SVD-based factored-form Cubature Kalman Filtering for continuous-time stochastic systems with discrete measurements
Maria V. Kulikova, Gennady Yu. Kulikov
TL;DR
The SVD-based methodology recently proposed for the classical Kalman filter is generalized on the nonlinear filtering problem and two estimators are suggested, formulated in terms of SVD factors of the filter error covariance matrix and belong to the class of stable factored-form (square-root) algorithms.
Abstract
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.