Estimation of State-Space Models with Gaussian Mixture Process Noise

Abstract

State-space models are widely used to estimate latent dynamic processes from noisy and low-dimensional observations. When applying these models to real data, it is commonly assumed that the state dynamics are governed by Gaussian statistics. However, this assumption does not hold in applications where the process noise is composed of various exogenous components with heterogeneous statistics, resulting in a multimodal distribution. In this work, we consider a state-space model with Gaussian mixture process noise to account for such multimodality. We integrate the Expectation Maximization algorithm with sequential Monte Carlo methods to jointly estimate the Gaussian mixture parameters and states from noisy and low-dimensional observations. We validate our proposed method using simulated data inspired by auditory neuroscience, which reveals significant gains in state estimation as compared to widely used techniques that assume Gaussian state dynamics.