Multistage parameter estimation algorithms for identification of bilinear systems

In this paper, two methods for parameter estimation of bilinear state-space systems with colored noise, which are expressed by ARMA model, are proposed. Using the hierarchical identification principle and gradient method, to reduce the computational cost, both the four-stage recursive least squares algorithm and the four-stage stochastic gradient algorithm are exploited by which parameter estimation error is reduced and the speed of convergence of parameters is increased. In addition, a bilinear state observer for state estimation is designed to make use of the estimated states in the four-stage recursive least squares and the four-stage stochastic gradient algorithms. Finally, a numerical example and a practical example are provided to indicate the superiority of the proposed methods. The results show that due to the data length increase, the estimation error of the parameters is reduced. Furthermore, the estimated parameters converge to the actual values in a short time.