Adaptive Identification with Multiple Forgetting Factors

Recently, several adaptive identification methods have been developed for non-stationary stochastic systems. Among those, much attentions have been paid to the use of an adaptive (time-varying) forgetting factor depending the level of alertness of the systems to estimate the time-varying parameters. However, its adjustment is usually complex and time-consuming. We propose in this paper an adaptive identification method called multiple forgetting factors method (MFF method) for non-stationary linear stochastic systems with time-varying parameters. The parameter estimates are constructed as a weighted sum of the estimates obtained by multiple recursive least squares methods operating in parallel with a constant forgetting factor. The weights are adjusted to fit the time variation of the parameters using modified Bayes rule. Thus, the identification method has a simple structure and is quite easy to implement. It is shown by simulation experiments that the proposed method works well not only for systems with gradually changing parameters but also for systems with abruptly changing ones.