Statistics

State observer

Data modeling

Database

Artificial intelligence

Kalman filter

Estimation theory

Physics

Nonlinear system

Bilinear interpolation

Adaptive filter

Mathematics

Mathematical optimization

Estimator

Quantum mechanics

Computer science

Algorithm

Recursive least squares filter

Control (management)

Observer (physics)

State space

System identification

Covariance

Control theory (sociology)

State (computer science)

Least-squares function approximation

International Journal of Systems Science

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.

Hierarchical parameter and state estimation for bilinear systems