Moving data window gradient-based iterative algorithm of combined parameter and state estimation for bilinear systems

The combined iterative parameter and state estimation problem is considered for bilinear state-space systems with moving average noise in this paper. There are the product terms of state variables and control variables in bilinear systems, which makes it difficult for the parameter and state estimation. By designing a bilinear state estimator based on the Kalman filtering, the states are estimated using the input-output data. Furthermore, a moving data window (MDW) is introduced, which can update the dynamical data by removing the oldest data and adding the newest measurement data. A state estimator-based MDW gradient-based iterative (MDW-GI) algorithm is proposed to estimate the unknown states and parameters jointly. Moreover, given the extended gradient-based iterative (EGI) algorithm as a comparison, the MDW-GI algorithm can reduce the impact of noise to parameter estimation and improve the parameter estimation accuracy. The numerical simulation examples validate the effectiveness of the proposed algorithm.