xxii
INTRODUCTION
this introduction.
For
example, the states of a motor might include the currents
through the windings, and the position and speed of the motor shaft. The states
of an orbiting satellite might include its position, velocity, and angular orientation.
The states of an economic system might include per-capita income,
tax
rates, un-
employment, and economic growth. The states of a biological system might include
blood sugar levels, heart and respiration rates, and body temperature.
State estimation is applicable to virtually all areas of engineering and science.
Any discipline that is concerned with the mathematical modeling of its systems is
a likely (perhaps inevitable) candidate for state estimation. This includes electrical
engineering, mechanical engineering, chemical engineering, aerospace engineering,
robotics, economics, ecology, biology, and many others. The possible applications of
state estimation theory are limited only by the engineer’s imagination, which is why
state estimation has become such
a
widely researched and applied discipline in the
past few decades. State-space theory and state estimation was initially developed in
the
1950s
and
1960s,
and since then there have been a huge number of applications.
A
few applications are documented in
[Sor85].
Thousands of other applications can
be discovered by doing an Internet search on the terms “state estimation” and
“application,”
or
“Kalman filter” and ”application.”
State estimation is interesting to engineers for
at
least
two
reasons:
0
Often, an engineer needs to estimate the system states in order to implement
a
state-feedback controller.
For
example, the electrical engineer needs to
estimate the winding currents of a motor in order to control its position. The
aerospace engineer needs to estimate the attitude of a satellite in order to
control its velocity. The economist needs to estimate economic growth in
order to try to control unemployment. The medical doctor needs to estimate
blood sugar levels in order to control heart and respiration rates.
0
Often an engineer needs to estimate the system states because those states are
interesting in their own right.
For
example, if an engineer wants to measure
the health of an engineering system, it may be necessary to estimate the inter-
nal condition of the system using a state estimation algorithm. An engineer
might want to estimate satellite position in order to more intelligently sched-
ule future satellite activities. An economist might want to estimate economic
growth in order to make a political point, A medical doctor might want to
estimate blood sugar levels in order to evaluate the health of a patient.
There are many other fine books on state estimation that are available (see
Appendix
B).
This begs the question: Why yet another textbook on the topic of
state estimation? The reason that this present book has been written is to offer
a
pedagogical approach and perspective that
is
not available in other state estimation
books. In particular, the hope is that this book will offer the following:
0
A
straightforward, bottom-up approach that assists the reader in obtaining a
clear (but theoretically rigorous) understanding of state estimation. This is
reminiscent
of
Gelb’s approach [Ge174], which has proven effective for many
state estimation students of the past few decades. However, many aspects
of Gelb’s book have become outdated. In addition, many of the more recent
books on state estimation read more like research monographs and are not
entirely accessible to the average engineering student. Hence the need for the
present book.
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