State Estimation in Unknown Non-Gaussian Measurement Noise using Variational Bayesian Technique

The problem of state space estimation of linear systems in an unknown non-Gaussian noise field is considered. A finite Gaussian mixture model (GMM) is used to model the non-Gaussian measurement noise with unknown statistics. A variational Bayesian expectation maximization (VBEM) algorithm is proposed to estimate the system states as well as the unknown parameters. In the variational Bayesian expectation (VBE) step, approximate inference is established to estimate the system state. The Gaussian mixture parameters are then updated in the variational Bayesian maximization (VBM) step. We also derive the true marginal posteriors to verify the performance of the proposed VBEM method. Computer simulations show that the proposed method has an improved estimation performance compared with other conventional approaches.