Optimal Filtering Problems

A Ahlén and M Sternad

Chapter 5 in K Hunt, ed: Polynomial Methods in Optimal Control and Filtering,
pp120-161, Control Engineering Series, Peter Peregrinus, London, 1993.

Outline:

In this chapter, we discuss the utility of the polynomial approach in the area of signal processing and communications. By studying specific model structures, considerable engineering insight can be gained.

Abstract:

Minimisation of mean-square error criteria by linear filters is considered. We focus on the optimisation of realisable discrete-time IIR-filters, to be used for prediction, filtering or smoothing of signals. Stochastic models of possibly complex-valued signals are assumed known.

We discuss how the classical Wiener approach and the inner-outer factorisation approach relate to the polynomial methods based on variational arguments and completing the squares. The purpose of this discussion is not only to compare advantages and drawbacks, but also to emphasise similarities, to link and increase understanding of the different approaches. To understand how they relate to each other, design equations for a simple filtering problem is derived using each approach.

The polynomial approach, based on variational arguments, is then used to study a collection of signal processing and communications problems. Numerical examples are not included, but can be found in the papers indicated below.

Contents:

5.1. Introduction

5.2. A set of filtering problems

5.3. Solution methods

5.4. Multisignal deconvolution

5.5. Differentiation and state estimation

5.6. Decision feedback equalization

5.7. Concluding remarks

Related publications:

Paper in IEEE Trans. AC 1995, on a probabilistic approach to multivariable robust filtering and open-loop control.
Paper in IEEE Trans. SP 1991 on multivariable Wiener filter design using polynomial equations.
Paper in IEEE Trans. ASSP 1989 on design of scalar deconvolution estimators.
Paper in IEEE Trans. SP 1991 on the differentiating filters of Section 5.5.
Paper in IEEE Trans. IT 1990 on the decision feedback equalizer of Section 5.6.
Later book chapter (Academic Press 1994), which includes design examples.

Source:

Chapter In Pdf