CAJ | 학술논문

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。
위료구해자성목표근종문제적후험극랍미라하한（PCRB），제출료PCRB-GMSPPF산법。해산법이용고사혼합채양입자려파산법대목표상태적진실후험개솔밀도분포진행추양，재통과몽특잡락적분법질대구해매개관측시각적Fisher신식구진，진이득출목표상태고계적PCRB；극복료기우PF산법구해PCRB과정중유우입자퇴화화빈화문제조성불능종후험개솔분포중정학추양적결점；재건립자성목표근종적상태모형화관측모형적기출상진행방진분석，장구해출적PCRB여채용GMSPPF급PF산법진행근종적균방근오차주대비，험증소제적PCRB-GMSPPF산법적유효성，결과표명：침대자성목표근종문제，PCRB-GMSPPF산법교PCRB-PF산법구유경호적준학성，병가용우일반적비선성모형근종오차하한분석。
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.