稀疏网格平方根求积分非线性滤波器

摘要

针对具有加性噪声的非线性高斯动态系统的状态估计问题,本文提出一种新的基于稀疏网格法的平方根求积分滤波器(SSRQF),该滤波器通过稀疏网格取点来近似计算多维积分并进行平方根滤波.与常规QF的积分点数随着维数呈指数增长相比,该方法的积分点数随着维数呈多项式增长,减少了计算量;理论分析表明,无味卡尔曼滤波器(UKF)只是稀疏网格求积分滤波器(SQF)的一个特例,因此SSRQF在精度和取点上比UKF更为灵活.仿真实验表明,SSRQF的滤波精度均高于UKF和扩展卡尔曼滤波器(EKF),是一种效率较高的高精度非线性滤波算法.%For nonlinear estimation with additive noise, we utilized the sparse-grid theory to propose a novel nonlinear filter, Sparse-grid Square-Root Quadrature Filter (SSRQF). The quadrature points for the conventional QF increases exponentially with the dimension. However, the new filter SSRQF uses the sparse-grid theory to reduce the number of quadrature points to a polynomial with the dimension,which alleviates the computation burden greatly. Through the theoretical analysis, we proposed that Unscented Kalman Filter (UKF) is only a special case for Sparse-grid Quadrature Filter (SQF), thus SSRQF is more flexible in terms of choosing points and controlling accuracy.The simulation results show that the SSRQF achieves higher accuracy than the UKF and the Extended Kalman Filter (EKF) .Thus,it is a high accuracy nonlinear filter algorithm with computationally efficient.