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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 17 State Estimation:Filtering (the Kalman Filter)

Summary

A recursive mean-squared state filter is called a Kalman filter, because it was developed by Kalman around 1959. Although it was originally developed within a community of control theorists, and is regarded as the most widely used result of so-called “modern control theory,” it is no longer viewed as a control theory result. It is a result within estimation theory; consequently, we now prefer to view it as a signal-processing result.

A filtered estimate of state vector x(k) uses all of the measurements up to and including the one made at time 4. The main purpose of this lesson is to derive the Kalman filter. Another purpose is to view the Kalman filter from many perspectives. ...

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