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Tutorial on Filtering, Restoration, and State Estimation |
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@TechReport{Brown:TR95b,
author = {Christopher M. Brown},
title = {Tutorial on Filtering, Restoration, and State Estimation},
institution = {Computer Science Dept. University of Rochester},
year = {1995},
number = {534},
address = {Rochester NY},
month = {June},
abstract = {
This tutorial is dedicated to our long-suffering 442 students, and to the
excellent authors from whom I shamelessly cribbed this work. It is a pure
cut-and-paste job from my favorite sources on this material. This is not my
own work---think of me as an editor working without his authors' permissions.
Readers should know that original authors are usually easier to understand than
rehashed versions. If this presentation helps you, good. If not it at least
helped me sort a few things out.
I assume knowledge of all necessary linear systems theory, differential
equations, statistics, control theory, etc. We start with the ideas of
filtering, smoothing, prediction, and state estimation. Wiener filtering and
its associated intellectual framework follows, with a brief foray into ARMA
filtering. The idea of recursive estimation is introduced to give some
motivation for the slog ahead, and then we start with basic concepts in maximum
likelihood, maximum a posteriori, and least-squares estimation. The strategy
is to work toward the Kalman filtering equations by showing how they are simply
related to general least-squares estimation. After Kalman filtering, some
simpler versions of recursive filters are presented. There are appendices on
the orthogonality principle, the matrix inversion lemma, singular value
decomposition, partial C and LISP code, and a worked example. }
}