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

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5

CLASSICAL BAYESIAN STATE–SPACE PROCESSORS

5.1 INTRODUCTION

In this chapter we introduce the concepts of statistical signal processing from the Bayesian perspective using state–space models. We first develop the Bayesian paradigm using the generic state–space representation of the required conditional distributions and show how they propagate within the Bayesian framework. Next we start with the linear (time-varying) Gauss-Markov model and develop the required conditional distributions leading to the well-known Kalman filter processor [1]. Based on this fundamental theme, we progress to the idea of linearization of the nonlinear state–space system developed in the previous chapter, where we derive the linearized Bayesian processor (LZ-BP). It is shown that the resulting processor provides a solution (time-varying) to the nonlinear state estimation. We then develop the extended Bayesian processor (XBP) or equivalently the extended Kalman filter (EKF), as a special case of the LZ-BP linearizing about the most currently available estimate. Next we investigate a further enhancement of the XBP by introducing a local iteration of the nonlinear measurement system. Here the processor is called the iterated-extended Bayesian processor (IX-BP) and is shown to produce improved estimates at a small computational cost in most cases. We summarize the results with a case study implementing a 2D-tracking filter.

5.2 BAYESIAN APPROACH TO THE STATE–SPACE

In the previous chapter, we briefly developed ...

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