@ARTICLE\{IMM2000-01043, author = "H. A. Nielsen and T. S. Nielsen and A. K. Joensen and H. Madsen and J. Holst", title = "Tracking time-varying coefficient-functions", year = "2000", keywords = "Adaptive and recursive estimation; Non-linear models; Time-varying functions; Conditional parametric models; Non-parametric method.", pages = "813-828", journal = "International Journal of Adaptive Control and Signal Processing", volume = "14", editor = "", number = "8", publisher = "", url = "http://www2.compute.dtu.dk/pubdb/pubs/1043-full.html", abstract = "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.\$\backslash\$ the method allows for on-line 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." }