Discrete Stochastic Processes and Optimal Filtering, 2nd Edition

Introduction

The objective of this book is the progressive and rigorous presentation of the bases of discrete optimal filtering. The optimal character can be understood in the sense that we always choose that criterion at the minimum of the norm −L² of error.

Chapter 1 tackles random vectors, their principal definitions and properties.

Chapter 2 discusses the subject of Gaussian vectors. Given the practical importance of this notion, the definitions and results are accompanied by numerous commentaries and explanatory diagrams.

Chapter 3, “Introduction to Discrete Time Processes”, is by its very nature more “physics-based” than the preceding chapters and can be considered as an introduction to numerical filtering. Results that are essential for what follows will be given in this chapter.

Chapter 4, “Estimation”, brings us the pre-requisites essential for the construction of optimal filters. The results obtained on projections in Hilbert spaces make up the cornerstone of future demonstrations.

Chapter 5 discusses the Wiener filter, an electronic device well adapted to processing second-order stationary signals. Practical calculations of such filters, as an answer to finite or infinite pulses, will be developed.

Adaptive filtering, which is the subject of Chapter 6, can be considered as a relatively direct application of the determinist or stochastic gradient method. At the end of the adaptation or convergence process, we again encounter the Wiener filter.

This book is completed with ...