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Bayesian Signal Processing: Classical, Modern and Particle Filtering Methods by James V. Candy

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4

STATE–SPACE MODELS FOR BAYESIAN PROCESSING

4.1 INTRODUCTION

In this chapter we investigate the development of models for Bayesian estimation [1–15] using primarily the state–space representation—a versatile and robust model especially for random signals. We start with the definition of state and the basic principles underlying these characterizations and then show how they are incorporated as propagation distributions for Bayesian processors in the following chapter. We review 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. Next we develop the stochastic version leading to Gauss-Markov representations when the models are driven by white noise and then proceed to the nonlinear case [6–15]. Here we again drive the models with white Gaussian noise, but the results are not necessarily Gaussian. We develop linearization techniques based on Taylor-series expansions to arrive at linearized Gauss-Markov models.

State–space models are easily generalized to multichannel, nonstationary, and nonlinear processes. They are very popular for model-based signal processing primarily because most physical phenomena modeled by mathematical relations naturally occur in state–space form (see [13] for details). With this motivation in mind, let us proceed to investigate the state–space representation in a more general form to at least “touch” ...

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