基于平方根卡尔曼滤波的粒子滤波算法

在普通粒子滤波器中,基于先验概率的重要性密度不能容纳最新测量信息,导致跟踪精度难以提高。针对该问题,给出一种基于平方根卡尔曼滤波(SRUKF)的新型粒子滤波算法(SRUPF)。该算法以普通粒子滤波器(PF)为基础,运用SRUKF生成重要性密度。与运用先验知识生成重要性密度的普通粒子滤波器不同,SRUPF的重要性密度中包含了最新的观测信息,从而能够更好地逼迫状态变量的分布规律。此外,由于SRUPF在计算重要性密度时不需要在每一个迭代步骤都对状态协方差阵进行分解,因而SRUPF比PF具有更好的数值稳定性。在非线性测角跟踪问题中的应用表明:SRUPF滤波器的跟踪精度优于PF和SRUKF。

Particle Filtering Algorithm Based on Square Root Unscented Kalman Filtering

In common particle filtering,the importance density based on prior probability can not contain new measurement information,so the tracking precision is hard to improve.To solve the problem,a novel particle filter algorithm was developed.The new filtering algorithm was implemented according to the procedure adopted in common particle filter(PF).It made use of a recently developed square root unscented Kalman filter(SRUKF) to generate the importance density.Unlike the former PF which simply applied the prior information as the importance density,the presented algorithm embodied the latest observation information,so it could well approximate the distribution of the state variable.Moreover,SRUPF did not need to factorize the state covariance at each step when it was calculating the importance density,thus,it had a good numerical stability.The use of the algorithm for nonlinear angle-only tracking showed that the precision of the SRUPF was higher than that of PF and the SRUKF.