Parameter tracking with partial forgetting method

This paper concerns the Bayesian tracking of slowly varying parameters of a linear stochastic regression model. The modelled and predicted system output is assumed to possess time-varying mean value, whereas its dynamics are relatively stable. The proposed estimation method models the system output mean value by time-varying offset. It formulates three extreme hypotheses on model parameters’ variability: (i) no parameter varies; (ii) all parameters vary; and (iii) the offset varies. The Bayesian paradigm then provides a mixture as posterior distribution, which is appropriately projected to a feasible class. Exponential forgetting at ‘second’ hypotheses level allows tracking of slow variations of respective hypotheses. The developed technique is an example of a general procedure called partial forgetting. Focus on a simple example allows to demonstrate essence of the approach. Moreover, it is important per se as it corresponds with a varying load of otherwise (almost) time-invariant dynamic system. Copyright © 2011 John Wiley & Sons, Ltd.