平方根求积分卡尔曼滤波器

Square-Root Quadrature Kalman Filter

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,本文提出一种近似递归的高斯滤波器:平方根求积分卡尔曼滤波器(SRQKF).该滤波器是在求积分卡尔曼滤波器(QKF)基础上的平方根实现形式,使用统计线性回归的方法,通过一套参数化高斯密度的高斯-厄米特积分点来线性化非线性函数的;滤波器采用平方根的实现方法,不仅增强了数值的鲁棒性,确保了状态协方差矩阵的半正定性,而且在一定程度上提高了滤波精度.仿真实验表明,SRQKF的滤波精度比QKF提高约12%,且均高于无味滤波器(UF)和扩展卡尔曼滤波器(EKF),但这二者的计算复杂度均比UF和EKF大.对滤波精度要求比较高的非线性场合,新滤波器是一种很有效的非线性滤波算法.

Develope an approximate, recursive Gaussian filters for nonlinear dynamics with additive noise, square-root quadrature Kalman filter （SRQKF）. This filter is the square-root implementation on the basis of the quadrature Kalman filter （QKF） ,it linearizes the nonlinear functions using statistical linear regression method through a set of Gaussian-Hermite quadrature points that parameterize the Gaussian density. The squre-root implementation of the new filter not only enhances the numerical stability, guarantees positive semi-definiteness of the state covariance, but also increases the filtering accuracy. The simulation shows that the tracking accuracy of the SRQKF is 12% higher than that of QKF,and the tracking accuracy of QKF is higher than that of the unscented Kalman filter （UF） and extended Kalman filter （EKF）,but the computational cost of them are all higher than that of UF and EKF. The new filter is an effective nonlinear filtering algorithm in the place required high filtering accuracy.