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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 20 State Estimation: Smoothing

Summary

This is the first of two lessons on smoothing. A smoothed estimate of state vector x(k) not only uses measurements that occur earlier than tk, plus the one at tk, but also uses measurements to the right of tk, Consequently, smoothing can never be carried out in real time, because we have to collect “future” measurements before we can compute a smoothed estimate. If we don’t look too far into the future, then smoothing can be performed subject to a delay of LT sec, where T is our data sampling time and L is a fixed positive integer that describes how many sample points to the right of tk are to be used in smoothing.

Depending on how many future measurements are used and how they are used, it is possible ...

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