Recursive estimation algorithms based on the least squares and their convergence for a class of time-varying systems

For the identification of time-varying systems, most traditional methods use various adaptive factors to track the dynamic change, which have not taken the changing law of the time-varying parameter into account. To overcome this problem, this paper models the time-varying parameter as the autoregressive process and constructs the identification model with regard to the unknown autoregressive coefficients. Furthermore, in terms of the phenomenon that the past time-varying parameters exist in the autoregressive process, a recursive identification method is presented to estimate the autoregressive coefficients based on the interaction estimation theory. For the purpose of enhancing computational efficiency, a parameter separation scheme is developed by the changing laws of the system parameters. Then two sub-algorithms are proposed for the time-varying parameter estimation based on the decomposition technique. Moreover, the convergence property and upper bound of the parameter estimation error of the proposed algorithms are analyzed by the martingale hyperconvergence theorem. The computational burden comparison is given and the simulation result is provided to illustrate the effectiveness of the proposed algorithms.

Automated summary

This paper proposes an identification method for time-varying systems by modeling the time-varying parameter as an autoregressive process and estimating the autoregressive coefficients using a recursive identification method. A parameter separation scheme is designed to enhance computational efficiency. The convergence property and upper bound of the parameter estimation error are analyzed, and simulation results demonstrate the effectiveness of the proposed method.