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Lessons in Estimation Theory for Signal Processing, Communications, and Control, Second Edition by Jerry M. Mendel - Department of Electrical Engineering, University of Southern California, Los Angeles, California

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Lesson 3 Least-squares Estimation: Batch Processing

Summary

The main purpose of this lesson is the derivation of the classical batch formula of (weighted) least squares. The term batch means that all measurements are collected together and processed simultaneously. A second purpose of this lesson is to demonstrate that least-squares estimates may change in numerical value under changes of scale. One way around this difficulty is to use normalized data.

Least-squares estimates require no assumptions about the nature of the generic linear model. Consequently, the formula for the least-squares estimator (LSE) is easy to derive. We will learn in Lesson 8, that the price paid for ease in derivation is difficulty in performance evaluation.

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