Tracking time-varying-coefficient functions

A method for adaptive and recursive estimation in a class of non-linear aut oregressive models with external input is proposed. The model class conside red is conditionally parametric ARX-models (CPARX-models), which is convent ional ARX-models in which the parameters are replaced by smooth, but otherw ise unknown, functions of a low-dimensional input process. These coefficien t functions are estimated adaptively and recursively without specifying a g lobal parametric form, i.e, the method allows for on-line tracking of the c oefficient functions. Essentially, in its most simple form, the method is a combination of recursive least squares with exponential forgetting and loc al polynomial regression. It is argued, that it is appropriate to let the f orgetting factor vary with the value of the external signal which is the ar gument of the coefficient functions. Some of the key properties of the modi fied method are studied by simulation. Copyright (C) 2000 John Wiley & Sons , Ltd.