平方根递推更新高斯粒子滤波

Square-Root Recursive Update Gaussian Particle Filter

对于高斯粒子滤波器重要性密度函数(IDF)的构建,递推更新高斯滤波器(RUGF)依据非线性测量函数梯度对目标运动状态进行渐进式的更新,可以有效克服线性最小均方误差准则的限制,从而得到更接近于真实分布的后验状态估计,但在递推过程中目标状态协方差矩阵易非正定而出现递推中断。针对这一问题,该文首先分析了RUGF的平方根实现策略,并借助容积卡尔曼滤波对平方根(SR)RUGF进行具体实现,然后利用SR-RUGF为高斯粒子滤波器选取IDF,进而得到平方根递推更新高斯粒子滤波器。仿真实验表明,本文算法可有效解决递推中断问题,并获得较高精度的估计结果。

For the construction of importance density function (IDF) of Gaussian particle filter, recursive update Gaussian filter (RUGF) which can effectively overcome the limitation of linear minimum mean square error criterion, updates the target state incrementally based on the gradient of nonlinear measurement function. Consequently, the posterior state estimation that is closer to the real distribution is obtained, but non-positive definite state covariance matrix will lead to recursive interruption. To solve this problem, the square-root implementation strategy of RUGF is firstly analyzed and then square-root recursive update Gaussian filter (SR-RUGF) is implemented by using cubature Kalman filter. Based on that, SR-RUGF is used to construct IDF for Gaussian particle filter. Simulation results demonstrate that the proposed algorithm can effectively solve the recursive interruption problem and obtain estimation result with higher accuracy.