A comparison of three non-linear filters

Abstract

This paper examines three distinct methods for the recursive estimation of the state variables of a continuous time non-linear plant on the basis of measuring the time discrete outputs of the plant in the presence of noise. The three suboptimal estimation algorithms are the Extended Kalman filter, a second-order non-linear filter, and a single stage iteration filter. The three filters are derived from the same theoretical basis in order to facilitate their comparison. Simulation results are used to compare the performance of the filters in the cases of linear plant dynamics and a non-linear output, non-linear plant dynamics and a linear output, and non-linear plant dynamics and non-linear output. We are able to conclude that the single stage iteration filter has superior mean squared error performance under all conditions, followed by the second-order filter. The second-order filter appears to be more of an unbiased estimator than the other filters. The results also show that both the single stage iteration filter and second order filter have more capability in treating non-linearities in the plant dynamics than in treating output non-linearities.