Hierarchical parameter and state estimation for bilinear systems

The identification of state-space models of bilinear systems is studied in this paper. The parameters to be identified of the considered system are coupled with the unknown states, which makes the identification problem more difficult than that of the linear state-space model. For the coupled variables, this paper introduces the interaction estimation theory to study an on-line algorithm for joint state-parameter estimation. To be more specific, a state observer in the bilinear form is established by minimising the state estimation error covariance matrix in the same way of a Kalman filter on the condition that the parameters are known. Then, a bilinear state observer based recursive least squares algorithm is developed using the least squares method. Moreover, for the purpose of improving the computational efficiency, a bilinear state observer based two-stage recursive least squares algorithm and a bilinear state observer based multi-stage recursive least squares algorithm are proposed by decomposing the system into several subsystems based on the hierarchical identification. Finally, a numerical simulation is employed to show the specific performance of the proposed approaches.