Filtering-based maximum likelihood hierarchical recursive identification algorithms for bilinear stochastic systems

This paper focuses on the identification of bilinear state space stochastic systems in presence of colored noise. First, the state variables in the model is eliminated and an input–output representation is provided. Then, based on the obtained identification model, a filtering based maximum likelihood recursive least squares (F-ML-RLS) algorithm is developed to improve the parameter estimation accuracy by combining the data filtering technique and the maximum likelihood identification principle. Furthermore, based on the hierarchical identification principle, the original complex bilinear system is decomposed into two subsystems with smaller dimensions, and a filtering based maximum likelihood hierarchical recursive least squares (F-ML-HRLS) algorithm is presented to reduce the computational burden. Compared with the F-ML-RLS algorithm, the F-ML-HRLS algorithm has superior performance in computational efficiency and parameter estimation accuracy. Simulation results demonstrate the excellent performance of the proposed algorithms.