Time-varying parameter estimation in continuous-time under colored perturbations using “equivalent control concept” and LSM with forgetting factor

This paper deals with time problem of time-varying parameters estimation of stochastic systems under colored noise perturbations. 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 original stochastic process with unknown parameters to an auxiliary one. This equivalence does not cancel the noise effects, but allows to estimate the model in a “regression form” for a sufficient short time. In the second step, the Least Squares Method with a scalar forgetting factor is applied to estimate the time-varying parameters of the given model. Two examples illustrate the effectiveness of the proposed approach, the first shows an application in a system of location and motion, and the second an estimation of a growth rate of a population dynamic.