Comparative analysis of a nonlinear observer and nonlinear Kalman filters for magnetic position estimation

This paper analyzes state estimation for nonlinear systems in the presence of sensor noise and process disturbances. A class of systems involving nonlinear functions of vector arguments in the output equations is considered. A nonlinear observer that satisfies a H∞ disturbance rejection constraint in addition to providing asymptotic stability in the absence of disturbances is developed using Lyapunov analysis. The observer is shown analytically to provide a guaranteed upper bound on the norm of the estimation error. The performance of the nonlinear observer is compared with the performance of two of the most popular and powerful methods for estimation in nonlinear systems - the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A magnetic position estimation problem is utilized as the real-world application for the evaluation. In the case of the disturbances being gaussian noise, the UKF and the nonlinear observer provide approximately the same level of performance and they both surpass the performance of the EKF. However, in the case of 2-norm-bounded non gaussian noise such as spikes/ pulses, the nonlinear observer is shown to significantly outperform both the UKF and the EKF.