Robust Continuous-Time Matrix Estimation under Dependent Noise Perturbations: Sliding Modes Filtering and LSM with Forgetting

This paper deals with time-varying parameter estimation of stochastic systems under dependent noise perturbations. The filter, which generates this dependent noise from a standard “white noise,” is assumed to be partially known (a nominal plant plus a bounded deviation). The considered approach consists of two consecutive steps. At the first step, the application of a sliding-mode-type algorithm is suggested, providing a finite-time equivalence of the original stochastic process with unknown parameters to an auxiliary one. Such an “equivalence” does not cancel the noise effects, but allows one to identify the model in the “regression form” for a sufficiently short time and, simultaneously, to transform the dependent noise, keeping bounded uncertainties as an external unmeasured dynamics. At the second step the least squares method with a scalar forgetting factor (LSMFF) is applied to estimate time-varying parameters of the given model. A convergence zone analysis is presented. A numerical example illustrates the effectiveness of the proposed approach.