Iterative state and parameter estimation algorithms for bilinear state-space systems by using the block matrix inversion and the hierarchical principle

This paper is concerned with the identification of the bilinear systems in the state-space form. The parameters to be identified of the considered systems are coupled with the unknown states, which makes the identification problem difficult. To deal with such a difficulty, the iterative estimation theory is considered to derive the joint parameter and state estimation algorithm. Specifically, a moving data window least squares-based iterative (MDW-LSI) algorithm is derived to estimate the parameters of the systems by using the window data, and the unknown states are estimated by a bilinear state estimator. Furthermore, in order to improve the computational efficiency, a matrix decomposition-based MDW-LSI algorithm and a hierarchical MDW-LSI algorithm are developed according to the block matrix inversion lemma and the hierarchical identification principle. Finally, the computational efficiency is discussed and the numerical examples are employed to test the proposed approaches.