Uncertainty-guided sensor array network distributed probability consensus optimization cooperative positioning method

Abstract

The invention relates to an uncertainty-guided sensor array network distributed probability consensus optimization cooperative positioning method. The method comprises the following steps: step 1, establishing a cooperative positioning model for a non-cooperative radiation source; step 2, establishing an independent sensing model of the sensor array network to a non-cooperative radiation source target; 3, establishing an angle confidence interval overlapping feature region; 4, scheduling optimization of information interaction among nodes of the sensor array network is guided; step 5, proposing a consistency collaborative fusion strategy based on uncertainty measurement guidance; and 6, iteratively fusing the local estimation information of the adjacent nodes by adopting a consistency fusion strategy until the algorithm converges. The method can adapt to a complex impulse noise environment and is suitable for a non-cooperative scene; and the accuracy of radiation source number estimation and target positioning in the pulse noise environment is remarkably improved. And the data pairing problem is effectively overcome. And efficient and reliable distributed cooperative positioning is realized.

Description

Technical Field

[0001] This invention relates to the field of passive positioning technology, specifically to an uncertainty-guided distributed probabilistic consensus optimization collaborative positioning method for sensor array networks. Background Technology

[0002] Passive positioning technology is widely used in target perception due to its convenient information acquisition, simple implementation, and high concealment. Current passive positioning methods can be divided into two categories based on the positioning steps: two-step positioning and direct positioning. Direct positioning methods directly estimate the position based on the received electromagnetic signals from the radiation source, and can improve the positioning effect by utilizing the potential constraints of signal parameters. However, direct positioning suffers from drawbacks such as difficulty in joint modeling of multiple features, high communication costs, and over-reliance on fusion centers. Traditional two-step positioning is a common method for passive positioning, comprising two key steps: parameter estimation and position calculation. In target positioning scenarios based on angle of arrival (AHA), it is necessary to obtain position-related AHA parameters from the received signals, and then combine the parameter estimation results from multiple observation stations to construct a positioning mathematical model, thereby solving for the target position. However, traditional AHA estimation is susceptible to interference from noise and multipath effects, resulting in limited parameter estimation accuracy. When multi-target positioning is involved, the position calculation step, because it does not consider the distinguishing constraints of different signal parameters corresponding to their respective radiation sources, is prone to target association errors and parameter confusion, making it difficult to achieve optimal positioning results.

[0003] Existing passive localization technologies face numerous bottlenecks in practical, non-cooperative scenarios. First, most algorithms rely on prior information about the number of radiation sources, which is often difficult to obtain in non-cooperative environments, severely limiting their practicality. Second, traditional methods are typically based on the Gaussian noise assumption, which simplifies model design but struggles to handle non-Gaussian interference such as impulse noise common in real-world electromagnetic environments, leading to significant performance degradation or even failure. Furthermore, at the information fusion level, existing solutions often employ a centralized architecture, requiring the transmission of large amounts of raw data back to the fusion center. This not only incurs enormous communication overhead but also introduces high computational load and single-point-of-failure risks, failing to meet the real-time, low-power, and scalable requirements of distributed sensor networks. Therefore, developing a localization method capable of robust parameter estimation under unknown radiation source numbers, robust to impulse noise, and achieving efficient and targeted information fusion based on a distributed collaborative architecture has become crucial for driving technological advancement in this field. Summary of the Invention

[0004] This invention aims to provide an uncertainty-guided distributed probabilistic consensus optimization collaborative localization method for sensor array networks, in order to solve the problems of unknown signal source quantity, insufficient robustness and resolution of impulse noise, complex and inefficient multi-node information fusion, high centralized computing load and limited scalability in existing passive localization technologies.

[0005] The technical solution of this invention to solve the above-mentioned technical problems is as follows: an uncertainty-guided distributed probabilistic consensus optimization cooperative localization method for sensor array networks, comprising the following steps:

[0006] Step 1: For multi-sensor array network cooperative sensing scenarios, and considering non-Gaussian impulse noise conditions, a cooperative localization model for non-cooperative radiation sources is established, and a robust distributed cooperative localization framework is proposed.

[0007] Step 2: Using the signal and probability modeling of the distributed cooperative localization framework in Step 1, and to facilitate subsequent parameter solving using the variational Bayesian method, the likelihood function is written in a product form. The joint probability model is transformed into a hierarchical probabilistic graphical model structure, establishing an independent sensing model of the sensor array network for non-cooperative radiation source targets. This yields direct estimates of the following localization parameters: number of radiation source targets. Azimuth ; and model latent variable signal components Variance of Gaussian noise The variance γ of the Gaussian distribution, the prior γ of the inverse gamma distribution, and the variance of the complex Gaussian distribution. Bernoulli variables and its parameters Model parameters ;

[0008] Step 3: Characterize the probability distribution of the positioning parameters obtained in Step 2. An overlapping feature region of the angle confidence interval is established, and the grid points within the region are density-clustered to provide a reliable initial location for distributed estimation; each observation station performs DOA estimation on the received signal to obtain the DOA estimation result;

[0009] Step 4: Obtain the posterior probability distribution from the DOA estimation results obtained in Step 3, construct the spatial likelihood function for the target location, extract the radiation source location information and its uncertainty measure to obtain the local estimation information for the radiation source target, thereby guiding the scheduling optimization of information interaction between nodes in the sensor array network.

[0010] Step 5: Based on the posterior probability distribution of the target location obtained in Step 4, a consensus collaborative fusion strategy guided by uncertainty measurement is proposed. This strategy decomposes the uncertainty contribution of the candidate observation station set to the target location into: redundant information, unique information of each station and collaborative information. The nodes select the nodes to participate in the collaboration based on the contribution of the information provided and the weighted selection function.

[0011] Step 6: Using the local estimation information of each radiation source target obtained in Step 4 and the optimization criteria in Step 5, the local estimation information of adjacent nodes is iteratively fused using a consistency fusion strategy until the algorithm converges.

[0012] Based on the above technical solution, the present invention can be further improved as follows:

[0013] Furthermore, step 1 is detailed as follows:

[0014] Step 1.1, Let L be a matrix composed of L signal components, and its probability model is as follows: ,in,

[0015] Used for weight modeling , for The Row vector, probability of existence of signal components ;

[0016] Step 1.2, Angle Prior Probability Distribution Modeled by the von Mises distribution, where, and They are The mean direction and concentration parameters, It is a zeroth-order Bessel function of the first kind;

[0017] Step 1.3, noise probability modeling is as follows ,in, For mixed probabilities, The variance of Gaussian noise is modeled using a gamma distribution. and Let be the hyperparameters of the gamma distribution. The generalized t-distribution is used to model the heavy-tailed characteristics of mixed impulse noise. It is constructed using a hierarchical Bayesian model, with variance... and Applying an inverse gamma distribution prior, and For the shape and scale parameters of the gamma distribution;

[0018] Step 1.4: Each distributed positioning observation station has a uniform linear array consisting of M array elements, with the element spacing... , The signal wavelength is denoted as ; the set of incident azimuth angles is . Construct an array response for a distributed positioning sensor; under T snapshots, the received signal of the distributed positioning sensor is The position of each sensor node is denoted as ,exist The first far-field narrowband radiation source, The location of each radiation source is denoted as ;

[0019] Step 1.5: Construct a distributed positioning framework under local communication conditions through received signal modeling and probability modeling.

[0020] Furthermore, step 2 is detailed as follows:

[0021] Step 2.1: Obtain the hierarchical probability graphical model representation through the joint likelihood function;

[0022] Step 2.2: Using the hierarchical probability map obtained in step 2.1, variational Bayes inference is performed to solve for the localization parameters.

[0023] Furthermore, step 3 is detailed as follows:

[0024] Step 3.1, the estimation result of DOA is derived from the probability distribution. This means that the confidence level of the VM distribution is approximated using the confidence metric of the Gaussian distribution;

[0025] Step 3.2: Divide the monitoring area into a grid to obtain a set of grid points. Iterate through each grid point and filter out those that fall within the confidence half-angle range;

[0026] Step 3.3: Use the density-aware algorithm to perform spatial clustering analysis to obtain preliminary location results of candidate targets.

[0027] Furthermore, step 4 is detailed as follows:

[0028] The target position likelihood function constructed based on the posterior probability distribution of the observation station regarding the target position azimuth is: The mean and variance of the candidate target locations are extracted as follows: and .

[0029] Furthermore, step 5 is detailed as follows:

[0030] Step 5.1, Node With the target location Mutual information between them ,node The amount of joint information is ,in, For target location variance, Given the Gaussian conditional covariance, the joint observation covariance matrix of the two nodes is: ;

[0031] Step 5.2 involves partially decomposing the mutual information into redundant information, unique information for each station, and collaborative information. To provide overlapping information for the target location, and For nodes Unique information about the target location This refers to collaborative information generated jointly by the two stations;

[0032] Step 5.3: Construct the weighted PID gain of each node within the existing node set, and use this as the node selection function, where... This represents the independent information contribution of node r relative to other nodes. This represents the collaborative information between node r and other nodes in the set. This represents redundant information about node r relative to the set. These are the weighting coefficients.

[0033] Furthermore, step 6 is detailed as follows:

[0034] Step 6.1, Array Node Set Each array node Can receive neighbor nodes The sent local estimation message, in which, Represents a node The set of direct neighbors, Represents all neighboring nodes The mean vector, For the covariance matrix, the nodes The posterior mean vector and covariance matrix are respectively , ;

[0035] Step 6.2 Dynamically select interaction nodes in each iteration. Receive from the optimal node according to the selection criteria. mean vector Covariance Matrix And calculate its information matrix;

[0036] Step 6.3: Based on the characteristic parameters transmitted by the preferred receiving node, the estimation is continuously updated through a consensus fusion algorithm to reduce uncertainty. Finally, the estimation values ​​of all nodes converge asymptotically to obtain the estimation result of the radiation source location.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0038] This method can adapt to complex impulse noise environments, avoid grid mismatch problems, and reduce computational complexity. It also does not require a known number of information sources, making it suitable for non-cooperative scenarios. It significantly improves the accuracy of radiation source quantity estimation and target localization in impulse noise environments and provides a measure of uncertainty in orientation angle estimation. The distributed multi-target localization method based on angle confidence effectively overcomes the data pairing problem and exhibits high estimation performance. In the distributed architecture, each node dynamically selects and collaborates with the node with the maximum information gain, converging to a globally consistent localization result. This significantly enhances the system's scalability and robustness, achieving efficient and reliable distributed cooperative localization. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating an uncertainty-guided distributed probabilistic consensus optimization collaborative localization method for sensor array networks in an embodiment of the present invention.

[0040] Figure 2 This is a diagram of a hierarchical probability graph model in an embodiment of the present invention;

[0041] Figure 3 This is a schematic diagram of multi-target localization based on angle confidence in an embodiment of the present invention;

[0042] Figure 4 As described in the embodiments of the present invention Performance analysis of multi-target localization under different GSNR under stable distributed noise;

[0043] Figure 5 As described in the embodiments of the present invention Performance analysis of multi-target localization with different snapshot numbers under stable noise distribution;

[0044] Figure 6 This invention provides an analysis of the multi-target localization performance under different SNRs in GMM noise.

[0045] Figure 7 This invention provides an analysis of the multi-target localization performance under different snapshot numbers in GMM noise conditions in this embodiment. Specific implementation methods

[0046] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0047] like Figure 1 As shown, an uncertainty-guided distributed probabilistic consensus optimization cooperative localization method for sensor array networks includes the following steps:

[0048] Step 1: For collaborative sensing scenarios using multi-sensor array networks, and considering non-Gaussian impulse noise conditions, a robust distributed collaborative localization framework is proposed by establishing a collaborative localization model for non-cooperative radiation sources.

[0049] Step 1.1: By introducing a noise distribution weighting factor, the unknown noise is modeled, making the model more accurately reflect the noise characteristics in the actual electromagnetic environment; signal Essentially, it is a row-sparse vector. To characterize its sparsity, a set of Bernoulli variables is introduced. ,in , used to indicate The row vector Whether it is a non-zero value. Specifically, when hour, ;when , The signal components can be modeled using a Bernoulli-Gaussian probability model:

[0050] (1)

[0051] (2)

[0052] in This represents the probability of each signal component existing. Represents the Dirac function, Indicates a complex Gaussian distribution. This represents the variance of the complex Gaussian distribution. express The unit vector.

[0053] Step 1.2: Obtain the signal direction by applying a priori knowledge. The prior probability distribution can be expressed as:

[0054] (3)

[0055] in, Modeled using the von Mises distribution:

[0056] (4)

[0057] in, and They are The mean direction and concentration parameters, For a zeroth-order Bessel function of the first kind. Specifically, when When the equation (4) degenerates into a uniform distribution: .

[0058] Step 1.3: Model the statistical characteristics of impulse noise using a Gaussian-generalized t-mixture distribution. Assuming that the elements in the noise matrix are statistically independent, the probability distribution expression is obtained as follows:

[0059] (5)

[0060] in, For mixed probabilities, The variance of Gaussian noise is modeled using a gamma distribution:

[0061] (6)

[0062] in, and Let be the hyperparameter of the gamma distribution. It follows a generalized t-distribution.

[0063] Step 1.4: Model the array received signal by assuming a physical scenario and the principle of electromagnetic wave propagation. Each distributed positioning observation station has a uniform linear array consisting of M array elements. Consider one... Uniform linear array of array elements, with element spacing , The signal wavelength is [wavelength]. Within the monitoring area, there exists [signal wavelength]. There are several far-field narrowband radiation sources, with incident azimuth angles set as follows: .

[0064] No. The array of snapshots receives the following signals:

[0065] (7)

[0066] in, For the observation vector, For the received first The signal from the radiation source For noise vectors, For the first Array steering vector of each radiation source:

[0067] (8)

[0068] If the number of quick shots is The expression for the received signal is:

[0069] (9)

[0070] The array receives the signal as follows The superposition and coupling of radiation source signals and noise mean that the received signal is re-expressed using the idea of ​​line spectrum estimation: assuming the received signal contains... There are 1 signal components, each of which is statistically independent. Only 1 of them is statistically independent. One signal component is non-zero, the rest Let each signal component be zero. Equation (9) can be rewritten as:

[0071] (10)

[0072] in, Must meet ,because The maximum number of resolvable targets in a uniform linear array of elements is . Assumption Each signal component For an overcomplete perception matrix. The signal expression for each snapshot is:

[0073] (11)

[0074] in, , , Consider a... indivual A sensor array network consisting of a uniform linear array of array elements, wherein the position of each sensor node is denoted as . ,exist The first far-field narrowband radiation source, The location of each radiation source is denoted as .

[0075] Step 1.5: Through received signal modeling and probabilistic modeling, a distributed positioning framework under local communication conditions is constructed. This system architecture consists of distributed sensor nodes and a central node. Sensor nodes are responsible for receiving radiation source signals, modeling unknown noise using a Gaussian-generalized t-mixture distribution, and extracting the angle of arrival (AOA) feature parameters from the signals. The number of different angles observed by each sensor node corresponds to the number of radiation sources in its field of view. Each sensor node transmits the extracted local angle information to the corresponding central node within its sub-network. Based on the collected angle information, the central node calculates the angle confidence interval and identifies overlapping feature regions, further processing it using a density clustering algorithm to obtain preliminary candidate regions where the target location may exist.

[0076] Step 2: Using the signal and probability modeling of the distributed positioning framework in Step 1, and to facilitate subsequent parameter solving using the variational Bayesian method, the likelihood function is written in a product form. The joint probability model is transformed into a hierarchical probabilistic graphical model structure, establishing an independent sensing model of the sensor array network for non-cooperative radiation source targets. This yields direct estimates of positioning-related parameters, including the number of radiation source targets. Azimuth ; and model latent variable signal components Variance of Gaussian noise Gaussian distribution variance Inverse gamma distribution prior Variance of complex Gaussian distribution Bernoulli variables and its parameters Model parameters .

[0077] Step 2.1: As Figure 2 As shown, the hierarchical probabilistic graphical model can be obtained through the joint likelihood function. Bernoulli variables are introduced. and define , Rewriting the likelihood function in product form, the likelihood function expression is:

[0078] (12)

[0079] Each element in the matrix is ​​statistically independent and follows a Bernoulli distribution, which is expressed as:

[0080] (13)

[0081] Each element in the matrix is ​​statistically independent and follows a beta distribution, which is expressed as:

[0082] (14)

[0083] Among them, and For shape parameters. To simplify the representation, a set of implicit variables is defined. Given the model parameter set, the likelihood function expression is:

[0084] (15)

[0085] Equation (15) can be used as follows Figure 2 The hierarchical probability graphical model shown is used to represent this.

[0086] Step 2.2: Obtain the parameter solution by performing variational Bayesian inference using the probabilistic graphical model described in Step 2.1.

[0087] Step 2.2.1: Inference :

[0088] (16)

[0089] in, for The set of non-zero elements in Indicates taking the real part, This represents the estimation of the covariance matrix. For the noise matrix, Approximated as a VM distribution: Then, based on the properties of the VM distribution, we can obtain... and Update expression:

[0090] (17)

[0091] (18)

[0092] Step 2.2.2: Inference and :

[0093] Assumption Quality Concentration Above, that is . for The set of non-zero elements in the set. The posterior probability expression is:

[0094] (19)

[0095] For ease of calculation, the expression is defined as follows:

[0096] (20)

[0097] (twenty one)

[0098] in, express The first in the matrix Okay, number Column elements. According to equation (25), in order to obtain First, we need to calculate :

[0099] (twenty two)

[0100] in, , According to equation (25), It can be viewed as a deterministic but unknown vector, in order to determine We define The lower bound of logarithmic evidence:

[0101] (twenty three)

[0102] therefore, The expression for the estimated value is:

[0103] (twenty four)

[0104] In seeking Subsequently, the estimated number of radiation sources was... .

[0105] Step 2.2.3: Inference :

[0106] (25)

[0107] From the above formula, we can conclude that If it follows a gamma distribution, then its parameter update expression is:

[0108] (26)

[0109] Step 2.2.4: Inference :

[0110] (27)

[0111] From the above formula, we can conclude that Follows an inverse gamma distribution: Its parameter expression is as follows:

[0112] (28)

[0113] Step 2.2.5: Inference :

[0114] (29)

[0115] From the above formula, we can conclude that It follows a gamma distribution, and its parameter update expression is:

[0116] (30)

[0117] Step 2.2.6: Inference :

[0118] (31)

[0119] From the above formula, we can conclude that Follows Bernoulli distribution:

[0120] (32)

[0121] It is a The normalization constant that holds true, and the corresponding parameter update expression are:

[0122] (33)

[0123] in, It is a double gamma function.

[0124] Step 2.2.7: Inference :

[0125] (34)

[0126] From the above formula, we can conclude that If it follows a beta distribution, then its parameter update rule is:

[0127] (35)

[0128] Step 2.2.8: Update model parameters and

[0129] (36)

[0130] The expected expressions involved in step 2 are as follows:

[0131] (37)

[0132] In summary, for each latent variable and each model parameter The process is repeated iteratively until the set convergence threshold is reached.

[0133] Step 3: Characterize the probability distribution of the azimuth parameters obtained in Step 2. This invention proposes a multi-radiation source localization method based on angle confidence and clustering. The angle confidence is quantized by a VM distribution, and density clustering is performed on the overlapping regions of confidence domain clusters to provide a reliable initial location for distributed estimation. Intersections near real targets will cluster into high-density clusters, while false points will be randomly distributed. The method effectively solves the data pairing problem. (Note: The original text also mentions establishing overlapping feature regions within angle confidence intervals and performing density clustering within these regions, but this seems unrelated to the main point about radiation source localization.)

[0134] Step 3.1, consider a... indivual A sensor array network consisting of a uniform linear array of array elements, wherein the position of each sensor node is denoted as . Array element spacing , The signal wavelength is [wavelength]. Within the monitoring area, there exists [signal wavelength]. The first far-field narrowband radiation source, The location of each radiation source is denoted as Each observation station performs DOA estimation on the received signal to obtain the DOA estimation result. The probability distribution of its angle information.

[0135] Based on the statistical model described in step 2, the confidence half-angle can be calculated: when Distribution When it is large, for example At that time, the VM distribution approximates a Gaussian distribution. In this case, the confidence level of the VM distribution can be approximated using the confidence metric of the Gaussian distribution: given Its confidence half-angle can be approximated by the expression:

[0136] (38)

[0137] in, The confidence level.

[0138] Step 3.2: Divide the monitoring area into a grid to obtain a set of grid points. And initialize the weights of each grid point. . No. The coordinates of the grid points are Iterate through each grid point, mapping the coordinates of each grid point to the observation station. The azimuth expression is:

[0139] (39)

[0140] Determine the azimuth of the grid point Does it satisfy the following expression:

[0141] (40)

[0142] If this condition is met, it means that the grid point is in Within the confidence region, at this point, the weight of the grid point is increased by 1, i.e.: The above steps are performed for each observation station, and then the weights of all grid points are normalized to obtain a weighted grid map.

[0143] Step 3.3: Based on the confidence half angle of the azimuth, select the grid points in the monitoring area that satisfy equation (48), and then use the DBSCAN algorithm to perform cluster analysis to obtain the location estimate of the radiation source target.

[0144] Step 4: Using the posterior probability distribution of the DOA estimate obtained in Step 3, construct a spatial likelihood function for the target location, extract radiation source location information and its uncertainty measure, and use this to guide the scheduling optimization of information interaction among nodes in the sensor array network. From the posterior probability distribution of the observation station regarding the azimuth of the target location obtained in Step 3, construct the likelihood value of the target location under this azimuth posterior distribution:

[0145] (41)

[0146] For the candidate regions obtained by density clustering in step 3 Extract candidate target parameters, including mean and variance:

[0147] (42)

[0148] (43)

[0149] Step 5: Based on the posterior probability distribution of the target location obtained in Step 4, a consensus collaborative fusion strategy guided by uncertainty measurement is proposed. This strategy divides the uncertainty contribution of the candidate observation station set to the target location into three parts using partial information decomposition (PID): redundant information, unique information for each station, and collaborative information. Nodes select the nodes to participate in the collaboration based on their contribution of information provided and a weighted selection function.

[0150] Step 5.1, assume the target position vector Observation station collection , No. The variables output by each node are denoted as follows: , and The joint distribution is obtained from the posterior probability distribution in step 4; the joint observation of any two nodes is denoted as... Under the Gaussian assumption, nodes With the target location The mutual information between them is:

[0151] (44)

[0152] in Represents a node The greater the mutual information provided about the overall target location, the more significantly the station reduces the uncertainty of the target location. For target location variance, The Gaussian conditional covariance can be calculated as follows:

[0153] (45)

[0154] For nodes The joint observations have the following joint information content:

[0155] (46)

[0156] The calculation method is the same as in equation (45), where the joint observation covariance matrix of the two nodes is:

[0157] (47)

[0158] Step 5.2, for characterizing nodes and Regarding the information relationships of the target location, the above mutual information is partially decomposed:

[0159] (48)

[0160] when When the value is positive, it indicates that joint observations of the nodes can reveal new target location information, and can be selected preferentially.

[0161] The overlapping information provided for the target location, i.e., the portion that can be interpreted by both, is represented as:

[0162] (49)

[0163] and For nodes The unique information about the target location is represented as follows:

[0164] (50)

[0165] (51)

[0166] The collaborative information generated by the joint efforts of the two stations, i.e., the new information revealed after the joint effort, is represented as:

[0167] (52)

[0168] Step 5.3, with nodes As a candidate, its weighted PID gain under the selected set S is defined as:

[0169] (53)

[0170] This represents the independent information contribution of node r relative to other nodes. This represents the collaborative information between node r and other nodes in the set. This represents redundant information about node r relative to the set. The weighting coefficients represent the amount of uncertainty reduction at the target location by each node and the synergistic and redundant effects between nodes. When the mutual information of the observations of two nodes regarding the target location is highly correlated, it indicates that the information provided by the two nodes regarding the target location is redundant, and their contribution to positioning is limited. Using Shannon entropy, mutual information gain, etc., to measure the degree of uncertainty reduction at the target location by each node is prone to limitations such as information duplication, synergistic benefits, and low information utilization. It is difficult to optimally reflect the information structure of positioning estimation among multiple nodes using only these indicators. In this invention, Gaussian approximation partial information decomposition is used, and mutual information and covariance can be calculated analytically, making the information complementarity of the observation nodes stronger.

[0171] The calculation of the objective function relies only on local information interaction between nodes. The entire process does not conflict with local communication and ultimately obtains the fusion result in a distributed manner.

[0172] Step 6: Obtain the local estimation information of each radiation source target through Step 4, namely the position mean vector and covariance matrix of each target, as well as the optimization criteria in Step 5. Iteratively fuse the local estimation information of adjacent nodes using a consistency fusion strategy until the algorithm converges.

[0173] Step 6.1, Define the array node set , The set of all communicable links in the network, i.e., if array nodes and Within the communication range, then Each array node Can receive neighbor nodes The sent local estimation message, in which, Represents a node The set of direct neighbors.

[0174] According to the selection criteria It is the optimal node dynamically selected from the entire set of nodes in an interaction, capable of bringing the greatest information gain. In each iteration ,node Receive from all nodes mean vector Covariance Matrix Then calculate its information matrix:

[0175] (54)

[0176] The contributions of neighboring nodes can then be represented in the form of information vectors:

[0177] (55)

[0178] node It merges its local estimate with information from all neighboring nodes to update its own estimate:

[0179] (56)

[0180] (57)

[0181] in, and For nodes The information matrix and information vector of the local estimate.

[0182] Step 6.2: Based on the fused information matrix and information vector, calculate the node... The posterior mean vector and covariance matrix:

[0183] (58)

[0184] (59)

[0185] node The updated and Broadcast to all neighboring nodes Then proceed to the next iteration, when the estimated change value of two consecutive iterations... It may stop when the maximum number of iterations is reached.

[0186] Step 6.3: Based on the characteristic parameters transmitted by the preferred receiving node, the estimation is continuously updated through a consensus fusion algorithm to reduce uncertainty. Finally, the estimation values ​​of all nodes converge asymptotically to obtain the estimation result of the radiation source location.

[0187] In this invention, a robust distributed cooperative localization framework is first established for scenarios involving impulse noise environments and non-cooperative radiation source localization. A joint probability model including positioning parameters such as the target azimuth angle is constructed and transformed into a hierarchical probabilistic graphical model structure, with variational inference methods used for parameter solving. Furthermore, overlapping feature regions of angle confidence intervals are established based on the probability distribution of the azimuth angle parameters, and density clustering is used to provide initial position priors for distributed estimation. Subsequently, a spatial likelihood function of the target position is constructed based on the posterior probability distribution of the DOA estimation, extracting position information and its uncertainty measure to guide the scheduling optimization of information interaction between nodes. To achieve efficient collaboration, a consistency fusion strategy based on uncertainty measure and information gain is proposed. Nodes select cooperative nodes based on the maximum entropy difference and maximum mutual information criteria to ensure the effectiveness and relevance of information exchange. Finally, each node interacts with feature information based on the selection results, and through continuous fusion of local estimates, the estimated values ​​of all nodes gradually converge. The beneficial effects achieved by this invention are verified through experiments below.

[0188] Consider a sensor array network consisting of four uniform linear arrays of 15 elements each, with an element spacing of half a wavelength, and 500 Monte Carlo experiments. The array node positions are (0 m, 0 m), (2000 m, 0 m), (3500 m, 0 m), and (5000 m, 0 m), and the monitoring area is 5000 m × 5000 m. Set to 1.2, the parameter of GMM noise. Set it to 0.1. Set to 100. There are two radiation source targets, located at (1000 m, 2200 m) and (3500 m, 3000 m) respectively. For each observation station, the DOA estimate and its probability distribution are obtained using the GGTM-VBI algorithm. The proposed angle confidence-based multi-target localization method is used for localization, and compared with the DOA intersection clustering method and nonlinear least squares method under the same conditions. RMSE is defined as:

[0189] (60)

[0190] in, For the first Location estimation for this experiment This represents the actual target location.

[0191] The proposed method can not only obtain the azimuth angle of the radiation source target, but also the posterior probability distribution of the azimuth angle parameters, which characterizes the uncertainty of angle measurement, such as... Figure 3As shown, each azimuth ray can be quantified to have a confidence angle range, which is then mapped to the location domain. This indicates that the radiation source is located in an uncertain region in that direction. The confidence regions of multiple arrays will overlap, and the region with the highest degree of overlap has the highest probability of containing the radiation source. The confidence of the angle is quantified by the VM distribution. Density clustering is performed using the overlapping regions of the confidence domain clusters to locate the radiation source. This method can effectively solve the data pairing problem.

[0192] like Figure 4 and Figure 5 As shown Experimental results on multi-target localization performance analysis under stable distributed noise, for Simulation experiments were conducted on multi-target localization under stable distributed noise. The performance was verified by evaluating the RMSE under different GSNR and different snapshot numbers. The RMSE results of the localization results are shown below. Figure 4 and Figure 5 As shown, the confidence-based multi-target localization algorithm effectively solves the data pairing problem, can correctly locate multiple targets, and has good localization accuracy.

[0193] like Figure 6 and Figure 7 The experimental results of multi-target localization performance analysis under GMM noise are shown. Simulation experiments were conducted under different SNR and snapshot numbers. The experimental results verify the effectiveness of the confidence-based multi-target localization algorithm under different SNR and snapshot numbers.

[0194] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An uncertainty-guided distributed probabilistic consensus optimization cooperative localization method for sensor array networks, characterized in that, The steps include the following: Step 1: For multi-sensor array network cooperative sensing scenarios, and considering non-Gaussian impulse noise conditions, a cooperative localization model for non-cooperative radiation sources is established, and a robust distributed cooperative localization framework is proposed. Step 2: Using the signal and probability modeling of the distributed cooperative localization framework in Step 1, and to facilitate subsequent parameter solving using the variational Bayesian method, the likelihood function is written in a product form. The joint probability model is transformed into a hierarchical probabilistic graphical model structure, establishing an independent sensing model of the sensor array network for non-cooperative radiation source targets. This yields direct estimates of the following localization parameters: number of radiation source targets. Azimuth ; and model latent variable signal components Variance of Gaussian noise The variance γ of the Gaussian distribution, the prior γ of the inverse gamma distribution, and the variance of the complex Gaussian distribution. Bernoulli variables and its parameters Model parameters ; Step 3: Characterize the probability distribution of the positioning parameters obtained in Step 2. An overlapping feature region of the angle confidence interval is established, and the grid points within the region are density-clustered to provide a reliable initial location for distributed estimation; each observation station performs DOA estimation on the received signal to obtain the DOA estimation result; Step 4: Obtain the posterior probability distribution from the DOA estimation results obtained in Step 3, construct the spatial likelihood function for the target location, extract the radiation source location information and its uncertainty measure to obtain the local estimation information for the radiation source target, thereby guiding the scheduling optimization of information interaction between nodes in the sensor array network. Step 5: Based on the posterior probability distribution of the target location obtained in Step 4, a consensus collaborative fusion strategy guided by uncertainty measurement is proposed. This strategy decomposes the uncertainty contribution of the candidate observation station set to the target location into: redundant information, unique information of each station and collaborative information. The nodes select the nodes to participate in the collaboration based on the contribution of the information provided and the weighted selection function. Step 6: Using the local estimation information of each radiation source target obtained in Step 4 and the optimization criteria in Step 5, the local estimation information of adjacent nodes is iteratively fused using a consistency fusion strategy until the algorithm converges.

2. The uncertainty-guided distributed probabilistic consensus optimization cooperative localization method for sensor array networks according to claim 1, characterized in that, Step 1 is described in detail as follows: Step 1.1, Let L be a matrix composed of L signal components, and its probability model is as follows: ,in, Used for weight modeling , for The Row vector, probability of existence of signal components ; Step 1.2, Angle Prior Probability Distribution Modeled using the von Mises distribution, where, and They are The mean direction and concentration parameters, It is a zeroth-order Bessel function of the first kind; Step 1.3, noise probability modeling is as follows ,in, For mixed probabilities, The variance of Gaussian noise is modeled using a gamma distribution. and Let be the hyperparameters of the gamma distribution. The generalized t-distribution is used to model the heavy-tailed characteristics of mixed impulse noise. It is constructed using a hierarchical Bayesian model, with variance... and Applying an inverse gamma distribution prior, and For the shape and scale parameters of the gamma distribution; Step 1.4: Each distributed positioning observation station has a uniform linear array consisting of M array elements, with the element spacing... , The signal wavelength is denoted as ; the set of incident azimuth angles is . Construct an array response for a distributed positioning sensor; under T snapshots, the received signal of the distributed positioning sensor is The position of each sensor node is denoted as ,exist The first far-field narrowband radiation source, the The location of each radiation source is denoted as ; Step 1.5: Construct a distributed positioning framework under local communication conditions through received signal modeling and probability modeling.

3. The uncertainty-guided distributed probabilistic consensus optimization cooperative localization method for sensor array networks as described in claim 1, characterized in that, Step 2 is described in detail below: Step 2.1: Obtain the hierarchical probability graphical model representation through the joint likelihood function; Step 2.2: Using the hierarchical probability map obtained in step 2.1, variational Bayes inference is performed to solve for the localization parameters.

4. The uncertainty-guided distributed probabilistic consensus optimization cooperative localization method for sensor array networks according to claim 1, characterized in that, Step 3 is as follows: Step 3.1, the estimation result of DOA is derived from the probability distribution. This means that the confidence level of the VM distribution is approximated using the confidence metric of the Gaussian distribution; Step 3.2: Divide the monitoring area into a grid to obtain a set of grid points. Iterate through each grid point and filter out those that fall within the confidence half-angle range; Step 3.3: Use the density-aware algorithm to perform spatial clustering analysis to obtain preliminary location results of candidate targets.

5. The uncertainty-guided distributed probabilistic consensus optimization cooperative localization method for sensor array networks according to claim 1, characterized in that, Step 4 is as follows: The target position likelihood function constructed based on the posterior probability distribution of the observation station regarding the target position azimuth is: The mean and variance of the candidate target locations are extracted as follows: and .

6. The uncertainty-guided distributed probabilistic consensus optimization cooperative localization method for sensor array networks according to claim 1, characterized in that, Step 5 is described in detail below: Step 5.1, Node With the target location Mutual information between them ,node The amount of joint information is ,in, For target location variance, Given the Gaussian conditional covariance, the joint observation covariance matrix of the two nodes is: ; Step 5.2 involves partially decomposing the mutual information into redundant information, unique information for each station, and collaborative information. To provide overlapping information for the target location, and For nodes Unique information about the target location This refers to collaborative information generated jointly by the two stations; Step 5.3: Construct the weighted PID gain of each node within the existing node set, and use this as the node selection function, where... This represents the independent information contribution of node r relative to other nodes. This represents the collaborative information between node r and other nodes in the set. This represents redundant information about node r relative to the set. These are the weighting coefficients.

7. The uncertainty-guided distributed probabilistic consensus optimization cooperative localization method for sensor array networks according to claim 1, characterized in that, Step 6 is as follows: Step 6.1, Array Node Set Each array node Can receive neighbor nodes The sent local estimation message, in which, Represents a node The set of direct neighbors, Represents all neighboring nodes The mean vector, For the covariance matrix, the nodes The posterior mean vector and covariance matrix are respectively , ; Step 6.2 Dynamically select interaction nodes in each iteration. Receive from the optimal node according to the selection criteria. mean vector Covariance Matrix And calculate its information matrix; Step 6.3: Based on the characteristic parameters transmitted by the preferred receiving node, the estimation is continuously updated through a consensus fusion algorithm to reduce uncertainty. Finally, the estimation values ​​of all nodes converge asymptotically to obtain the estimation result of the radiation source location.

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