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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 21 State Estimation: Smoothing (General Results)

Summary

The purpose of this lesson is to develop general formulas for fixed-interval, fixed-point, and fixed-lag smoothers. The structure of our “most useful” fixed-interval smoother is very interesting, in that it is a two-pass signal processor. First, data are processed in the forward direction by a Kalman filter to produce the sequence of innovations Image Then these innovations are processed in a backward direction by a time-varying recursive digital filter that resembles a backward-running recursive predictor. The noncausal nature of the fixed interval smoother is very apparent from this ...

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