A proposal for a nonlinear Kalman filter using state dependent linear representation system and its performance analysis by numerical simulations

Abstract

This paper considered a new nonlinear state estimation method based on the Kalman filter. In this method, we employed a state-dependent linear representation which is rewritten the system nonlinear equation into pseudo linear equation without any approximation, then applied a linear kalman filter to estimate the system state using the observed output. The method is inspired by a method based on the state-dependent Riccati equation (SDRE), which is a method for designing controllers or observers for nonlinear systems. Our filter approach is very simple and can be implemented more easily than the conventional methods of similar nonlinear state estimation methods such as extended Kalman filter (EKF) and unscented Kalman filter (UKF). The effectiveness of the proposed method was verified by numerical simulations. As a result, we confirmed that the proposed method is faster in computation time and easier in design than the SDRE-based observer. In addition, from the comparison between the estimation results by the proposed method and the estimation results of EKF and UKF, it was confirmed that the proposed method can be applied to the same state estimation problems as EKF and UKF.

Keywords

• state estimation
• nonlinear system
• state dependent linear representation system
• extended kalman filter (ekf)
• unscented kalman filter (ukf)