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Machine Learning by Sergios Theodoridis

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Chapter 4

Mean-Square Error Linear Estimation

Abstract

In this chapter, mean-square linear estimation is discussed and the normal equations are derived. The orthogonality theorem concerning random variables is introduced as an alternative for their derivation. Issues concerning complex random variables, such as widely-linear estimation and Wirtinger’s calculus are presented. Some typical applications of MSE, such as image deblurring, interference cancellation, system identification and channel equalization are defined. Issues related to the efficient solution of the normal equations in the context of linear filtering are discussed and the Levinson and lattice-ladder algorithms are derived. The Gauss-Markov theorem for MSE of linear models ...

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