A Strong Tracking Proportional Integral Kalman Filter for Nonlinear System State Estimation

In this paper, we propose a Strong Tracking Proportional Integral Kalman Filter (TIEKF) for nonlinear state estimation. In the TIEKF, the tracking ability for the states improved and the static errors of the states estimated are eliminated. To do these, modifications are made on two aspects considering on the defects of the Proportional-Integral (PI) Kalman filter while used in nonlinear systems. First, to improve the tracking ability, the proportional gains is redesigned based on covariance scaling. The redesign aims at rendering the stochastic covariance matrix of the estimated states altering with the practical situation, with the assistance of the system measurements. Second, the integral item is also redesigned to give an optimal estimation of the integration of the estimating error of the states in nonlinear systems. On this aspect, the estimating methods adopted in conventional Kalman Filter are utilized. In terms of cumulating errors, the performance of the new filter is also presented based on a badly modeled nonlinear function, with the results compared with the EKF and other modified forms of EKF.