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Tracking time‐varying‐coefficient functions
Author(s) -
Nielsen Henrik Aa.,
Nielsen Torben S.,
Joensen Alfred K.,
Madsen Henrik,
Holst Jan
Publication year - 2000
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/1099-1115(200012)14:8<813::aid-acs622>3.0.co;2-6
Subject(s) - autoregressive model , parametric statistics , mathematics , polynomial , parametric model , recursive least squares filter , exponential function , control theory (sociology) , simple (philosophy) , computer science , algorithm , statistics , adaptive filter , mathematical analysis , artificial intelligence , philosophy , control (management) , epistemology
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 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. Copyright © 2000 John Wiley & Sons, Ltd.