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Kalman filtering and sequential Bayesian analysis

In this paper we present an overview of the state of the art in Kalman filtering and dynamic Bayesian linear and nonlinear models. We present some of the basic results including the derivation of Kalman filtering equations as well as recent advances in Kalman filter models and their extensions including non‐Gaussian state‐space models. In so doing, we take a Bayesian perspective and discuss parameter learning in state‐space models which typically involves Markov chain Monte Carlo and sequential Monte Carlo methods. We present particle filtering and Bayesian particle learning techniques for state space models and discuss recent advances.