Three-dimensional underwater target tracking method based on improved particle filtering

Abstract

The invention discloses a three-dimensional underwater target tracking method based on improved particle filtering, which belongs to the technical field of underwater wireless sensor networks, and comprises the following steps: collecting three-dimensional target tracking data of an underwater target; constructing a target tracking model and a measurement model according to the three-dimensional target tracking data; the method comprises the following steps: improving a particle filtering algorithm based on unscented Kalman filtering, constructing an importance density function based on the improved particle filtering algorithm, a target tracking model and a measurement model, and re-sampling particles; a dynamic adaptive hierarchical weight factor is introduced to correct different particle weights, and normalization processing is performed on the corrected particle weights; performing anomaly detection on the three-dimensional target tracking data based on an optimized Grubbs criterion; and fusing the data of the trusted nodes by adopting an information entropy weighting strategy to obtain a fused target state estimation value, and realizing three-dimensional tracking of the underwater target. According to the invention, high-precision and high-reliability underwater target three-dimensional tracking can be realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater wireless sensor networks, and particularly relates to a three-dimensional underwater target tracking method based on improved particle filtering. Background Technique

[0002] With the increasingly prominent strategic position of ocean resource development, underwater wireless sensor networks (UWSN) have been widely used in the ocean field. And the UWSN target tracking technology is one of the core technologies for realizing ocean resource exploration, target reconnaissance, underwater attack and defense, and other fields.

[0003] Target tracking is one of the key technologies in UWSN. Traditional target tracking algorithms mainly include Kalman Filter (KF) and its extended forms, such as Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). These algorithms perform well in dealing with linear Gaussian noise systems, but when facing underwater strong nonlinear dynamic systems and non-Gaussian noise coupling scenarios, the state estimation accuracy is significantly reduced. In contrast, Particle Filter (PF) can effectively characterize the posterior probability distribution of nonlinear non-Gaussian systems through a non-parametric Monte Carlo sampling mechanism, so it shows significant advantages in the field of UWSN underwater target tracking.

[0004] However, in practical applications, especially in underwater target positioning and tracking, the standard particle filter algorithm often has problems of particle degradation and particle impoverishment, which seriously affect the accuracy of underwater target tracking. To solve these problems, existing research has proposed various improvement schemes, such as improving particle diversity by optimizing the importance density function and designing an adaptive resampling strategy. For example, Ran Xinghao et al. generated the importance density function through the square root of the covariance matrix in the second-order central difference filter, and combined with the idea of weight optimization to increase the diversity of the particle set; Zhao et al. used UKF as the importance probability density function and introduced a weight optimization mechanism to suppress the phenomenon of particle impoverishment. In addition, Zhang Hongwei et al. based on a dual-observation station architecture, generated the proposal distribution of the particle filter through UKF, and used the unscented transform technology to update the target state to improve the state estimation accuracy.

[0005] In terms of data fusion, Zhang Ying et al. proposed a method for eliminating interference information based on the Grubbs criterion, and improved the distributed particle filter by combining the mutual information entropy weighted fusion strategy. Zhu Hongbo et al. designed a distributed filtering framework, screened the local state estimation data through the K-medoids trust mechanism, and adopted the diffusion fusion strategy to achieve the dynamic update of state estimation, improving the robustness of the system.

[0006] Although the existing research has made certain progress, the following main problems still exist:

[0007] In the existing weight optimization strategy based on resampling, the weight factors are mostly fixed parameters, which are difficult to dynamically respond to the particle degradation degree and the changes in the actual situation, lacking self-adaptability. When the existing abnormal data detection methods deal with multi-dimensional state estimation data, they fail to effectively coordinate the data coupling and heteroscedastic characteristics between different dimensions, resulting in difficulty in synchronously guaranteeing the accuracy of abnormal determination and dimension compatibility.

[0008] Aiming at the problems existing in the prior art, it is urgent to propose a three-dimensional underwater target tracking method based on improved particle filter. Summary of the Invention

[0009] To solve the above technical problems, the present invention provides a three-dimensional underwater target tracking method based on improved particle filter. First, construct an importance density function, and improve the particle filter algorithm by combining a dynamic adaptive hierarchical weight optimization mechanism to achieve high-precision estimation of the target state; second, introduce the Grubbs criterion based on Mahalanobis distance to detect abnormalities in multi-dimensional state parameters such as the target position and speed, and construct a node trust mechanism to screen high-reliability data sources; finally, design a weighted fusion strategy based on information entropy for the trusted node set, and quantify the reliability of node data through entropy values, so as to achieve target tracking under complex underwater conditions.

[0010] The present invention proposes a three-dimensional underwater target tracking method based on improved particle filter, including the following steps:

[0011] Collect three-dimensional target tracking data of underwater targets based on the sensors of the observation station;

[0012] Construct a target tracking model and a measurement model according to the three-dimensional target tracking data;

[0013] Improve the particle filter algorithm based on the unscented Kalman filter, and construct an importance density function based on the improved particle filter algorithm, the target tracking model and the measurement model, and resample the particles;

[0014] During the resampling process, introduce a dynamic adaptive hierarchical weight factor to correct the weights of different particles, and normalize the corrected particle weights;

[0015] After resampling, based on the optimized Grubbs criterion, perform anomaly detection on the three-dimensional target tracking data, mark the sensors corresponding to the outliers as untrusted nodes, and mark the remaining sensors as trusted nodes;

[0016] Adopt an information entropy weighted strategy to fuse the data of trusted nodes, obtain the fused target state estimation value, and further achieve three-dimensional tracking of underwater targets.

[0017] Optionally, the process of constructing the target tracking model includes:

[0018] When the underwater target maintains a uniformly accelerated linear motion mode in both the horizontal and vertical directions in the three-dimensional underwater environment, obtain the product of the state transition matrix and the state vector at the current moment, and the product of the system perturbation matrix and the Gaussian random process noise at the current moment. Sum the two obtained products to obtain the state vector of the underwater target at the next moment, and then complete the construction of the target tracking model.

[0019] Optionally, the process of constructing the measurement model includes:

[0020] Based on the coordinate positions of the observation station sensors, obtain the distance between the underwater target and the observation station sensors at the current moment, the azimuth angle of the observation station sensors relative to the underwater target, and the elevation angle of the observation station sensors relative to the underwater target; based on the functional relationship between the distance between the underwater target and the observation station sensors at the current moment, the azimuth angle of the observation station sensors relative to the underwater target, the elevation angle of the observation station sensors relative to the underwater target, and the observation noise covariance matrix of the observation station sensors, complete the construction of the measurement model.

[0021] Optionally, based on the improved particle filter algorithm, as well as the target tracking model and the measurement model, the process of constructing the importance density function and resampling the particles includes:

[0022] In the initialization stage, collect particles from the prior distribution and initialize the particle weights;

[0023] At each moment, use the unscented Kalman filter for each particle to generate an updated particle state estimation value, and calculate the sigma point set using the unscented transform;

[0024] Propagate the sigma point set through the system state transition equation to predict the state mean and covariance;

[0025] Reconstruct the sigma point set according to the predicted state mean and covariance, substitute it into the measurement equation, obtain the predicted point set and mean, incorporate the latest observation value, and calculate the relevant covariance matrix and Kalman filter gain matrix of the particles;

[0026] Construct an importance density function based on the updated particle state estimation value and the relevant covariance matrix, and perform resampling.

[0027] Optionally, during the resampling process, the process of introducing a dynamic adaptive hierarchical weight factor to correct the weights of different particles includes:

[0028] In the resampling stage, divide the particle set into three weight levels: high, medium, and low, and introduce a dynamic adaptive hierarchical weight factor to correct the weights of particles in different levels.

[0029] Optionally, the process of performing outlier detection on three-dimensional target tracking data based on the optimized Grubbs criterion includes:

[0030] Calculate the global mean and total covariance matrix of the three-dimensional target tracking data; for each three-dimensional target tracking data, calculate the Mahalanobis distance; based on the mean and standard deviation of the Mahalanobis distance, calculate the maximum Mahalanobis distance and the statistic; use the significance level parameter and the corresponding critical value as thresholds to detect the statistic of the three-dimensional target tracking data. If the statistic is greater than the critical value, determine the corresponding sensor data as an outlier, and mark the sensor corresponding to the outlier as a non-trusted node. The outlier data and its non-trusted node do not participate in the subsequent data fusion.

[0031] Optionally, the process of fusing the data of trusted nodes using the information entropy weighting strategy to obtain the fused target state estimation value, and further realizing the three-dimensional tracking of underwater targets includes:

[0032] Set the fusion weight coefficient of the non-trusted node to zero; calculate the information entropy of the trusted node based on the size of the sensor noise covariance matrix; the weight fusion coefficients of the remaining trusted nodes are allocated according to the inverse principle of information entropy to calculate the fusion weight coefficients; perform weighted fusion on the data set of trusted nodes based on the fusion weight coefficients, and output the fused target state estimation value.

[0033] The present invention also proposes a computer device, including a memory, a processor, and a computer program stored on the memory, and the processor executes the computer program to implement the steps of the method.

[0034] The present invention also proposes a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the method.

[0035] The present invention also proposes a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the steps of the method.

[0036] Compared with the prior art, the present invention has the following advantages and technical effects:

[0037] Based on the technical means of constructing a target tracking model and a measurement model, and improving the particle filter algorithm using the unscented Kalman filter, the present invention achieves the technical effect of being able to more accurately construct the importance density function and perform particle resampling, thereby improving the accuracy and efficiency of the particle filter algorithm in underwater target tracking. At the same time, a dynamic adaptive hierarchical weight factor is introduced and normalized, further optimizing the particle weight distribution, enhancing particle diversity, effectively suppressing the phenomena of particle degradation and impoverishment, and further improving the tracking accuracy and algorithm stability. Based on the optimized Grubbs criterion for anomaly detection, abnormal data can be accurately identified and removed, and the sensors corresponding to the outliers are marked as untrusted nodes, thereby improving the reliability and accuracy of the data. Finally, an information entropy weighted strategy is used to fuse the data of trusted nodes, which can dynamically allocate weights according to the uncertainty of each sensor data, further improving the accuracy of the fused target state estimation value, and thus realizing high-precision and high-reliability three-dimensional underwater target tracking, effectively solving the problems of insufficient accuracy of the particle filter algorithm in underwater target tracking and limited ability to process abnormal data in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The drawings forming a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation of this application. In the drawings:

[0039] Figure 1 It is a schematic flowchart of the method of the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] It should be noted that, without conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The following will refer to the drawings and combine the embodiments to detail this application.

[0041] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a set of computer-executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0042] Embodiment 1

[0043] As Figure 1 shown, this embodiment provides a three-dimensional underwater target tracking method based on an improved particle filter, including the following steps:

[0044] Collect three-dimensional target tracking data of an underwater target based on the observation station sensors;

[0045] Construct a target tracking model and a measurement model according to the three-dimensional target tracking data;

[0046] Improve the particle filter algorithm based on the unscented Kalman filter. Based on the improved particle filter algorithm, as well as the target tracking model and measurement model, construct the importance density function and resample the particles.

[0047] During the resampling process, introduce a dynamic adaptive hierarchical weight factor to correct the weights of different particles, and normalize the corrected particle weights.

[0048] After resampling, perform outlier detection on the three-dimensional target tracking data based on the optimized Grubbs criterion, mark the sensors corresponding to the outliers as untrusted nodes, and mark the remaining sensors as trusted nodes.

[0049] Adopt an information entropy weighted strategy to fuse the data of trusted nodes, obtain the fused target state estimation value, and thus achieve three-dimensional tracking of underwater targets.

[0050] Implementable, the construction process of the target tracking model includes:

[0051] Assume that the target maintains a uniformly accelerated linear motion mode in both the horizontal and vertical directions in a three-dimensional underwater environment. Its dynamic motion equation can be described as:

[0052] X k+1 =F·X k +Q·W k ( )

[0053] Where X k+1 is the state vector of the target at time k, represented by the vector [x k ,y k ,z k ,v k,x ,v k,y ,v k,z ,a k,x ,a k,y ,a k,z T . x k , y k and z k respectively represent the positions of the target on the x-axis, y-axis, and z-axis at time k. v k,x , v k,y and v k,z respectively represent the velocities of the target on the x-axis, y-axis, and z-axis at time. a k,x , a k,y and a k,z respectively represent the accelerations of the target on the x-axis, y-axis, and z-axis at time k. W k represents the Gaussian random process noise of the system. F and Q represent the state transition matrix and the system perturbation matrix respectively.​

[0054] Implementable. The process of constructing the measurement model includes:

[0055] Assuming that the coordinate position of the observation station sensor is (xi s, yi s, zi s), the measurement model of the system at time k can be expressed as:

[0056] ( )

[0057] ( )

[0058] Where, The first line of the formula represents the distance between the sensor of the observation station at time k, and The second and third lines of the formula represent the azimuth angle and elevation angle of the observation station relative to the target at time k, respectively. v k Is the observation noise covariance matrix of the observation station sensor, and the process noise W k Is uncorrelated with the observation noise v k

[0059] Implementable. The implementation process of the standard particle filter algorithm includes:

[0060] As a typical probability estimation algorithm, the basic principle of particle filter is to use Monte Carlo simulation technology to achieve recursive state estimation of dynamic systems. In the estimation process, importance sampling and resampling techniques are used to gradually update the state and weight of the particles, so as to achieve accurate estimation of the state of the dynamic system. Its expression is:

[0061] x k = f(x k-1 , w k-1 )( )

[0062] z k = h(x k , v k )( )

[0063] Where, x k Is the state vector, f(·) represents the state transition function, w k Is the process noise of the system, z k Represents the measurement vector of the system, h(·) represents the measurement function of the system, and v k Is the measurement noise of the system.

[0064] Let the posterior probability density at k - 1 be , then The state prediction equation of the target at time is:​

[0065] ( )

[0066] The state update equation of the system is:

[0067] ( )

[0068] Then the posterior probability density function is:

[0069] ( )

[0070] Where, is the Dirac function, and wik is the weight of the i-th particle at time k.

[0071] Let the importance probability density function be , and the importance weight update formula is:

[0072] ( )

[0073] Normalize the weights, and its expression is:

[0074] ( )

[0075] Calculate the effective number of particles N eff , and its expression is:

[0076] ) ( )

[0077] Judge whether N eff < N thr holds. N thr is the set threshold. If it holds, resampling is performed to update the particle set {xi k}N i=1.

[0078] Output the node state estimation value, and its expression is:

[0079] ( )

[0080] The principle of the implementable and improved particle filter algorithm:

[0081] The standard particle filter has inherent defects in the importance sampling process, namely, the particle weight distribution shows skewness during the iterative process, causing the weights of a large number of particles to approach zero, while a small number of particles dominate the weight, resulting in the state estimation accuracy being severely dependent on a finite particle set. This phenomenon is called particle degeneracy. Traditional resampling strategies can temporarily alleviate the degeneracy problem by replicating high-weight particles, but they will trigger the secondary risk of particle diversity attenuation, that is, high-weight particles are repeatedly replicated, causing low-weight particles to be systematically eliminated, ultimately leading to the problem of particle impoverishment.

[0082] When constructing the importance sampling function for the standard particle filter algorithm, the prior probability model of the system state is usually directly selected as the proposal distribution, which easily leads to the sampling particles deviating from the true posterior probability distribution, thereby causing state estimation bias. To solve this problem, this embodiment introduces the unscented transformation mechanism of the unscented Kalman filter (UKF), and realizes the recursive optimization of the state mean and covariance matrix by fusing the latest measurement data, constructs a proposal distribution that is closer to the target distribution, and thus suppresses the particle degeneracy phenomenon. The specific implementation steps are as follows:

[0083] (1) In the initialization stage (k = 0), N particles {xi k}N i = 1 are sampled from the prior distribution p(x0). Calculate the mean of the particles and the error covariance , and initialize the particle weight wi 0 = 1 / N.

[0084] (2) At the k - 1 moment, for each particle xi k - 1, use UKF to generate the importance density function, and calculate 2n + 1 sigma point sets by using the unscented transformation. Its expression is:

[0085] ( )

[0086] where n is the dimension of the state vector, is the scaling parameter.

[0087] (3) Propagate the sigma points through the system state transition equation f(·), and calculate the predicted state mean and the predicted covariance . The specific expressions are:

[0088] ( )

[0089] ( )

[0090] where Q k is the process noise covariance, and wi j and wc j are weight coefficients.

[0091] (4) According to the predicted state mean and the predicted covariance re - construct the sigma - point set, substitute it into the system measurement equation, and obtain the predicted point set and the mean . Incorporate the latest observation value, calculate the autocovariance matrix of the particles, the cross - correlation covariance matrix and the Kalman filter gain matrix .

[0092] (5) Based on the particle state estimate value xi,k and the covariance matrix pi,k updated by UKF, construct an importance density function that follows a Gaussian distribution, and perform resampling.

[0093] During the resampling process, aiming at the problem of particle depletion caused by traditional resampling, in this embodiment, a dynamic adaptive hierarchical weight factor is introduced during the particle normalization weight process to correct the weights of different particles, improve the diversity of particle samples, effectively avoid the phenomenon of particle impoverishment, and ensure that the particle state distribution after resampling can cover the real system state.

[0094] The standard particle filter normalization weight formula is shown in Equation (10). Set the dynamic adaptive hierarchical weight factor as (0 < < 1), introduce in the particle normalization weight, then the corrected expression of the weight of the i - th particle at time k is:

[0095] ( )

[0096] The weight factor can be adjusted in real - time according to the number of effective particles. When the particle degradation is severe, it indicates that the number of effective particles is less, so the weight adjustment amplitude should be appropriately increased. When the particle degradation is mild, it indicates that the number of effective particles is more, and it should be kept relatively stable. The calculation formula is: <S

[0097] ( )

[0098] Among them, represents the maximum preset range of the weight drift factor, represents the minimum preset range of the weight drift factor, and the size of the number of effective particles is inversely proportional to the degree of particle degradation.

[0099] To more precisely correct the distribution characteristics of particles with different weights and refine weight regulation. In this embodiment, the particle set is divided into three levels: high, medium, and low according to the weight size, and different adjustment strategies are designed for each level. Specifically, first, the weights of all particles at the current moment are sorted in descending order, and then the levels are divided according to a preset threshold: the high-weight layer should suppress excessive replication and use a larger correction factor to reduce the weight ratio; the weights of the medium-weight layer particles are moderately corrected to maintain their stability; the weights of the low-weight layer particles need to be significantly increased due to insufficient sampling, and a smaller correction factor is used to enhance their representation ability in the state space. The expression formula is:

[0100] ( )

[0101] Among them, is the hierarchical adjustment coefficient, and dynamic weighting is performed according to the weight level to which the particles belong. The calculation formula for the updated normalized weight of the particles is:

[0102] ( )

[0103] Through the above dynamic weight transformation mechanism, the improved algorithm realizes the dynamic regulation of the particle weights: the weights of the low-weight particles are increased, effectively alleviating the phenomenon of marginal particle annihilation; the weights of the high-weight particles are suppressed, avoiding the over-dominance of the dominant particles in the posterior distribution; this strategy effectively enhances the diversity of the particle set and the completeness of the posterior estimation by adjusting the state space coverage density of particles at different levels.

[0104] Implementable, the process of weighted fusion based on the information entropy of the optimized Grubbs criterion includes:

[0105] Compared with neural network, expert inference, and artificial intelligence data fusion algorithms, the data weighted fusion algorithm has been widely used due to its advantages such as simple and efficient, no need for prior knowledge, and relatively high fusion accuracy. Traditional weighted fusion algorithms mainly include average weighted fusion algorithm, minimum variance weighted fusion algorithm, and least squares weighted fusion algorithm, etc. Among them, the average weighted fusion algorithm only evenly distributes weights according to the number of sensor nodes, completely ignoring the reliability differences of node information; the minimum variance weighted fusion algorithm dynamically adjusts the weight distribution through the noise variance, and nodes with smaller variances are given higher weights; the least squares weighted fusion algorithm determines the optimal weights with the optimization goal of minimizing the error between the observed data and the true value. Although the minimum variance and least squares weighted fusion algorithms can improve the rationality of weight distribution through noise variance or error optimization, their performance is still limited by the following core problems: both algorithms highly depend on the statistical characteristics of sensor data, and when there are outliers in the input data, the weight distribution is extremely likely to deviate from the theoretical optimal value.

[0106] Data analysis to optimize Grubbs's criterion:

[0107] Due to the complexity and variability of the underwater environment, it is easy for local nodes of the sensor to fail or generate abnormal data. Such failures will introduce significant deviations in the state estimation process, resulting in relatively obvious outliers, which directly affect the target tracking accuracy. In order to improve the robustness of data fusion, it is necessary to identify data in a timely manner and isolate the impact of faulty nodes. This embodiment uses the Grubbs criterion to realize abnormal data detection. Considering that the traditional Grubbs criterion can effectively detect univariate data anomalies, its standardized residual calculation method is difficult to adapt to the multidimensional data processing requirements of three-dimensional underwater target tracking scenarios, this embodiment combines the multidimensional data characteristics of three-dimensional underwater target tracking and introduces the Mahalanobis distance to replace the traditional standardized residual test method. By quantifying the statistical deviation degree of multidimensional data points from the overall distribution, anomaly discrimination is achieved, and the preprocessing requirement of original data sorting is avoided. Therefore, this embodiment uses the improved Grubbs criterion to perform anomaly verification on three-dimensional target tracking data.

[0108] Assume that in underwater target tracking, a set of target data measured by M sensors at time k is X1k, X2k, …, XMk, and its noise covariance matrix is R1k, R2k, …, RMk. The specific steps to remove abnormal data are as follows:

[0109] (1) Calculate the global mean of the measurement data and the total covariance matrix The specific expression is:

[0110] ( )

[0111] ( )

[0112] (2) For each measurement data , calculate its Mahalanobis distance The specific expression is:

[0113] ( )

[0114] in, is the inverse of the noise covariance matrix.

[0115] (3) Calculate the mean of Mahalanobis distance and its standard deviation The calculation formula is:

[0116] ( )

[0117] ( )

[0118] (4) Calculate the maximum Mahalanobis distance D max and the statistic G k . The expression is:

[0119] ( )

[0120] ( )

[0121] (5) Using as the significance level parameter and its corresponding critical value G c , detect the G k of the measurement data. If G k > G c , determine that the corresponding sensor data Xi k is an outlier. Based on the verified data type, establish a sensor node trust mechanism, divide it into trust and non-trust estimates according to the test results, mark the sensors corresponding to the abnormal data as non-trusted nodes, and the abnormal data and its non-trusted nodes do not participate in the subsequent data fusion of the sensors.

[0122] (6) Eliminate the abnormal data and retain the data of the trusted nodes, and update the relevant measurement data set .

[0123] Further, the process of information entropy weighted data fusion includes:

[0124] Information entropy, also known as Shannon entropy, is a quantitative measure of the uncertainty of a system. The higher the entropy value of the system, the greater the degree of information chaos, and vice versa, it indicates stronger certainty. Therefore, in the field of multi-sensor data fusion, using information entropy to measure the uncertainty of sensor data and enhance the robustness of the fusion system has significant advantages. In this embodiment, a multi-dimensional continuous distribution information entropy is used to construct a noise uncertainty measurement model, which can effectively characterize the coupling correlation characteristics of multi-dimensional parameters and accurately quantify the interference intensity of heteroscedastic noise on state estimation, so as to allocate appropriate weight fusion coefficients for sensor nodes. The analytical expression of its entropy is:

[0125] ( )

[0126] where H i represents the information entropy of the i-th sensor, n is the dimension of the state vector. In this embodiment, the dimension of the vector is three, corresponding to the three-axis parameters of position, velocity, and acceleration respectively. R i represents the noise covariance matrix of the i-th sensor, det(Ri ) represents the determinant value of the covariance matrix.

[0127] During the target tracking process, there is a significant correlation between the sensor noise interference intensity and the uncertainty of its measurement data: when the noise interference increases, the determinant value det(R of the sensor covariance matrix i ) increases accordingly, which in turn leads to an increase in the information entropy. Conversely, when the system stability is improved, det(R i ) and the information entropy decrease synchronously. Based on this, in this embodiment, the weight fusion coefficient a is constructed to have a negative correlation with the information entropy. By dynamically adjusting the fusion weight ratio of each sensor node, the contribution degree of high-noise nodes can be adaptively suppressed, thereby reducing the sensitivity of the fusion result to uncertain factors and effectively improving the accuracy of multi-source data fusion. The specific steps are as follows:

[0128] (1) Check the trusted node status of each sensor. If a node is identified as a non-trusted node, its fusion weight coefficient is set to zero and does not participate in subsequent fusion calculations.

[0129] (2) Calculate the information entropy based on the size of the sensor noise covariance matrix, and the formula is shown in Equation (27).

[0130] (3) Assume that n abnormal nodes are detected, and the weight fusion coefficient allocation of the remaining M - n trusted nodes follows the inverse information entropy principle: the smaller the information entropy, the larger the corresponding weight fusion coefficient a i ; conversely, the smaller the weight coefficient. Its expression is:

[0131] ([[]] )

[0132] (4) According to the fusion weight coefficient calculated above, perform weighted fusion on the data set of trusted nodes and finally output the fused target state estimation value . Its output formula is:

[0133] ([[]] )

[0134] Feasible, experimental results and analysis:

[0135] In this embodiment, based on the MATLAB R2023b simulation platform, the proposed OGIE-IPF algorithm is verified for target tracking performance, and comparative experiments are carried out with traditional PF, EPF, and UPF under different data conditions. The Root Mean Square Error (RMSE) is selected as the core evaluation index for tracking accuracy, and its formula is as follows:

[0136] ( )

[0137] Among them, Mt represents the number of simulation times of the Monte Carlo experiment, and respectively represent the true three-dimensional position coordinates of the target at time k and the estimated position coordinates of the algorithm.

[0138] Simulation parameter settings:

[0139] In this experiment, the underwater target tracking area is set as a three-dimensional cube space of 1000×1000×1000 m 3 , and four stationary observation station sensors are arranged in this area. Let the positions of the four observation station sensors be: S1(0, 0, 0), S2(100, 800, 0), S3(600, 0, 0), S4(700, 700, 0). The spatial position coordinate system of the sensor nodes remains static and stable, and the interference of node drift error on system modeling is not considered. The simulation experiment parameters are as shown. The target tracking simulation scenario specifically includes the spatial distribution of the observation station nodes, the true motion trajectory of the target, and the original sensor observation trajectory without being processed by the filtering algorithm.

[0140] Table 1

[0141]

[0142] Comparison of particle weight distributions before and after optimization:

[0143] To verify the effectiveness of the improved particle filter algorithm in suppressing particle degradation and sample impoverishment phenomena and enhancing particle diversity, this experiment designed two groups of comparative experiments based on the setting that the number of particles is fixed at 100. By analyzing the differences in key indicators such as the weight distribution characteristics, the change of weight distribution variance, and the proportion of high- and low-weight particles of PF and IPF, the optimization effect of the algorithm was quantitatively evaluated.

[0144] The results show that in the PF algorithm, the proportion of low-weight particles with weights less than 0.01 is about 61%, while the proportion of high-weight particles with weights greater than 0.02 is only about 8%. The particle weight distribution shows significant polarization, indicating that there is a serious risk of particle set degradation, which directly affects the state estimation accuracy. In contrast, IPF effectively increases the weights of low-weight particles through a dynamic adaptive weight hierarchical optimization strategy, and at the same time moderately attenuates the weights of high-weight particles, making the distribution of different weight layers tend to be balanced. Experimental analysis shows that the weight distribution variance of IPF at this moment is reduced by about 98.27% compared with PF.

[0145] To further evaluate the time stability of the algorithm, the weight distribution characteristics of all particles of the two algorithms within the time span T = 50 were further compared. The results show that in the PF algorithm, the proportion of particles with low weights is relatively large, while only a small part of the particles have high weights. This non-uniform distribution will seriously affect the decision-making quality of the resampling process. On the contrary, the weight distribution of the IPF algorithm shows significant homogenization characteristics, effectively suppressing the extreme differentiation of weight differences. Statistical results show that the variance of the particle weight distribution of IPF is reduced by about 97.26% compared with PF during the whole period. The significant decrease in the weight dispersion indicates that the particle diversity has been systematically improved.

[0146] The above experimental results show that the proposed UKF-based proposal distribution and adaptive hierarchical weight optimization mechanism in this embodiment can maintain the dynamic balance of particle weights, avoid the particle depletion phenomenon caused by the excessive replication of a small number of high-weight particles in the later stage of iteration, significantly improve the sampling diversity of the particle set, and ensure the spatial coverage integrity of the posterior probability estimation.

[0147] The influence of the data fusion algorithm on the target tracking accuracy:

[0148] To verify the robustness of different weighted fusion algorithms in an abnormal noise environment, this experiment analyzes the performance by setting the sensor observation noise to be significantly abnormal, and compares the performance differences of four fusion algorithms under the IPF framework. The specific comparison algorithms include: the optimized Grubbs information entropy weighted fusion algorithm (Optimized Grubbs Information Entropy Weighted Fusion, OGIEWF), the traditional average weighted fusion algorithm (Weighted Average Fusion, WAF), the minimum variance weighted fusion algorithm (Minimum Variance Weighted Fusion, MVWF), and the standard information entropy weighted fusion algorithm (Information Entropy Weighted Fusion, IEWF). In this experiment, the noise covariance of the sensors at the four observation stations are set as: R1 = 36, R2 = 0.81, R3 = 25, R4 = 1.69. Among them, the noise levels of R1 and R3 are significantly higher, which are used to simulate the states under abnormal sensors.

[0149] Comparing the tracking trajectories, it can be seen that in the case of sensor anomalies, the tracking trajectory of IEWF is closer to the true state than those of WAF and MVWF, and the tracking accuracy of OGIEWF is further superior to that of IEWF. The temporal characteristics of RMSE during target tracking are as follows: in the initial stage, the RMSE differences of the four algorithms are small; as time goes by, the RMSE of WAF and MVWF increases significantly, the increase of IEWF is relatively slow, while OGIEWF always maintains a low RMSE level. The average RMSE of the X, Y, and Z axes was compared, and the results show that the error difference in the Z-axis direction is the most significant. The average RMSE of OGIEWF is the lowest on all three axes, and the peak Z-axis error is only 16.1% of WAF and 25.6% of MVWF. Comprehensive data analysis shows that the average RMSE of OGIEWF on the three axes is approximately 25.2%, 29.1%, and 49.1% of WAF, MVWF, and IEWF, respectively. And during the entire period T, the average RMSE of OGIEWF is reduced by 75.27%, 69.59%, and 48.25% compared with WAF, MVWF, and IEWF, respectively. The above experiments show that OGIEWF effectively suppresses the interference of abnormal noise through the strategy of dynamically allocating weight fusion coefficients and the Grubbs anomaly detection mechanism based on Mahalanobis distance, verifying the robustness and effectiveness of the OGIEWF algorithm in an abnormal noise environment.

[0150] Effect of observation noise variance on underwater target tracking accuracy:

[0151] To study the tracking performance of different filtering algorithms in different underwater noise environments, in this embodiment, comparative experiments are carried out by adjusting the level of the observation noise variance. The experiment is divided into two noise scenarios: in the low-noise scenario, the noise covariance of the observation station is R1 = 1, R2 = 0.64, R3 = 1.44, R4 = 1.21; in the high-noise scenario, the noise covariance is adjusted to R1 = 16, R2 = 21.16, R3 = 17.64, R4 = 14.44 respectively. In this embodiment, the information entropy weighted fusion algorithm based on the optimized Grubbs criterion is uniformly used to analyze the target tracking performance of IPF, PF, EPF, and UPF respectively. The experimental results show that the tracking effect of IPF is better than that of PF, EPF, and UPF in both low-noise and high-noise cases. Especially in the high-noise scenario in the later stage of target tracking, the trajectory of IPF fits the true state best, while the PF algorithm shows obvious deviation. Further analysis of the root mean square error shows that: in the initial stage of target tracking, the RMSE of the four filtering algorithms has little difference; as time goes by, especially in the middle and later stages of target turning, the RMSE of the PF algorithm fluctuates violently, and the maximum increase at a certain moment reaches 45.64%, while the RMSE of IPF remains relatively low and stable throughout the process. In the low-noise environment, the average RMSE of PF, EPF, UPF, and IPF within the entire time T are 14.29m, 8.70m, 6.63m, and 2.89m respectively. The RMSE of IPF is reduced by 79.78%, 66.78%, and 56.41% compared with PF, EPF, and UPF respectively; in the high-noise environment, the average RMSE of PF, EPF, UPF, and IPF within time T are 24.17m, 13.54m, 5.12m, and 4.01m respectively. The RMSE of IPF is reduced by approximately 83.41%, 70.38%, and 21.68% compared with PF, EPF, and UPF respectively, and the fluctuation amplitude of IPF is approximately 17.02%, 30.6, 1%, and 57.46% of that of PF, EPF, and UPF respectively.

[0152] The comprehensive experimental results show that the OGIE-IPF algorithm proposed in this embodiment exhibits stable tracking performance under different noise conditions, verifying the robustness of the improved filtering algorithm to complex noise environments.

[0153] Stability and real-time performance of the algorithm:

[0154] By It can be seen that under the condition of the same number of particles, the root mean square error of the average position of OGIE-IPF is significantly lower than that of the PF algorithm, but its single-step running time is relatively high. This is because the OGIE-IPF algorithm introduces UKF as the importance density function, the dynamic adaptive weight correction mechanism, the abnormal data detection mechanism, and the information entropy fusion coefficient determination process, resulting in an increase in computational complexity. Although the computational complexity is increased, the tracking accuracy is significantly improved. Compared with the UPF algorithm with lower error, the increase in the average single-step running time of OGIE-IPF is smaller, but the decrease in RMSE is significant, indicating that its accuracy improvement efficiency is higher. Further comparing the performance of PF and OGIE-IPF under different numbers of particles, it can be seen that as the number of particles increases from 200 to 400, the average RMSE of both algorithms shows a downward trend, but the change range of the average RMSE of the improved filtering algorithm is relatively small, indicating that the increase in the number of particles has limited improvement on the tracking accuracy of the OGIE-IPF algorithm and will instead increase the computational time. To sum up, the OGIE-IPF algorithm can maintain a high target tracking accuracy under a lower number of particles compared with traditional filtering algorithms, and does not significantly increase the time complexity. Therefore, the comprehensive performance of the OGIE-IPF algorithm is better than that of traditional filtering methods.

[0155] Table 2

[0156]

[0157] To explore the influence of different noise variances R and the number of particles N on the algorithm performance, in this experiment, a low noise variance R i was defined, and the sampling time was increased to 300 s. When the number of particles of the PF algorithm was 300 or 400, and the noise was R i or 4R i , the PF algorithm would diverge in the later stage of iteration, but the divergence time would be postponed for some time. When the number of particles was the same but the noise variance increased from R i to 4R i , the divergence degree of the PF algorithm increased significantly. In contrast, the OGIE-IPF algorithm always maintained a stable low error level under different noise and particle number conditions. The above experiments show that OGIE-IPF effectively balances the computational efficiency and tracking accuracy, and has strong stability while ensuring real-time performance.

[0158] In summary, aiming at the problem of poor target tracking accuracy of traditional particle filtering algorithms in complex underwater conditions, this embodiment proposes an information entropy weighted data fusion method and an improved particle filtering algorithm based on the optimized Grubbs criterion. The algorithm improves the target tracking accuracy through the following steps: First, the UKF is introduced to construct the importance density function, and the posterior distribution of the nonlinear system state is accurately approximated through the unscented transformation, effectively improving the state estimation accuracy; Second, a dynamic adaptive hierarchical weight optimization mechanism is designed to suppress the particle depletion phenomenon through hierarchical correction of the weights; In addition, the Grubbs criterion is improved based on the Mahalanobis distance to realize the anomaly detection of multi-dimensional state data and the screening of credible nodes; Finally, combined with the information entropy dynamic weighted fusion strategy, the node weight fusion coefficient is adaptively allocated to generate a high-precision global state estimation. The simulation results show that compared with the traditional PF, EPF, and UPF algorithms, the OGIE-IPF algorithm proposed in this embodiment has a tracking result that is more consistent with the true state estimation of the target, a lower root mean square error, and still maintains stable tracking performance in the scenarios of limited number of particles and abnormal noise.

[0159] Embodiment 2

[0160] This embodiment also discloses a computer device, including a memory, a processor, and a computer program stored on the memory. The processor executes the computer program to implement the steps of the method described in Embodiment 1.

[0161] Embodiment 3

[0162] This embodiment also discloses a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the method described in Embodiment 1.

[0163] Embodiment 4

[0164] This embodiment also discloses a computer program product, including a computer program. When the computer program is executed by a processor, it implements the steps of the method described in Embodiment 1.

[0165] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed in the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A three-dimensional underwater target tracking method based on improved particle filter, characterized in that It includes the following steps: Collect three-dimensional target tracking data of underwater targets based on the sensors of the observation station; Construct a target tracking model and a measurement model according to the three-dimensional target tracking data; Improve the particle filter algorithm based on the unscented Kalman filter. Based on the improved particle filter algorithm, the target tracking model and the measurement model, construct an importance density function and resample the particles; During the resampling process, introduce a dynamic adaptive hierarchical weight factor to correct the weights of different particles, and normalize the corrected particle weights; After resampling, perform anomaly detection on the three-dimensional target tracking data based on the optimized Grubbs criterion, mark the sensors corresponding to the outliers as untrusted nodes, and mark the remaining sensors as trusted nodes; Adopt an information entropy weighted strategy to fuse the data of trusted nodes, obtain the fused target state estimation value, and thus achieve three-dimensional tracking of underwater targets.

2. The method according to claim 1, wherein The process of constructing the target tracking model includes: When the underwater target maintains a uniformly accelerated linear motion mode in both the horizontal and vertical directions in the three-dimensional underwater environment, obtain the product of the state transition matrix and the state vector at the current moment and the product of the system perturbation matrix and the Gaussian random process noise at the current moment, sum the two obtained products, obtain the state vector of the underwater target at the next moment, and thus complete the construction of the target tracking model.

3. The method according to claim 1, wherein The process of constructing the measurement model includes: Based on the coordinate positions of the sensors of the observation station, obtain the distance between the underwater target and the sensors of the observation station at the current moment, the azimuth angle of the sensors of the observation station relative to the underwater target, and the pitch angle of the sensors of the observation station relative to the underwater target; based on the functional relationship between the distance between the underwater target and the sensors of the observation station at the current moment, the azimuth angle of the sensors of the observation station relative to the underwater target, the pitch angle of the sensors of the observation station relative to the underwater target, and the observation noise covariance matrix of the sensors of the observation station, complete the construction of the measurement model.

4. The method according to claim 1, wherein The process of constructing the importance density function and resampling the particles based on the improved particle filter algorithm, the target tracking model and the measurement model includes: In the initialization stage, collect particles from the prior distribution and initialize the particle weights; At each moment, use the unscented Kalman filter to generate an updated particle state estimation value for each particle, and calculate the sigma point set using the unscented transform; Propagate the sigma point set through the system state transition equation to predict the state mean and covariance; Reconstruct the sigma point set according to the predicted state mean and covariance, substitute it into the measurement equation, obtain the predicted point set and mean, incorporate the latest observation value, and calculate the relevant covariance matrix and Kalman filter gain matrix of the particles; Construct an importance density function based on the updated particle state estimation value and the relevant covariance matrix, and perform resampling.

5. The method according to claim 4, wherein During the resampling process, the process of introducing a dynamic adaptive hierarchical weight factor to correct the weights of different particles includes: In the resampling stage, the particle set is divided into three weight levels: high, medium, and low, and a dynamic adaptive hierarchical weight factor is introduced to correct the weights of particles at different levels.

6. The method according to claim 1, wherein The process of performing anomaly detection on three-dimensional target tracking data based on the optimized Grubbs criterion includes: Calculating the global mean and total covariance matrix of the three-dimensional target tracking data; for each three-dimensional target tracking data, calculating the Mahalanobis distance; based on the mean and standard deviation of the Mahalanobis distance, calculating the maximum Mahalanobis distance and statistic; using the significance level parameter and the corresponding critical value as thresholds to detect the statistic of the three-dimensional target tracking data. If the statistic is greater than the critical value, the corresponding sensor data is determined to be an outlier, and the sensor corresponding to the outlier is marked as a non-trusted node. The outlier data and its non-trusted node do not participate in subsequent data fusion.

7. The method according to claim 6, wherein The process of using the information entropy weighting strategy to fuse the data of trusted nodes to obtain the fused target state estimation value and further achieve three-dimensional tracking of underwater targets includes: Setting the fusion weight coefficient of non-trusted nodes to zero; calculating the information entropy of trusted nodes based on the size of the sensor noise covariance matrix; the weight fusion coefficients of the remaining trusted nodes are assigned according to the inverse principle of information entropy to calculate the fusion weight coefficients; performing weighted fusion on the data sets of trusted nodes based on the fusion weight coefficients to output the fused target state estimation value.

8. A computer device, comprising a memory, a processor, and a computer program stored on the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1-7.

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