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.

翻译：针对一类可通过高斯混合模型建模的状态空间系统，本文提出了一种贝叶斯滤波算法。通常，该滤波问题的精确解涉及混合项数量的指数增长，本文通过在时间更新和量测更新后分别引入高斯混合约简步骤来处理这一问题。此外，本文还给出了该统一算法的平方根实现，并在多个仿真系统上对该算法进行了性能评估，包括对两个严格超出本文所考虑类别之非线性系统的状态估计。