Computing point estimates from a non-Gaussian posterior distribution using a probabilistic k-means clustering approach

The Kalman filter algorithm gives an analytical expression for the point estimates of the state estimates, which is the mean of their posterior distribution. Conventional Bayesian state estimators have been developed under the assumption that the mean of the posterior of the states is the 'best estimate'. While this may hold true in cases where the posterior can be adequately approximated as a Gaussian distribution, in general it may not hold true when the posterior is non-Gaussian. The posterior distribution, however, contains far more information about the states, regardless of its Gaussian or non-Gaussian nature. In this study, the information contained in the posterior distribution is explored and extracted to come up with meaningful estimates of the states. The need for combining Bayesian state estimation with extracting information from the distribution is demonstrated in this work. (C) 2013 Elsevier Ltd. All rights reserved.