Gaussian Mixtures (GMs) can be used as a universal density approximator. As such, they can capture multimodal, skewed, and heavy-tailed characteristics of densities describing dynamic behaviour, which appear throughout finance, robotics, and fault detection. In this seminar, we consider smoothing for a class of state-space models where linear Gaussian Mixture Models (GMMs) are used to describe the process and measurement models. The GMM class allows for describing stochastically switched linear Gaussian systems, which exhibit multi-modal state and/or measurement noise, and outliers.

We use the Two-Filter (TF) approach to estimate the smoothed density accurately without a large computational cost. The proposed method offers significant improvements in accuracy for smoothing GMMs over the existing deterministic estimators, whilst being computationally cheaper than Sequential Monte Carlo (SMC) methods.