Fundamentals of Estimation Theory

Contents

Fundamentals of Estimation Theory#

Applications of estimation theory typically require obtaining an estimate either of

  • a specific parameter

  • a desired waveform.

In parameter estimation, we consider two cases:

  • known distribution

  • unknown distributions of the observables.

We also study properties of estimators, which characterize the performance and behavior of the estimates.

We will consider various estimation methods on estimating:

  • single deterministic parameter

  • vector deterministic parameters

  • random single parameter

  • random vector parameters In each of these cases, knowledge of specific distributions is presumed.

Observables are used to produce an estimate of the parameters of interest

An important question to resolve is: How good is the estimate?

To answer the question of the quality of the estimate, it is important to understand properties associated with a good estimate, such as

  • unbiased

  • consistent

  • invariant

  • minimum variance

  • efficient

References#

The contents of the sections in this chapter are based on the following materials.

  • T. Schonhoff and A. Giordano, Detection and Estimation Theory and its Applications. Prentice Hall, 2006 , Chapter 10

Contents