Simultaneous States and Parameters Estimation for Nonlinear Systems by Robust Approximated Minimum Variance Unbiased Filter

摘要

This paper addresses robust states and parameters estimator for nonlinear systems. We first derive approximated linear dynamics of state estimation error by applying an Unscented Statistical Linearization (USL). For this approximated linear system, influences of parameter error are considered as a disturbance. Then, we consider applying an unbiased minimum-variance estimation to eliminate the influence of parameter error. However, since the approximated linear system contains uncertainties and linearization error, we cannot calculate the exact value of the error covariance matrix. Therefore, we consider the upper bound of the error covariance matrix including effects of linearization error due to the USL. Then, we solve an optimization problem to minimize the upper bound of the error covariance matrix so as to satisfy a condition which eliminates the influence of the parameter estimation error. We confirm the validity of the proposed methods by numerical simulations. Our proposed filter should be a promising alternative to the joint estimation which is commonly applied in engineering fields.