Influence of Model Order on Change Detection in Noise-Free, Complex System

In all adaptation problems it is essential to estimate the system's (or signal's) characteristics as quickly as possible. There are several design variables that effect this ability. Forgetting factors in recursive algorithms, band-pass filtering to select interesting frequency ranges, and similar, are of major importance for this problem. Also the model order will affect the speed of adaptation since it influences both the "noise" level arising from unmodelled dynamics and the "variance" that depends on the number of estimated parameters. We discuss in this contribution the role of the model order for adaptation. The conclusion is that provided appropriate regularization is applied there are no disadvantages in the use of (very) high order models other than the computational burden.