A 3D Underwater Target Tracking Algorithm with Integrated Grubbs-Information Entropy and Improved Particle Filter
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摘要: 为解决三维空间中水下无线传感器网络(UWSN)在异常情况下进行目标跟踪时精度不佳的问题，该文提出一种基于优化Grubbs准则的信息熵加权数据融合和改进粒子滤波(IPF)的三维水下目标跟踪算法(OGIE-IPF)。首先，在粒子滤波框架中融合无迹卡尔曼滤波(UKF)算法以构建重要性密度函数，从而抑制粒子退化现象；同时，在重采样阶段提出一种动态自适应分层权重优化机制，通过差异化修正高、中、低权重粒子的分布，以增强粒子多样性并抑制贫化现象。其次，基于标准Grubbs准则提出以马氏距离替代传统的标准化残差思想构建异常统计量，通过融合多维变量的协方差矩阵，实现多维数据的异常检测。最后，基于IPF实现局部目标跟踪，结合优化的Grubbs准则进行异常检测与传感器信任评估，并通过信息熵加权的多源融合算法完成全局状态估计。仿真实验结果表明，所提改进算法相较于PF算法，粒子权重分布方差降低了约97.26%，而在低噪声和高噪声场景下相比于粒子滤波(PF)、扩展粒子滤波(EPF)、无迹粒子滤波(UPF)均方根误差分别降低了79.78%, 66.78%, 56.41%和83.41%, 70.38%, 21.68%。该文所提改进算法有效提高了水下异常情况下的目标跟踪精度，展现出良好的鲁棒性。Abstract:
Objective To address the limited target tracking accuracy of traditional Particle Filter (PF) algorithms in three-dimensional Underwater Wireless Sensor Networks (UWSNs) under abnormal conditions, this study proposes a three-dimensional underwater target tracking algorithm (OGIE-IPF). The algorithm integrates an optimized Grubbs criterion–based information entropy–weighted data fusion with an Improved Particle Filter (IPF). Conventional PF algorithms often suffer from particle degeneracy and impoverishment, which restrict estimation accuracy. Although weight optimization strategies introduced during resampling can enhance particle diversity, existing approaches mainly rely on fixed weighting factors that cannot dynamically adapt to real-time operating conditions. Moreover, current anomaly detection methods for multi-source data fusion fail to effectively address data coupling and heteroscedasticity across dimensions. To overcome these challenges, a dynamic adaptive hierarchical weight optimization strategy is designed for the resampling phase, enabling adaptive particle weighting across hierarchy levels. Additionally, a Mahalanobis distance discrimination mechanism is incorporated into the Grubbs criterion–based anomaly detection method, achieving effective multi-dimensional anomaly detection through covariance-sensitive analysis. Methods The proposed OGIE-IPF algorithm enhances target tracking accuracy under underwater abnormal conditions through a distributed data processing framework that integrates multi-source data fusion and adaptive filtering. First, the Unscented Kalman Filter (UKF) is incorporated into the particle filtering framework to construct the importance density function, thereby alleviating particle degeneracy. Simultaneously, a dynamic adaptive hierarchical weight optimization mechanism is proposed during the resampling phase to improve particle diversity. Second, the Mahalanobis distance replaces the conventional standardized residual method in the standard Grubbs criterion for anomaly statistic construction. By incorporating the covariance matrix of multidimensional variables, the method achieves effective anomaly detection for multi-dimensional data. Finally, local target tracking is performed using the IPF combined with the optimized Grubbs criterion for anomaly detection and sensor credibility evaluation, whereas global state estimation is realized through an information entropy–weighted multi-source fusion algorithm. Results and Discussions The IPF developed in this study is designed to enhance particle set diversity through optimization of the importance density function and refinement of the resampling strategy. To evaluate algorithm performance, a comparative experimental group with a particle population of 100 is established. Simulation results indicate that the weight distribution variances of the IPF at specific time points and over the entire tracking period are reduced by approximately 98.27% and 97.26%, respectively, compared with the traditional PF ( Figs. 3 and4 ). These findings suggest that the improved strategy effectively regulates particles with varying weights, resulting in a balanced distribution across hierarchical weight levels. Sensor anomalies are simulated by introducing substantial perturbations in observation noise. The experimental data show that the OGIE-IPF algorithm maintains optimal error metrics throughout the operational period (Figs. 5 and6 ), demonstrating superior capability in suppressing abnormal noise interference. To further assess algorithm robustness, two representative scenarios under low-noise and high-noise conditions are constructed for multi-algorithm comparison. The results indicate that OGIE-IPF achieves Root Mean Square Error (RMSE) reductions of 79.78%, 66.78%, and 56.41% compared with the PF, Extended Particle Filter (EPF), and Unscented Particle Filter (UPF) under low-noise conditions, and reductions of 83.41%, 70.38%, and 21.68% under high-noise conditions (Figs. 9 and12 ).Conclusions The OGIE-IPF algorithm proposed in this study enhances target tracking accuracy in three-dimensional underwater environments through two synergistic mechanisms. First, tracking precision is improved by refining the PF framework to optimize the intrinsic accuracy of the filtering process. Second, data fusion reliability is strengthened via an anomaly detection framework that mitigates interference from erroneous sensor measurements. Simulation results confirm that the OGIE-IPF algorithm produces state estimations more consistent with ground truth trajectories than conventional PF, EPF, and UPF algorithms, achieving lower RMSE and maintaining stable tracking performance under limited particle populations and abnormal noise conditions. Future work will extend the model to incorporate dynamic marine environmental factors and address the effects of malicious node interference within underwater network security systems. -
表 1 实验参数
参数名 参数值 目标初始位置(m) (100,400,20) 目标初始速度(v) (60,9,12) 目标初始加速度(m/s2) (-4,1,2) 初始粒子数 200 过程噪声协方差阵 diag(12 3,0.12 3,0.012 3) 观测噪声协方差阵 diag(1002,0.12,0.12) 
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表 2 算法平均位置误差和单步计算时间
滤波算法 粒子数(个) 平均RMSE(m) 平均单步时间(s) EPF 100 12.412 1 0.006 2 200 8.699 9 0.011 8 UPF 100 9.271 5 0.013 7 200 6.633 1 0.020 3 PF 100 18.481 3 0.003 5 200 14.291 5 0.006 1 300 12.668 9 0.008 4 400 10.962 5 0.010 3 OGIE-IPF 100 3.753 5 0.014 2 200 2.894 1 0.021 0 300 2.413 0 0.027 4 400 2.075 4 0.033 1
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