Abstract: Cubature quadrature rule is a kind of higher algebra precision integration method to improve nonlinear state estimate problems. To enhance the stability of nonlinear filter, based on a square root decomposition of covariance matrix, a new Square Root Cubature Quadrature Kalman Filter（SRCQKF） is proposed. The spherical radial cubature rule and Gauss-Laguerre quadrature rule are applied to compute the integral points. The square root of covariance matrix is obtained and propagated by matrix QR decomposition. Two typical nonlinear examples show that the SRCQKF improves the accuracy of nonlinear estimation and has more stability.

Key words: square root filter, cubature Kalman filter, nonlinear state estimation, cubature rule

摘要： 体积积分是一种新的具有较高代数精度的积分方法。为了提高非线性滤波算法的精度和数值稳定性，将体积积分规则和平方根分解引入卡尔曼滤波框架中，提出了平方根体积积分卡尔曼滤波算法（SRCQKF）。新算法采用球半径体积规则和高斯-拉盖尔积分规则计算积分点，利用矩阵的QR分解得到协方差矩阵的平方根并传播平方根。两个典型的非线性系统的实验结果表明，与体积卡尔曼滤波相比，新算法提高了非线性状态的估计精度，具有较高的数值稳定性。

关键词: 平方根滤波, 体积卡尔曼滤波, 非线性状态估计, 体积规则