In this paper, a singular value decomposition (SVD) approach is developed for implementing the cubature Kalman filter. The discussed estimator is one of the most popular and widely used method for solving nonlinear Bayesian filtering problem in practice. To improve its numerical stability (with respect to roundoff errors) and practical reliability of computations, the SVD-based methodology recently proposed for the classical Kalman filter is generalized on the nonlinear filtering problem. More precisely, we suggest the SVD-based solution for the continuous–discrete cubature Kalman filter and design two estimators: (i) the filter based on the traditionally used Euler–Maruyama discretization scheme; (ii) the estimator based on advanced Itô-Taylor expansion for discretizing the underlying stochastic differential equations. Both estimators are formulated in terms of SVD factors of the filter error covariance matrix and belong to the class of stable factored-form (square-root) algorithms. The new methods are tested on a radar tracking problem.

在本文中，开发了一种用于实现库尔曼卡尔曼滤波器的奇异值分解（SVD）方法。讨论的估计器是解决非线性贝叶斯滤波问题的最流行和广泛使用的方法之一。为了提高其数值稳定性（相对于舍入误差）和实用的计算可靠性，最近针对经典卡尔曼滤波器提出的基于SVD的方法被归纳为非线性滤波问题。更准确地说，我们为连续离散的库尔曼滤波器建议基于SVD的解决方案，并设计两个估计器：（i）基于传统使用的Euler-Maruyama离散化方案的滤波器；（ii）基于高级Itô-Taylor展开的估计器，用于离散基础随机微分方程。这两个估计量都是根据滤波器误差协方差矩阵的SVD因子来表示的，并且属于稳定因式（平方根）算法的一类。在雷达跟踪问题上测试了新方法。