Parameter tracking with partial forgetting method

SUMMARY 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.