A Bayesian Filtering Algorithm for Gaussian Mixture Models
This work addresses state estimation for systems modelled with Gaussian mixtures, but it appears incremental as it builds on existing reduction techniques without claiming major breakthroughs.
The authors tackled the problem of exponential growth in mixture terms for Bayesian filtering in Gaussian mixture state-space models by introducing a reduction step after updates, and demonstrated the algorithm on simulated systems including non-linear ones outside the model class.
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.