Abstract
This paper addresses state estimation problems for parametric uncertain nonlinear systems. We developed Robust Nonlinear Kalman filters (RNKF) by using two linearization methods to consider the influence of parameter uncertainties of covariance matrixes. The first method is Taylor expansion which is used in Extended Kalman Filter and another is equivalent linearization. The RNKF is more accurate than conventional NKF. However the RNKF has some disadvantages: (1) when there is no parameter uncertainty, estimation accuracy of the RNKF may be inferior to that of the NKF and (2) the estimated values of the RNKF can have some offsets by the influence of parameter uncertainties. So, we developed an adaptive RNKF by introducing an adaptive scheme into RNKF to automatically tune the influence of parameter uncertainties. We also developed Approximated Minimum Variance Unbiased Filter (AMVUF) by solving constrained optimization problem to reduce the influence of parameter uncertainties. Furthermore, we develop a new simultaneous states and parameters estimator for nonlinear systems based on the AMVUF. We confirm the validity of the proposed methods by Monte Carlo simulations.
