磁性目标跟踪的后验克拉美罗下限分析与计算

Computing the recursive posterior Cramer-Rao bound for magnetic target tracking

为了求解磁性目标跟踪问题的后验克拉美罗下限(PCRB),提出了PCRB-GMSPPF算法。该算法利用高斯混合采样粒子滤波算法对目标状态的真实后验概率密度分布进行抽样,再通过蒙特卡洛积分法迭代求解每个观测时刻的Fisher信息矩阵,进而得出目标状态估计的PCRB;克服了基于PF算法求解PCRB过程中由于粒子退化和贫化问题造成不能从后验概率分布中正确抽样的缺点;在建立磁性目标跟踪的状态模型和观测模型的基础上进行仿真分析,将求解出的PCRB与采用GMSPPF及PF算法进行跟踪的均方根误差做对比,验证所提的PCRB-GMSPPF算法的有效性,结果表明:针对磁性目标跟踪问题,PCRB-GMSPPF算法较PCRB-PF算法具有更好的准确性,并可用于一般的非线性模型跟踪误差下限分析。

The PCRB-GMSPPF algorithm is proposed in order to achieve the computation of posterior Cramer-Rao bound in magnetic target tracking issues. In the proposed method,the GMSPPF algorithm is adopted to perform the sampling toward the actual posterior distribution of target state,hence the Fisher information matrix at each observation time in PCRB computation can be approximated using Monte Carlo integral method. The proposed method overcomes the depletion and degeneracy problem which causes the failure to correctly sample in posterior distribution. The simulation analysis is performed on the basis of the establishment of magnetic target tracking state model and observation model. The proposed PCRB is compared with the mean square error performance of tracking using GMSPPF and PF algorithm to validate correctness of proposed PCRB computation algorithm. The results exhibits that PCRB-GMSPPF outperforms the PCRB-PF in accuracy for magnetic target tracking issues,and can be generalized for general non-linear tracking model analysis for error lower bound.