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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 15 Elements of Discrete-time Gauss-Markov Random Sequences

Summary

This is another transition lesson. Prior to studying recursive state estimation, we first review an important body of material on discrete-time Gauss-Markov random sequences. Most if not all of this material should be a review for a reader who has had courses in random processes and linear systems.

A first-order Markov sequence is one whose probability law depends only on the immediate past value of the random sequence; hence, the infinite past does not have to be remembered for such a sequence.

It is in this lesson that we provide a formal definition of Gaussian white noise. We also introduce the basic state-variable model. It consists of a state equation and a measurement ...

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