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. Some key points discussed in the book are-Reviews well-established non-Gaussian estimation methods including applications of techniquesCovers relaxation of gaussian assumptionDiscusses challenges in formulating non-liner non-Gaussian estimation frameworkIllustrates the applicability of the algorithms mentioned to real-life problemsExplores derivation of non-linear non-Gaussian estimation framework based on maximum correntropy criterionThis book is aimed at researchers and graduate students in electrical engineering, robotics, and dynamic systems.