State–Space Models for Bayesian Processing

This chapter investigates the development of models for Bayesian estimation using primarily the state‐space representation‐a versatile and robust model especially for random signals. It starts with the definition of state and the basic principles underlying these characterizations and then shows how they are incorporated as propagation distributions for Bayesian processors. The chapter reviews the basics of state‐space model development with all of their associated properties starting with the continuous‐time processes, then sampled‐data systems, and finally proceeding to the discrete‐time state‐space. It develops the stochastic version leading to Gauss‐Markov representations when the models are driven by white noise and then proceed to the nonlinear case. The chapter drives the models with white Gaussian noise, but the results are not necessarily Gaussian. It develops linearization techniques based on Taylor‐series expansions to arrive at linearized Gauss‐Markov models.