Extended Gradient-based Iterative Algorithm for Bilinear State-space Systems with Moving Average Noises by Using the Filtering Technique

This paper develops a filtering-based iterative algorithm for the combined parameter and state estimation problems of bilinear state-space systems, taking account of the moving average noise. In order to deal with the correlated noise and unknown states in the parameter estimation, a filter is chosen to filter the input-output data disturbed by colored noise and a Kalman state observer (KSO) is designed to estimate the states by minimizing the trace of the error covariance matrix. Then, a KSO extended gradient-based iterative (KSO-EGI) algorithm and a filtering based KSO-EGI algorithm are presented to estimate the unknown states and unknown parameters jointly by the iterative estimation idea. The simulation results demonstrate the effectiveness of the proposed algorithms.