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 finite-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 “semi-whitening” 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.