Modeling, Estimation and Optimal Filtration in Signal Processing

Chapter 8

H_∞ Estimation: an Alternative to Kalman Filtering?

8.1. Introduction

In the previous chapter, parametric approaches have proved to be powerful tools for the resolution of many problems in signal processing. Nevertheless, we must guard against over-estimating their usefulness and take proper account of their limitations.

Any given model is at best an approximation of the real world and modeling uncertainties always exist. The challenge in this approximation is twofold: choosing the most appropriate representation of the signal, and taking into account the properties of the noise which often disturbs the observations. It should be noted that this noise is itself modeled, leading to additional model uncertainties.

Further errors are introduced during the estimation of the model parameters. This estimation heavily depends on strong statistical assumptions. In Kalman filtering, for example, the maximum likelihood estimation of the state vector is obtained if and only if the driving process and the observation noise are both white, Gaussian and uncorrelated. Moreover, the classical algorithms give biased or non-consistent estimations when the observations are disturbed by an additive measurement noise. For further details on this matter; see section 2.2.6.7.

In this chapter, we analyze the relevance of the H_∞-based approaches in signal processing. The major advantage of these approaches is that the assumptions required for their implementation are less restrictive than those ...