Adaptive Step Size Control of Extended/Unscented Kalman Filter Using Event Handling Concept

Abstract

This paper presents a novel (Extended/Unscented) Kalman Filter by augmenting the event handling procedure of Ordinary Differential Equation (ODE) solvers with the predictor-corrector scheme of Extended/Unscented discrete Kalman Filter (EKF/UKF) introducing a variable step size Kalman Filter. This innovation allows a new quality of precision while operating Kalman Filters. The original Kalman Filter is based on a time-discrete predictor-corrector scheme considering fixed step size. The main new idea is to introduce and control step size handling not introduced before. Step size control of EKF/UKF will increase the performance when applied to switching/stiff systems. The step size is controlled based on the current performance (EKF/UKF innovation) and is adapted during the estimation procedure based on an event handling algorithm. The proposed event handling algorithm consists of two parts: relaxing sample time and restricting sample time (ST). Relaxing procedure is used to avoid high computational time when no rapid change exists in system dynamics. Restricting procedure is considered to improve the estimation performance by decreasing the EKF/UKF step size in the case of fast dynamical behavior (switching/stiff behavior). Effectiveness of the proposed approach is verified considering the well-known Van der Pol oscillator as a common example of stiff systems.