Continuous-time parameter estimation under colored perturbations using "equivalent control concept" and LSM with forgetting

This paper deals with time problem of time-varying parameters estimation of stochastic systems under colored noise perturbations. These perturbations, have a standard "white noise" in the input of a forming filter which is assumed to be partially known (a nominal plant plus a bounded deviations). A two step method is proposed. First, it is designed a tracking process, based in the "equivalent control" technique, providing the infine-time equivalence of the origin stochastic process with unknown parameters to an auxiliary one. This step does not eliminate the noise, but it permits (at a short enough time) to represent the model to be identified in the, so-called, "regression form" and, at the same time, to realize the "semiwhitening" of noise keeping bounded uncertainties as an external unmeasured dynamics. In the second step the Least Squares Method (LSM) with a scalar forgetting factor is applied to estimate time varying parameters of the given model. The convergence zone analysis is presented. A numerical example illustrates the effectiveness of the proposed approach.