Introduction

Kalman filtering is a powerful technology for state estimation of a dynamic system, which finds applications in many areas, including navigation, guidance, data integration, pattern recognition, tracking, and control systems. Kalman filtering yields an optimal estimator when the system is linear and innovation and noise are Gaussian. The Gaussian assumption is, however, seldom the case in real-world applications, where noise distributions tend to be skewed, multimodal, or heavy-tailed. This will create problems for Kalman filtering because the solution is no longer the optimal and state estimation performance may degrade seriously in the case of non-Gaussian noise. To solve the performance degradation in non-Gaussian noises, robust Kalman filtering including three categories is reviewed. Especially, Kalman filtering under information theoretic criteria can achieve excellent performance in complicated non-Gaussian noises with reasonable computation, yielding great practical application potential. In this chapter, the detailed introduction about these methods is presented.