On Gaussian filters for continuous-discrete nonlinear systems

Abstract

This paper considers a continuous-discrete (CD) nonlinear filtering problem in the framework of Gaussian filters. After reviewing the equivalent linearization of static nonlinearities, we derive the continuous-discrete exact Gaussian filter (CD-ExGF) and equivalent linearization Kalman filter (CD-EqKF). It is shown that two CD nonlinear filters have the same time update differential equations for the conditional mean and covariance matrix, and that a difference is in the Kalman gain for the measurement update. Numerical methods of integrating a stochastic differential equation and time update differential equations are developed using the Heun scheme. Results of two simulation studies are included to show the difference and similarity of the CD-EqKF, CD-ExGF and CD extended-Kalman filter (CD-EKF).