Approximate Recursive Bayesian Estimation of Dynamic Probabilistic Mixtures

Majority of complex non-linear systems can be successfully modelled by a finite probabilistic mixture of linear models. The mixture model can be handled analytically, which is important for control of the system as well as for decision making. Quality of the model is a crucial requirement of all tasks of this type. The exact Bayesian methodology can not be used for estimation of this model, because complexity of the posterior distribution grows exponentially with number of data. Therefore, approximation techniques such as the quasi-Bayes algorithm must be used. This paper introduces a new estimation algorithm, which is based on minimization of Kullback-Leibler distance between the proper Bayesian posterior density and an approximate posterior density. The approximate posterior distribution is chosen from the exponential family in order to achieve numerically efficient estimation.