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

• Through simulations, we have demonstrated how different criteria of computing a point estimate lead to different results. The different criteria are listed in a paper by Z. Chen.
• Use of a robust and automated clustering method is proposed to cluster multi-modal data around their modes.
• Comparison of state estimators using two different types of estimators and two criterion is included in the case studies.

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.