Online EM algorithm for joint state and mixture measurement noise estimation

In this study, we aim to estimate the unknown multi-modal measurement noise distribution of nonlinear state space models. The unknown noise distribution is modeled as a mixture of exponential family of distributions. We use the Expectation-Maximization (EM) method in order to jointly estimate the unknown parameters as well as the states. The online version of the EM algorithm is implemented by using particle filtering techniques. The resulting algorithm is a noise adaptive particle filter which is applicable to many sensor models having multi-modal noise distributions with unknown parameters.