Square-root information-type methods for continuous–discrete extended Kalman filtering

Abstract

In this paper, we derive several square-root information-type Extended Kalman filtering (EKF) methods for continuous–discrete stochastic systems. Square-root implementations are known to improve the numerical stability of the EKF (to roundoff), meanwhile, the information-type algorithms are the powerful estimation tools in case of limited or unknown a priori information about the state. Our continuous–discrete EKF methods are designed by using the Euler–Maruyama discretization scheme as well as the Cholesky and SVD factorizations for the square-root implementations. Unlike discrete-time information-type EKF methods, which rely on the invertibility of the Jacobian matrix of the process equation drift function, the continuous–discrete information-type EKF algorithms avoid this restriction. They exist for any Jacobian matrix value when the step-size (given by users) of the numerical integration scheme involved is sufficiently small. This makes the novel continuous–discrete information-type EKF algorithms more flexible and provides a good reason for using them in practice. Finally, the numerical tests include two benchmark problems from chemical engineering field and one example from mathematical neuroscience, respectively. The results obtained demonstrate the practical significance of novel information-type EKF implementation methods and their feasibility.