A three-dimensional underwater target tracking method based on improved particle filter

Abstract

The present invention discloses a three-dimensional underwater target tracking method based on an improved particle filter, belonging to the technical field of underwater wireless sensor networks. The method comprises the following steps: collecting three-dimensional target tracking data of an underwater target; constructing a target tracking model and a measurement model based on the three-dimensional target tracking data; improving the particle filter algorithm based on an unscented Kalman filter, constructing an importance density function based on the improved particle filter algorithm, the target tracking model, and the measurement model, and resampling the particles; introducing a dynamic adaptive hierarchical weighting factor to correct the weights of different particles, and normalizing 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 trusted nodes using an information entropy weighting strategy to obtain a fused target state estimate, thereby achieving three-dimensional tracking of the underwater target. The present invention can achieve high-precision and high-reliability three-dimensional underwater target tracking.

Description

Technical Field

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

[0002] As the strategic importance of marine resource development becomes increasingly prominent, underwater wireless sensor networks (UWSNs) are widely used in the marine field. UWSN target tracking technology is one of the core technologies for achieving marine resource detection, target reconnaissance, and underwater attack and defense.

[0003] Target tracking is a key technology in UWSNs. Traditional target tracking algorithms primarily include the Kalman filter (KF) and its extensions, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). These algorithms perform well when dealing with linear Gaussian noise systems, but their state estimation accuracy significantly degrades when faced with strongly nonlinear underwater dynamics and coupled non-Gaussian noise. In contrast, the particle filter (PF), through its nonparametric Monte Carlo sampling mechanism, can effectively characterize the posterior probability distribution of nonlinear, non-Gaussian systems, demonstrating significant advantages in the field of underwater target tracking in UWSNs.

[0004] However, in practical applications, especially in underwater target positioning and tracking, standard particle filter algorithms often suffer from particle degradation and particle depletion problems, which seriously affect the accuracy of underwater target tracking. To address these problems, existing studies have proposed a variety of improvement schemes, such as improving particle diversity by optimizing the importance density function and designing adaptive resampling strategies. For example, Ran Xinghao et al. generated the importance density function by taking the square root of the covariance matrix in the second-order central difference filter, and combined it 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 particle depletion phenomenon. In addition, Zhang Hongwei et al. generated the proposed distribution of the particle filter through UKF based on a dual-observatory architecture, and used the unscented transformation 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 combined it with a mutual information entropy weighted fusion strategy to improve distributed particle filtering. Zhu Hongbo et al. designed a distributed filtering framework that uses a K-medoids trust mechanism to filter local state estimation data and employs a diffusion fusion strategy to dynamically update state estimates, improving the robustness of the system.

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

[0007] Existing resampling-based weight optimization strategies often use fixed weighting factors, making them difficult to dynamically respond to changes in particle degradation and actual conditions, and lacking adaptability. Existing anomaly data detection methods, when processing multidimensional state estimation data, fail to effectively balance data coupling and heteroscedasticity across different dimensions, making it difficult to simultaneously ensure anomaly determination accuracy and dimensional compatibility.

[0008] In view of the problems existing in the existing technology, it is urgent to propose a three-dimensional underwater target tracking method based on improved particle filtering. Summary of the Invention

[0009] To solve the above technical problems, the present invention provides a three-dimensional underwater target tracking method based on an improved particle filter. First, an importance density function is constructed, and the particle filter algorithm is improved in combination with a dynamic adaptive hierarchical weight optimization mechanism to achieve high-precision estimation of the target state. Secondly, anomaly detection is performed on multidimensional state parameters such as target position and velocity by introducing the Grubbs criterion based on Mahalanobis distance, and a node trust mechanism is constructed to screen high-reliability data sources. Finally, a weighted fusion strategy based on information entropy is designed for the trusted node set, and the reliability of the node data is quantified by the entropy value, thereby achieving target tracking in complex underwater conditions.

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

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

[0012] constructing a target tracking model and a measurement model based on the three-dimensional target tracking data;

[0013] The particle filter algorithm is improved based on the unscented Kalman filter. Based on the improved particle filter algorithm, target tracking model and measurement model, the importance density function is constructed and the particles are resampled.

[0014] During the resampling process, a dynamic adaptive layered weight factor is introduced to correct the weights of different particles, and the corrected particle weights are normalized;

[0015] After resampling is completed, anomaly detection is performed on the 3D target tracking data based on the optimized Grubbs criterion. The sensors corresponding to the outliers are marked as untrusted nodes, and the remaining sensors are marked as trusted nodes.

[0016] The information entropy weighted strategy is used to fuse the data of the trust nodes to obtain the fused target state estimate, thereby realizing three-dimensional tracking of underwater targets.

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

[0018] When an underwater target maintains a uniformly accelerated linear motion mode in both the horizontal and vertical directions in a three-dimensional underwater environment, the product of the state transfer matrix and the state vector at the current moment, as well as the product of the system disturbance matrix and the Gaussian random process noise at the current moment, are obtained. The two products are summed to obtain the state vector of the underwater target at the next moment, thereby completing the construction of the target tracking model.

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

[0020] Based on the coordinate position of the observation station sensor, the distance between the underwater target and the observation station sensor at the current moment, the azimuth of the observation station sensor relative to the underwater target, and the pitch angle of the observation station sensor relative to the underwater target are obtained; based on the functional relationship between the distance between the underwater target and the observation station sensor at the current moment, the azimuth of the observation station sensor relative to the underwater target, the pitch angle of the observation station sensor relative to the underwater target and the observation noise covariance matrix of the observation station sensor, the measurement model is constructed.

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

[0022] In the initialization phase, particles are collected from the prior distribution and the particle weights are initialized;

[0023] At each moment, an unscented Kalman filter is used to generate an updated particle state estimate for each particle, and the sigma point set is calculated using an 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 based on the predicted state mean and covariance, and substitute it into the measurement equation to obtain the predicted point set and mean, incorporate the latest observations, and calculate the particle's related covariance matrix and Kalman filter gain matrix;

[0026] An importance density function is constructed based on the updated particle state estimates and the associated covariance matrix, and resampling is performed.

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

[0028] In the resampling stage, the particle set is divided into three weight levels: high, medium, and low. A dynamic adaptive hierarchical weight factor is introduced to correct the weights of particles at different levels.

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

[0030] Calculate the global mean and total covariance matrix of 3D target tracking data; calculate the Mahalanobis distance for each 3D target tracking data; calculate the maximum Mahalanobis distance and statistic based on the mean and standard deviation of the Mahalanobis distance; use the significance level parameter and the corresponding critical value as the threshold to test the statistics of the 3D target tracking data. If the statistic is greater than the critical value, the corresponding sensor data is judged as an outlier, and the sensor corresponding to the outlier is marked as an untrusted node. The outlier data and its untrusted nodes do not participate in subsequent data fusion.

[0031] Optionally, the process of fusing the data of the trust nodes using an information entropy weighting strategy to obtain a fused target state estimate, thereby achieving three-dimensional tracking of the underwater target includes:

[0032] The fusion weight coefficients of non-trusted nodes are set to zero; the information entropy of the trusted nodes is calculated based on the size of the sensor noise covariance matrix; the weight fusion coefficients of the remaining trusted nodes are distributed according to the inverse principle of information entropy, and the fusion weight coefficients are calculated; the data sets of the trusted nodes are weightedly fused based on the fusion weight coefficients, and the fused target state estimate is output.

[0033] The present invention also provides a computer device, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0034] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method when executed by a processor.

[0035] The present invention also provides a computer program product, comprising a computer program, which implements the steps of the method when executed by a processor.

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

[0037] The present invention is based on the technical means of constructing a target tracking model and a measurement model, and using an unscented Kalman filter to improve the particle filter algorithm. It achieves the technical effect of being able to more accurately construct an 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, the introduction of a dynamic adaptive hierarchical weight factor and normalization processing further optimizes the particle weight distribution, enhances particle diversity, effectively suppresses particle degradation and impoverishment, and further improves the tracking accuracy and algorithm stability. Anomaly detection based on the optimized Grubbs criterion can accurately identify and eliminate abnormal data, and mark the sensors corresponding to the abnormal values ​​as untrusted nodes, thereby improving the reliability and accuracy of the data. Finally, an information entropy weighting strategy is adopted to fuse the data of trusted nodes. It can dynamically assign weights according to the uncertainty of each sensor data, further improving the accuracy of the fused target state estimate, thereby achieving high-precision and high-reliability three-dimensional tracking of underwater targets, effectively solving the problems of insufficient accuracy and limited abnormal data processing capabilities of the particle filter algorithm in the prior art when tracking underwater targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0039] Figure 1 Schematic diagram of a method flow in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

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

[0042] Example 1

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

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

[0045] constructing a target tracking model and a measurement model based on the three-dimensional target tracking data;

[0046] The particle filter algorithm is improved based on the unscented Kalman filter. Based on the improved particle filter algorithm, target tracking model and measurement model, the importance density function is constructed and the particles are resampled.

[0047] During the resampling process, a dynamic adaptive layered weight factor is introduced to correct the weights of different particles, and the corrected particle weights are normalized;

[0048] After resampling is completed, anomaly detection is performed on the 3D target tracking data based on the optimized Grubbs criterion. The sensors corresponding to the outliers are marked as untrusted nodes, and the remaining sensors are marked as trusted nodes.

[0049] The information entropy weighted strategy is used to fuse the data of the trust nodes to obtain the fused target state estimate, thereby realizing three-dimensional tracking of underwater targets.

[0050] The process of building a feasible target tracking model includes:

[0051] Assuming 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] Among them, X k+1 is the state vector of the target at time k, expressed as [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 They represent the x-axis, y-axis, and z-axis positions of the target at time k, respectively. k,x 、v k,y and v k,z Respectively indicate the target The x-axis, y-axis and z-axis speeds at the moment, a k,x 、a k,y and a k,z W represents the acceleration of the target on the x-axis, y-axis and z-axis at time k. k represents the Gaussian random process noise of the system, F and Q represent the state transfer matrix and the system disturbance matrix respectively.

[0054] The feasible process of building a 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] in, The first line of the formula represents the distance between the k-th moment and the observation station sensor, and The second and third lines of formulas respectively represent the azimuth and elevation angles of the observation station relative to the target at time k, v k is the observation noise covariance matrix of the observation station sensor, and the process noise W k With the observation noise v k Not related to each other.

[0059] The implementation process of the standard particle filter algorithm that can be implemented includes:

[0060] As a typical probability estimation algorithm, the particle filter's basic principle is to use Monte Carlo simulation technology to achieve recursive state estimation of dynamic systems. During the estimation process, importance sampling and resampling techniques are used to gradually update the state and weight of particles, thereby achieving an 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] Among them, x k is the state vector, f(·) represents the state transfer 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, v k is the measurement noise of the system.

[0064] Assume that the posterior probability density of k-1 is ,but The state prediction equation of the target at a moment is:

[0065] ( )

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

[0067] ( )

[0068] Then the posterior probability density function is:

[0069] ( )

[0070] in, is the Dirac function, wi k is the weight of the i-th particle at time k.

[0071] Assume the importance probability density function is , the importance weight update formula is:

[0072] ( )

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

[0074] ( )

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

[0076] ( )

[0077] Judge N eff <N thr Is it established? N thr is the set threshold. If it holds, resampling is performed and the particle set {xi k}N i=1 is updated.

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

[0079] ( )

[0080] Principle of the implemented, improved particle filter algorithm:

[0081] Standard particle filters have inherent flaws in the importance sampling process. During the iteration process, the distribution of particle weights becomes skewed, causing a large number of particle weights to approach zero while a small number of particles dominate. This leads to a critical dependence of state estimation accuracy on a finite set of particles, a phenomenon known as particle degeneration. Traditional resampling strategies can temporarily alleviate this degeneration problem by replicating high-weight particles, but this carries the secondary risk of diminishing particle diversity. This is because repeated replication of high-weight particles systematically eliminates low-weight particles, ultimately leading to particle depletion.

[0082] When constructing the importance sampling function, the standard particle filter algorithm typically directly selects the prior probability model of the system state as the proposed distribution, which can easily cause the sampled particles to deviate from the true posterior probability distribution, thereby causing state estimation bias. To address this issue, this embodiment introduces the unscented transformation mechanism of the unscented Kalman filter (UKF). By integrating the latest measurement data, it performs recursive optimization of the state mean and covariance matrix, constructing a proposed distribution that is closer to the target distribution, thereby suppressing particle degradation. The specific implementation steps are as follows:

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

[0084] (2) At time k-1, the importance density function is generated for each particle xi k-1 using UKF, and 2n+1 sigma point sets are calculated using 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 point through the system state transfer equation f(·) and calculate the predicted state mean and the predicted covariance The specific expression is:

[0088] ( )

[0089] ( )

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

[0091] (4) According to the predicted state mean and the predicted covariance Reconstruct the sigma point set and substitute it into the system measurement equation to obtain the prediction point set and mean Incorporate the latest observations and calculate the particle autocovariance matrix , cross-correlation covariance matrix and the Kalman filter gain matrix .

[0092] (5) Based on the particle state estimate xi k and covariance matrix pi k after UKF update, the importance density function that obeys the Gaussian distribution is constructed , and perform resampling.

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

[0094] The standard particle filter normalized weight formula is shown in formula (10), and the dynamic adaptive layered weight factor is set to (0< <1), introduced in the particle normalization weight , then the modified 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 serious, it means that the number of effective particles is small, and the weight adjustment range should be appropriately increased. When the particle degradation is light, it means that the number of effective particles is large, and it should be kept relatively stable. The calculation formula is:

[0097] ( )

[0098] in, Indicates the maximum preset range of the weight drift factor, Indicates the minimum preset range of the weight drift factor, the number of effective particles The size is inversely proportional to the degree of particle degradation.

[0099] In order to more accurately correct the distribution characteristics of particles with different weights and refine the weight control. This embodiment divides the particle set into three levels: high, medium, and low according to the size of the weight, and designs differentiated adjustment strategies for each level. Specifically, first, all particle weights at the current moment are sorted in descending order, and then the levels are divided according to the 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 particles in the medium-weight layer are moderately corrected to maintain their stability; the particles in the low-weight layer need to significantly increase their weight ratio due to insufficient sampling, and a smaller correction factor is used to enhance their representation ability in the state space. Its expression formula is:

[0100] ( )

[0101] in, is the stratification adjustment coefficient, Dynamically assign weights based on the weight level to which the particles belong. The updated particle normalized weight calculation formula is:

[0102] ( )

[0103] Through the above-mentioned dynamic weight transformation mechanism, the improved algorithm realizes dynamic regulation of particle weights: the weights of low-weight particles can be increased, effectively alleviating the annihilation of edge particles; the weights of high-weight particles are suppressed to prevent dominant particles from excessively dominating the posterior distribution; this strategy effectively enhances the diversity of the particle set and the completeness of the posterior estimate by adjusting the state space coverage density of particles at different levels.

[0104] The feasible process of weighted fusion based on information entropy optimization of Grubbs criterion includes:

[0105] Compared to neural network, expert reasoning, and artificial intelligence-based data fusion algorithms, weighted data fusion algorithms have been widely used due to their simplicity, efficiency, lack of prior knowledge, and high fusion accuracy. Traditional weighted fusion algorithms mainly include average weighted fusion, minimum variance weighted fusion, and least squares weighted fusion. The average weighted fusion algorithm simply distributes weights equally based on the number of sensor nodes, completely ignoring the differences in node information reliability. The minimum variance weighted fusion algorithm dynamically adjusts weight distribution based on noise variance, assigning higher weights to nodes with smaller variances. The least squares weighted fusion algorithm determines the optimal weights by minimizing the error between observed data and true values. Although the minimum variance and least squares weighted fusion algorithms can improve the rationality of weight distribution by optimizing noise variance or error, their performance is still limited by the following core issues: both algorithms rely heavily on the statistical characteristics of sensor data. When outliers are present in the input data, the weight distribution can easily 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 statistic G k The expression is:

[0119] ( )

[0120] ( )

[0121] (5) is the significance level parameter and its corresponding critical value G c , for the measured data G k Perform the test, if G k >G c , the corresponding sensor data Xi k is determined to be an outlier. Based on the verified data type, a sensor node trust mechanism is established. According to the verification results, it is divided into trust and untrust estimation. The sensor corresponding to the abnormal data is marked as an untrusted node. The abnormal data and its untrusted nodes do not participate in the subsequent sensor data fusion.

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

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

[0124] Information entropy, also known as Shannon entropy, is a quantitative measure of system uncertainty. The higher the system entropy value, the greater the degree of information confusion, and vice versa, the stronger the 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. This embodiment uses multi-dimensional continuous distribution information entropy to construct a noise uncertainty measurement model. The model can effectively characterize the coupling correlation characteristics of multi-dimensional parameters and accurately quantify the interference intensity of heteroscedastic noise on state estimation, thereby assigning appropriate weight fusion coefficients to sensor nodes. The analytical expression of its entropy is:

[0125] ( )

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

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

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

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

[0130] (3) Assuming that n abnormal nodes are detected, the weight fusion coefficient distribution of the remaining Mn trust nodes follows the inverse principle of information entropy: the smaller the information entropy, the corresponding weight fusion coefficient a i The larger the value, the smaller the weight coefficient. The expression is:

[0131] ( )

[0132] (4) According to the fusion weight coefficient calculated above, the dataset of the trust node Perform weighted fusion and finally output the fused target state estimate . Its output formula is:

[0133] ( )

[0134] Feasible, experimental results and analysis:

[0135] This example uses the MATLAB R2023b simulation platform to verify the target tracking performance of the proposed OGIE-IPF algorithm and conducts comparative experiments with traditional PF, EPF, and UPF under different data conditions. The root mean square error (RMSE) is selected as the core evaluation indicator of tracking accuracy, and its formula is as follows:

[0136] ( )

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

[0138] Simulation parameter settings:

[0139] The underwater target tracking area in this experiment is set to 1000×1000×1000 m 3 In a three-dimensional cubic space, four stationary observation station sensors are arranged in the area. The positions of the four observation station sensors are: 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 statically stable, and the interference of node drift error on system modeling is not considered. The simulation experiment parameters are as follows: The target tracking simulation scenario specifically includes the spatial distribution of observation station nodes, the real motion trajectory of the target, and the original observation trajectory of the sensor that has not been processed by the filtering algorithm.

[0140] Table 1

[0141]

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

[0143] To verify the effectiveness of the improved particle filter algorithm in suppressing particle degradation and sample depletion and improving particle diversity, this experiment designed two sets of comparative experiments based on a fixed particle number of 100. By analyzing the differences between PF and IPF in key indicators such as weight distribution characteristics, weight distribution variance changes, and the proportion of high- and low-weight particles, the algorithm optimization effect was quantitatively evaluated.

[0144] The results show that in the PF algorithm, low-weight particles (weights less than 0.01) account for approximately 61%, while high-weight particles (weights greater than 0.02) account for only about 8%. The particle weight distribution shows significant polarization, indicating that the particle set is at serious risk of degradation, which directly affects the accuracy of state estimation. In contrast, IPF, through a dynamic adaptive weight layered optimization strategy, effectively increases the weight of low-weight particles while moderately attenuating the weight of high-weight particles, achieving a more balanced distribution across different weight layers. Experimental analysis shows that the variance of the weight distribution of IPF at this time is approximately 98.27% lower than that of PF.

[0145] To further evaluate the temporal stability of the algorithms, we compared the weight distribution characteristics of all particles in the two algorithms over a time span of T = 50. The results show that the PF algorithm has a higher proportion of low-weight particles, while high-weight particles only account for a smaller proportion. This uneven distribution can seriously affect the decision quality of the resampling process. In contrast, the weight distribution of the IPF algorithm exhibits a significantly more uniform characteristic, effectively suppressing extreme divergence in weight differences. Statistical results show that the variance of the particle weight distribution of IPF over the entire time period is approximately 97.26% lower than that of PF. This significant decrease in weight dispersion indicates a systematic improvement in particle diversity.

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

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

[0148] To verify the robustness of different weighted fusion algorithms in abnormal noise environments, this experiment conducted a performance analysis using a scenario where sensor observation noise exhibits significant anomalies. The performance of four fusion algorithms within the IPF framework was compared. The algorithms compared included the optimized Grubbs Information Entropy Weighted Fusion (OGIEWF) algorithm, the traditional Weighted Average Fusion (WAF) algorithm, the minimum variance weighted fusion (MVWF) algorithm, and the standard Information Entropy Weighted Fusion (IEWF) algorithm. In this experiment, the noise covariances of the sensors at the four observation stations were set to: R1=36, R2=0.81, R3=25, and R4=1.69, respectively. The noise levels of R1 and R3 were significantly higher, simulating sensor anomalies.

[0149] A comparison of tracking trajectories shows that, under sensor anomalies, IEWF's tracking trajectory is closer to the true state than WAF and MVWF, while OGIEWF's tracking accuracy further outperforms IEWF. The temporal characteristics of the RMSE during target tracking show that, in the initial stage, the RMSE differences among the four algorithms are small. Over time, the RMSE of WAF and MVWF increase significantly, while that of IEWF increases more slowly. OGIEWF maintains a consistently low RMSE. A comparison of the average RMSE along the X, Y, and Z axes reveals that the Z-axis error differs most significantly, with OGIEWF maintaining the lowest average RMSE across all three axes, with its peak Z-axis error being only 16.1% of that of WAF and 25.6% of that 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 that of WAF, MVWF, and IEWF, respectively. Over the entire time period T, OGIEWF reduces its average RMSE by 75.27%, 69.59%, and 48.25% compared to WAF, MVWF, and IEWF, respectively. These experiments demonstrate that OGIEWF effectively suppresses abnormal noise interference through its dynamic weighted fusion coefficient strategy and Mahalanobis distance-based Grubbs anomaly detection mechanism, validating the robustness and effectiveness of the OGIEWF algorithm in abnormal noise environments.

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

[0151] To study the tracking performance of different filtering algorithms in different underwater noise environments, this embodiment conducts comparative experiments by adjusting the level of 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, and R4=1.21; in the high-noise scenario, the noise covariance is adjusted to R1=16, R2=21.16, R3=17.64, and R4=14.44, respectively. This embodiment uniformly uses the information entropy weighted fusion algorithm based on the optimized Grubbs criterion 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 PF, EPF, and UPF in both low-noise and high-noise conditions. Especially in the high-noise scenario in the later stage of target tracking, the trajectory of IPF is most consistent with the true state, while the PF algorithm shows a significant deviation. The root mean square error analysis further shows that: in the initial stage of target tracking, the RMSE of the four filtering algorithms are relatively small; as time goes by, especially in the middle and late stages of target turning, the RMSE of the PF algorithm fluctuates violently, with the maximum increase reaching 45.64% at a certain moment, while the RMSE of the IPF remains relatively low and changes smoothly throughout the process. In a low-noise environment, the average RMSE of PF, EPF, UPF and IPF over the entire time T are 14.29m, 8.70m, 6.63m and 2.89m respectively, and the RMSE of IPF is reduced by 79.78%, 66.78% and 56.41% compared with PF, EPF and UPF respectively; in a high-noise environment, the average RMSE of PF, EPF, UPF and IPF over the entire time T are 24.17m, 13.54m, 5.12m and 4.01m respectively, and the RMSE of IPF is reduced by approximately 83.41%, 70.38% and 21.68% compared with PF, EPF and UPF respectively, while the fluctuation range of IPF is approximately 17.02%, 30.61% and 57.46% of that of PF, EPF and UPF respectively.

[0152] 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 in complex noise environments.

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

[0154] Depend on As can be seen, under the same particle number conditions, the average position root mean square error (RMSE) of the OGIE-IPF algorithm is significantly lower than that of the PF algorithm, but its single-step runtime is relatively long. This is due to the increased computational complexity of the OGIE-IPF algorithm due to its introduction of the UKF as an importance density function, a dynamic adaptive weight correction mechanism, an anomaly data detection mechanism, and an information entropy fusion coefficient determination process. Despite this increased computational complexity, tracking accuracy is significantly improved. Compared to the lower-error UPF algorithm, the average single-step runtime of the OGIE-IPF algorithm increases slightly, but the RMSE decreases significantly, indicating a more efficient accuracy improvement. Further comparison of the performance of the PF and OGIE-IPF algorithms under different particle numbers shows that as the particle number increases from 200 to 400, the average RMSE of both algorithms decreases, but the average RMSE of the improved filtering algorithm varies relatively narrowly, indicating that increasing the particle number has limited impact on the tracking accuracy of the OGIE-IPF algorithm and actually increases computational time. In summary, the OGIE-IPF algorithm can maintain high target tracking accuracy at lower particle counts without significantly increasing time complexity compared to traditional filtering algorithms. Therefore, the overall performance of the OGIE-IPF algorithm is superior to that of traditional filtering methods.

[0155] Table 2

[0156]

[0157] In order to explore the impact of different noise variance R and particle number N on the algorithm performance, this experiment defines the low noise variance R i , and increase the sampling time to 300s. When the number of particles in the PF algorithm is 300 or 400, and the noise is R i or 4R i When the number of particles is the same but the noise variance is different from R i Increased to 4R i When the noise level is 0.000, the divergence of the PF algorithm is significantly increased. In contrast, the OGIE-IPF algorithm maintains a stable low error level under different noise and particle number conditions. The above experiments show that OGIE-IPF effectively balances computational efficiency and tracking accuracy, ensuring real-time performance while maintaining strong stability.

[0158] In summary, to address the poor target tracking accuracy of traditional particle filter algorithms in complex underwater conditions, this embodiment proposes an information entropy-weighted data fusion method and an improved particle filter algorithm based on an optimized Grubbs criterion. This algorithm improves target tracking accuracy through the following steps: First, the UKF is introduced to construct an importance density function, accurately approximating the posterior distribution of the nonlinear system state through an unscented transformation, effectively improving state estimation accuracy. Second, a dynamic adaptive hierarchical weight optimization mechanism is designed to suppress particle depletion through weight stratification correction. Furthermore, the Grubbs criterion is improved based on the Mahalanobis distance to enable anomaly detection and trusted node screening for multidimensional state data. Finally, a dynamic information entropy-weighted fusion strategy is combined to adaptively assign node weight fusion coefficients to generate a high-precision global state estimate. Simulation results show that compared to traditional PF, EPF, and UPF algorithms, the OGIE-IPF algorithm proposed in this embodiment achieves tracking results that are more consistent with the target's true state estimate, with lower root mean square error (RMS) and stable tracking performance even in scenarios with limited particle numbers and abnormal noise.

[0159] Example 2

[0160] This embodiment further discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the first embodiment.

[0161] Example 3

[0162] This embodiment further discloses a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method described in the first embodiment are implemented.

[0163] Example 4

[0164] This embodiment further discloses a computer program product, including a computer program, which implements the steps of the method described in the first embodiment when executed by a processor.

[0165] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A three-dimensional underwater target tracking method based on improved particle filtering, characterized in that: The following steps are involved: Collect three-dimensional target tracking data of underwater targets based on observation station sensors; constructing a target tracking model and a measurement model based on the three-dimensional target tracking data; The particle filter algorithm is improved based on the unscented Kalman filter. Based on the improved particle filter algorithm, target tracking model and measurement model, the importance density function is constructed and the particles are resampled. During the resampling process, a dynamic adaptive layered weight factor is introduced to correct the weights of different particles, and the corrected particle weights are normalized; After resampling is completed, anomaly detection is performed on the 3D target tracking data based on the optimized Grubbs criterion. The sensors corresponding to the outliers are marked as untrusted nodes, and the remaining sensors are marked as trusted nodes. The information entropy weighting strategy is used to fuse the data of the trust nodes to obtain the fused target state estimate, thereby realizing the three-dimensional tracking of underwater targets. Based on the improved particle filter algorithm, target tracking model and measurement model, the importance density function is constructed and the particle resampling process includes: In the initialization phase, particles are collected from the prior distribution and the particle weights are initialized; At each moment, an unscented Kalman filter is used to generate an updated particle state estimate for each particle, and the sigma point set is calculated using an 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 based on the predicted state mean and covariance, and substitute it into the measurement equation to obtain the predicted point set and mean, incorporate the latest observations, and calculate the particle's related covariance matrix and Kalman filter gain matrix; Construct an importance density function based on the updated particle state estimates and the associated covariance matrix, and perform resampling; During the resampling process, the process of introducing dynamic adaptive layered weight factors 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. A dynamic adaptive hierarchical weight factor is introduced to modify the weights of particles at different levels. The process of anomaly detection for 3D target tracking data based on the optimized Grubbs criterion includes: Calculate the global mean and total covariance matrix of the 3D target tracking data; calculate the Mahalanobis distance for each 3D target tracking data; calculate the maximum Mahalanobis distance and statistic based on the mean and standard deviation of the Mahalanobis distance; test the statistics of the 3D target tracking data using the significance level parameter and the corresponding critical value as the threshold. 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 an untrusted node. The outlier data and its untrusted nodes are not included in subsequent data fusion; The process of fusing the data of the trust nodes using the information entropy weighting strategy to obtain the fused target state estimate and then realize the three-dimensional tracking of underwater targets includes: The fusion weight coefficients of non-trusted nodes are set to zero; the information entropy of the trusted nodes is calculated based on the size of the sensor noise covariance matrix; the weight fusion coefficients of the remaining trusted nodes are distributed according to the inverse principle of information entropy, and the fusion weight coefficients are calculated; the data sets of the trusted nodes are weightedly fused based on the fusion weight coefficients, and the fused target state estimate is output.

2. The method according to claim 1, characterized in that The process of building a target tracking model includes: When an underwater target maintains a uniformly accelerated linear motion mode in both the horizontal and vertical directions in a three-dimensional underwater environment, the product of the state transfer matrix and the state vector at the current moment, as well as the product of the system disturbance matrix and the Gaussian random process noise at the current moment, are obtained. The two products are summed to obtain the state vector of the underwater target at the next moment, thereby completing the construction of the target tracking model.

3. The method according to claim 1, characterized in that The process of building a measurement model includes: Based on the coordinate position of the observation station sensor, the distance between the underwater target and the observation station sensor at the current moment, the azimuth of the observation station sensor relative to the underwater target, and the pitch angle of the observation station sensor relative to the underwater target are obtained; based on the functional relationship between the distance between the underwater target and the observation station sensor at the current moment, the azimuth of the observation station sensor relative to the underwater target, the pitch angle of the observation station sensor relative to the underwater target and the observation noise covariance matrix of the observation station sensor, the measurement model is constructed.

4. A computer device comprising a memory, a processor, and a computer program stored in the memory, wherein: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 3.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

6. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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