates that even in scenarios with a limited number of sensors, this invention can still achieve partial positioning functionality.

[0148] In practical applications, there are scenarios where the number of sensor nodes is relatively small. To evaluate the positioning performance of this invention in such scenarios, corresponding simulation experiments were conducted, and the simulation results are as follows. Figure 8 As shown in the figure. The experiment was set with sensor nodes uniformly distributed within the grid area, and the number of sensor nodes was set to 15, 20, 25, and 30 respectively, while other simulation conditions remained consistent. The simulation curves show that: when the number of sensor nodes is 30, under the condition of unknown sparsity (i.e., the number of signal sources), the positioning accuracy is reduced by 1dB compared to the known sparsity scenario; and under a signal-to-noise ratio of 20dB, the positioning performance can reach over 95%. When the number of sensor nodes is 25, under a signal-to-noise ratio of 20dB, the positioning performance in the known sparsity scenario can reach over 90%, while the positioning performance in the unknown sparsity scenario is approximately 85%. When the number of sensor nodes is 20, under a signal-to-noise ratio of 25dB, the positioning performance in the known sparsity scenario is approximately 80%, while the positioning performance in the unknown sparsity scenario is approximately 65%. When the number of sensor nodes is 15, under a signal-to-noise ratio of 25dB, the positioning performance in the known sparsity scenario is approximately 60%, while the positioning performance in the unknown sparsity scenario is approximately 40%. In summary, even in scenarios with a small number of sensor nodes, the present invention can still achieve partial positioning functionality.

[0149] The present invention also provides a blind sparseness subspace backtracking homogeneous multi-source localization system 10 for residual divergence decision-making, the system comprising: The sparse observation model construction module 11 is used to divide the monitored area into grids. The monitored area includes signal source nodes at unknown locations and sensor nodes at known locations. The signal source nodes emit electromagnetic signals, and the sensor nodes collect electromagnetic signals. The actual received signal strength of the electromagnetic signals collected by the sensor nodes is obtained. The actual received signal strength is used as the observation vector, and a sparse observation model is constructed based on the grid position of the signal source nodes and the observation vector.

[0150] The candidate support set determination module 12 is used to take the observation vector as the residual vector, calculate the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model to obtain the correlation numerical sequence, determine the adaptive threshold based on the median absolute deviation and mean of the correlation numerical sequence, determine the candidate element based on the comparison between the adaptive threshold and each element in the correlation numerical sequence, and form the candidate support set through the grid position of the candidate element.

[0151] The location support set determination module 13 is used to filter the candidate support set based on the estimated received signal strength of the grid positions within the candidate support set, and generate the location support set for this iteration.

[0152] The signal source location determination module 14 is used to update the residual vector based on the location support set used for this iteration. After updating the residual vector in each iteration, it determines the theoretical probability distribution and the empirical probability distribution of the residual vector, compares the theoretical probability distribution and the empirical probability distribution to obtain the difference metric value, and stops the iteration process when the difference metric value meets the preset termination condition. The grid position corresponding to the location support set of the current iteration is the final location result of the signal source.

[0153] For example, in the sparse observation model construction module 11, the monitored area is divided into grids. The monitored area includes signal source nodes at unknown locations and sensor nodes at known locations. The signal source nodes emit electromagnetic signals, and the sensor nodes collect electromagnetic signals. The actual received signal strength of the electromagnetic signals collected by the sensor nodes is obtained. The actual received signal strength is used as the observation vector, and the existence of the signal source nodes at the grid locations is used as the sparse solution vector. A measurement matrix is ​​constructed with the sensor nodes as rows and the grid locations as columns. The Euclidean distance between the sensor nodes and the grid locations is determined based on the spatial coordinates of the sensor nodes and the grid locations. The path energy loss is determined based on the Euclidean distance, resulting in a path loss matrix. The sensing matrix is ​​determined by the product of the measurement matrix and the path loss matrix. Each row vector of the sensing matrix corresponds to a sensor node, and each column vector corresponds to a grid location. Based on the sensing matrix and the sparse solution vector, combined with the observation vectors collected by the sensor nodes, a sparse observation model is constructed.

[0154] In the candidate support set determination module 12, the observation vector is used as the residual vector; the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model is calculated to obtain the correlation numerical sequence; the elements in the correlation sequence are sorted in ascending order to obtain the first sorted sequence; the median of the first sorted sequence is determined; the absolute difference between each element in the sorted sequence and the median is calculated to construct the absolute deviation sequence; the absolute deviation sequence is sorted in ascending order to obtain the second sorted sequence; the median of the second sorted sequence is determined, and the median of the second sorted sequence is the median absolute deviation; the mean of the correlation sequence is determined; an adaptive threshold is determined based on the median absolute deviation and the mean; if an element in the correlation numerical sequence is greater than the adaptive threshold, then the element is the most relevant element, and the candidate support set is formed by the grid position corresponding to the most relevant element.

[0155] In the location support set determination module 13, column vectors corresponding to the grid positions in the candidate support set are extracted from the sensing matrix to form a sub-sensing matrix; the received signal strength estimates corresponding to the grid positions in the sub-sensing matrix are determined based on the sub-sensing matrix and the residual vector to form a received signal strength estimation matrix; the received signal strength estimates in the received signal strength estimation matrix are sorted in descending order, and a preset number of grid positions corresponding to the received signal strength estimates are selected as the location support set for this iteration.

[0156] In the signal source location determination module 14, after updating the residual vector in each iteration, the mean and variance of the residual vector are determined; the theoretical probability distribution is determined based on the mean and variance of the residual vector; the empirical probability distribution of the residual vector is determined through kernel density estimation; the difference metric is determined based on the theoretical probability distribution and the empirical probability distribution; when the difference metric is greater than a preset threshold, the iteration number is updated, and the step of calculating the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model is returned; when the difference metric is greater than or equal to the preset threshold, the iteration process is stopped, and the grid position corresponding to the position support set of this iteration is the final location result of the signal source.

[0157] The medium 20 provided by the present invention stores at least one computer program 21, which is executed by a processor to perform, as follows: Figure 1 , Figure 3 and Figure 4 The method shown is detailed above and will not be repeated here. In one embodiment, the medium 20 can be a storage chip, hard disk, portable hard disk, USB flash drive, optical disk, or other read / write storage device, or even a server, etc.

[0158] Furthermore, the processes depicted in the accompanying drawings do not necessarily have to be performed in the specific or sequential order shown to achieve the desired result. In some implementations, multitasking and parallel processing are possible or may be advantageous.

[0159] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0160] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A blind sparse subspace backtracking homogeneous multi-source localization method based on residual divergence decision, characterized in that, The method includes: The monitored area is divided into grids, which include signal source nodes at unknown locations and sensor nodes at known locations. The signal source nodes emit electromagnetic signals, and the sensor nodes collect the electromagnetic signals. The actual received signal strength of the electromagnetic signals collected by the sensor nodes is obtained, and the actual received signal strength is used as the observation vector. A sparse observation model is constructed based on the grid position of the signal source nodes and the observation vector. The observation vector is used as the residual vector; Calculate the normalized inner product of the residual vector with each column of the sensing matrix in the sparse observation model to obtain the correlation numerical sequence. Determine the adaptive threshold based on the median absolute deviation and mean of the correlation numerical sequence. Determine candidate elements based on the comparison between the adaptive threshold and each element in the correlation numerical sequence. Form a candidate support set based on the grid position of the candidate elements. Based on the estimated received signal strength values ​​of the grid positions within the candidate support set, the candidate support set is filtered to generate a position support set for this iteration; Update the residual vector according to the position support set used for this iteration; After each iteration of updating the residual vector, the theoretical probability distribution and the empirical probability distribution of the residual vector are determined. The theoretical probability distribution and the empirical probability distribution are compared to obtain a difference metric. When the difference metric meets the preset termination condition, the iteration process is stopped. The grid position corresponding to the position support set of the current iteration is the final positioning result of the signal source.

2. The blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making according to claim 1, characterized in that, The construction of the sparse observation model based on the grid position of the signal source node and the observation vector specifically includes: The existence of signal source nodes at grid locations is taken as a sparse vector to be solved; A measurement matrix is ​​constructed using the sensor nodes as rows and the grid positions as columns; Determine the Euclidean distance between the sensor node and the grid location where the signal source node is located based on the spatial coordinates of the sensor node and the grid location. The path energy loss is determined based on the Euclidean distance, and the path loss matrix is ​​obtained. The sensing matrix is ​​determined by the product of the measurement matrix and the path loss matrix, wherein each row vector of the sensing matrix corresponds to a sensing node and each column vector corresponds to a grid position. Based on the sensing matrix and the sparse vector to be solved, and combined with the observation vectors collected by the sensing nodes, a sparse observation model is constructed.

3. The blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making according to claim 1, characterized in that, The process of determining an adaptive threshold based on the median absolute deviation and mean of the correlation numerical sequence, determining candidate elements based on the comparison between the adaptive threshold and each element in the correlation numerical sequence, and forming a candidate support set through the grid positions of the candidate elements specifically includes: The elements in the correlation sequence are sorted in ascending order to obtain the first sorted sequence; Determine the median of the first sorted sequence, calculate the absolute difference between each element in the sorted sequence and the median, and construct an absolute deviation sequence; The absolute deviation sequence is sorted in ascending order to obtain a second sorted sequence; Determine the median of the second sorted sequence, where the median of the second sorted sequence is the absolute deviation of the median; Determine the mean of the correlation sequence; The adaptive threshold is determined based on the median absolute deviation and the mean. If an element in the correlation numerical sequence is greater than an adaptive threshold, then that element is the most relevant element, and a candidate support set is formed by the grid position corresponding to the most relevant element.

4. The blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making according to claim 1, characterized in that, The step of filtering the candidate support set based on the estimated received signal strength values ​​corresponding to the grid positions within the candidate support set to generate a location support set for this iteration specifically includes: Extract column vectors corresponding to grid positions within the candidate support set from the sensing matrix to form a sub-sensing matrix; Based on the sub-sensing matrix and the residual vector, the estimated value of the received signal strength corresponding to the grid position in the sub-sensing matrix is ​​determined, and the received signal strength estimation matrix is ​​formed. The received signal strength estimates in the received signal strength estimation matrix are sorted in descending order, and a preset number of grid positions corresponding to the received signal strength estimates are selected as the position support set for this iteration.

5. The blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making according to claim 4, characterized in that, The step of determining the received signal strength estimate corresponding to the grid position within the sub-sensing matrix based on the sub-sensing matrix and the residual vector, thereby constructing the received signal strength estimation matrix of the sub-sensing matrix, specifically includes: Replace the sensing matrix in the sparse observation model with the sub-sensing matrix; Based on the mapping relationship between the sub-sensing matrix and the observation vector in the sparse observation model, the estimated value of the received signal strength at each grid position in the sub-sensing matrix is ​​determined, and the estimated value of the received signal strength of the sub-sensing matrix is ​​obtained.

6. The blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making according to claim 1, characterized in that, The step of updating the residual vector based on the position support set used for this iteration specifically includes: Extract column vectors corresponding to the grid positions within the position support set from the sensing matrix to form the support set sensing matrix; The sensing matrix in the sparse observation model is replaced with the support set sensing matrix. Based on the mapping relationship between the support set sensing matrix and the observation vector in the sparse observation model, the received signal strength estimate of each grid position in the support set sensing matrix is ​​determined, and the received signal strength estimate matrix of the support set sensing matrix is ​​obtained. The sparse vector to be solved is replaced with the received signal strength estimation matrix of the support set sensing matrix to obtain the updated sparse observation model. The updated residual vector is determined based on the observation vector in the updated sparse observation model, the received signal strength estimation matrix of the support set sensing matrix, and the support set sensing matrix.

7. The blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making according to claim 1, characterized in that, After each iteration of updating the residual vector, the theoretical probability distribution and empirical probability distribution of the residual vector are determined. The theoretical probability distribution and empirical probability distribution are compared to obtain a difference metric. When the difference metric meets a preset termination condition, the iteration process stops. The grid position corresponding to the position support set of this iteration is the final localization result of the signal source. Specifically, this includes: After each iteration of updating the residual vector, the mean and variance of the residual vector are determined; The theoretical probability distribution is determined based on the mean and variance of the residual vector; The empirical probability distribution of the residual vector is determined by kernel density estimation; The difference measure value is determined based on the theoretical probability distribution and the empirical probability distribution; When the difference metric is greater than a preset threshold, update the iteration count and return to the step of calculating the normalized inner product of the residual vector and each column of the sensing matrix in the sparse observation model. When the difference metric is greater than or equal to a preset threshold, the iteration process stops, and the grid position corresponding to the position support set of this iteration is the final positioning result of the signal source.

8. A blind sparseness subspace backtracking homogeneous multi-source localization method for residual divergence decision-making according to claim 7, characterized in that, The step of determining the difference metric based on the theoretical probability distribution and the empirical probability distribution specifically includes: according to Determine the difference measure, where, This is a measure of difference. Let the empirical probability distribution of the residual vector be... This represents the theoretical probability distribution of the reference noise.

9. A blind sparse subspace backtracking homogeneous multi-source localization system based on residual divergence decision-making, characterized in that, The system includes: A sparse observation model construction module is used to divide the monitored area into grids. The monitored area includes signal source nodes at unknown locations and sensor nodes at known locations. The signal source nodes emit electromagnetic signals, and the sensor nodes collect the electromagnetic signals. The module obtains the actual received signal strength of the electromagnetic signals collected by the sensor nodes, uses the actual received signal strength as the observation vector, and constructs a sparse observation model based on the grid position of the signal source nodes and the observation vector. The candidate support set determination module is used to take the observation vector as a residual vector, calculate the normalized inner product of the residual vector with each column of the sensing matrix in the sparse observation model to obtain a correlation numerical sequence, determine an adaptive threshold based on the median absolute deviation and mean of the correlation numerical sequence, determine candidate elements based on the comparison between the adaptive threshold and each element in the correlation numerical sequence, and form a candidate support set through the grid position of the candidate elements. The location support set determination module is used to filter the candidate support set based on the estimated received signal strength of the grid positions within the candidate support set, and generate a location support set for this iteration; The signal source location determination module is used to update the residual vector according to the location support set used for this iteration. After updating the residual vector in each iteration, the module determines the theoretical probability distribution and the empirical probability distribution of the residual vector, compares the theoretical probability distribution and the empirical probability distribution to obtain a difference metric value, and stops the iteration process when the difference metric value meets the preset termination condition. The grid position corresponding to the location support set of the current iteration is the final location result of the signal source.

10. A computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method as claimed in any one of claims 1 to 8.

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