Data-Based Local Smoothing Technique for Parameters Estimation of Nonlinear ARX Models

This paper proposes a parameter estimation method for a kind of nonlinear auto-regressive (NARX) model, which is usually highly nonlinear because its parameters could vary very fast, since they are unknown nonlinear functions of past observations, called here as mapping-regressors. These parameters are poorly estimated by the standard recursive least-squares (RLS) filter since they vary much faster than standard time-varying parameters (TVP). So, our proposal reduces the fast parameters variability locally by reducing the a priori known mapping-regressors variability. This process is done by using both a reordering process according to the ascendant value of one of the mapping-regressors and the non-temporal windowing intersections of the remaining mapping-regressors. As a result, a set of local smoothed models, where a conventional recursive RLS filter works, is obtained. Experimentally, this approach works faster and simpler than alternative methods from the literature, which are discussed briefly through two simulated examples.