  A Bayesian filtering algorithm is developed for a class of state-space
systems that can be modelled via Gaussian mixtures. In general, the exact
solution to this filtering problem involves an exponential growth in the number
of mixture terms and this is handled here by utilising a Gaussian mixture
reduction step after both the time and measurement updates. In addition, a
square-root implementation of the unified algorithm is presented and this
algorithm is profiled on several simulated systems. This includes the state
estimation for two non-linear systems that are strictly outside the class
considered in this paper.
