Tracking time-varying coefficient-functions

A method for adaptive and recursive estimation in a class of non-linear autoregressive models with external input is proposed. The model class considered is conditionally parametric ARX-models (CPARX-models), which is conventional ARX-models in which the parameters are replaced by smooth, but otherwise unknown, functions of a low-dimensional input process. These coefficient functions are estimated adaptively and recursively without specifying a global parametric, form, i.e. the method allows for online tracking of the coefficient functions. Essentially, in its most simple form, the method is a combination of recursive least squares with exponential forgetting and local polynomial regression. It is argued, that it is appropriate to let the forgetting factor vary with the value of the external signal which is the argument of the coefficient functions. Some of the key properties of the modified method are studied by simulation