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Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

Because of the product item of the control input and the state vector, the identification of bilinear systems is difficult. This paper considers the combined parameter and state estimation problems of bilinear state‐space systems. On the basis of the observability canonical form and the model transformation, an identification model with a linear combination of the system parameters is obtained. Using the hierarchical principle, the identification model is decomposed into three submodels with fewer variables, and a three‐stage least squares‐based iterative (3S‐LSI) algorithm is presented to estimate the system parameters. Furthermore, we derive a state estimator (SE) for estimating the unknown states, and present an SE‐3S‐LSI algorithm for estimating the unknown parameters and states simultaneously. After that, the least squares‐based iterative algorithm is presented as a comparison. By analyzing the estimation results and the calculation amount, these two algorithms can identify the bilinear system effectively but the 3S‐LSI algorithm can improve the computational efficiency. The simulation results indicate the effectiveness of the proposed algorithms.