AM-ESG estimation algorithms for a class of systems with colored noises

This paper derives an identification model for a class of stochastic systems with colored noises. The information vector in the identification model contains both unknown noise-free outputs (i.e., true outputs) and unmeasurable noise terms, this is difficulty of identification. This paper establishes an auxiliary model by using the measurable information of the system and replaces the unknown noise-free outputs in the information vector with the outputs of the auxiliary model and noise terms in the information vector with the estimated residuals, and presents an auxiliary model based extended stochastic gradient (AM-ESG) algorithm. The algorithm proposed has significant computational advantage over existing least squares identification algorithms. The simulation example indicates that the parameter estimation errors become small as the data length increases.