Lessons in Estimation Theory for Signal Processing, Communications, and Control, Second Edition

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 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 ...