A Class of FFT Based Algorithms for Linear Estimation

摘要

In the past two decades since the advent of Kalman's recursive filter, numerous algorithms for linear estimation have emerged. Most of these algorithms are recursive and rely on solving a Riccati equation or equivalent recursive equations. It will be shown how some of the classical problems such as Linear Smoothing and Recursive Block Filtering problems can be solved exactly by some new nonrecursive algorithms which are based on the Fast Fourier Transform (FFT). Moreover, these algorithms are readily modified to generate the Riccati matrix at specified times, if this is desired. These results are then extended to a block filtering algorithm, where data is received and smoothed recursively block by block. Real time batch processing applications include image processing and array processing of signals.