This monograph aims to present the recent advances in state estimation, in terms of relaxing the conventional assumption that probability densities remain Gaussian. The book explains how MCC is integrated into the conventional Bayesian estimation framework and their implementation to real-life problems. Features:Reviews well-established non-Gaussian estimation methods including applications of techniques Covers relaxation of gaussian assumption Discusses challenges in formulating non-liner non-Gaussian estimation framework Illustrates the applicability of the algorithms mentioned to real-life problems Explores derivation of non-linear non-Gaussian estimation framework based on maximum correntropy criterion This book is aimed at researchers and graduate students in electrical engineering, robotics, and dynamic systems.