. . .
xv111 PREFACE
The approach is a balanced combination of mathematics
- linear systems and probability
theory - in order to understand how a state estimator should be designed, with the necessary
tools from statistics in order to interpret the results. The use of statistical techniques has been
somewhat neglected in the engineering literature pertaining to state estimation, but it is necessary
for (the nontrivial task of) interpreting stochastic data and answering the question whether a
design can be accepted as “good.” This is particularly important for practicing engineers and is
presented in sufficient detail based on our belief (and extensive experience with real systems)
that it should be an integral part of advanced engineering educati0n.l
The material covers the topics usually taught in control-oriented EELsystems and aeronauti-
cal engineering programs. The relevance extends to other areas dealing with control in mechan-
ical or chemical engineering. Recently, the state estimation techniques have been gaining wider
attention due to their applicability to such fields as robotics, computer vision for autonomous
navigation, and image feature extraction with application to medical diagnosis. While the course
is mainly directed toward the M.S. students, it is also part of the Ph.D. program at the University
of Connecticut, with the intent of providing the students with the knowledge to tackle real-world
problems, whether by using existing algorithms or by developing new ones. 2
The presentation of the material stresses the algorithms, their properties and the under-
standing of the assumptions behind them. We do not subscribe to the philosophy of “Give me
the facts and don’t bother me with details.” Consequently, proofs are given to the extent that
they are relevant to understanding the results. This is intended to be a modest step in bridging
the much talked about “gap between theory and practice” - it will illustrate to students the
usefulness of state estimation for the real world and provide to engineers and scientists working
in industry or laboratories a broader understanding of the algorithms used in practice. It might
also avoid the situation summarized by a participant at one of the continuing education courses
taught by the first author as follows: “Although I studied Kalman filters when I worked to-
ward my Ph.D. (at one of the major U.S. universities), I did not expect that they worked with
real data.” This happens when, because of the theorems, the students cannot see the forest of
applications.
Tuning of a KF - the choice of its design parameters - is an art. One of the contributions
of this text is to make it less of a black magic technique and more of a systematic approach
by connecting the filter parameters to physical system parameters, namely, the object motion
uncertainty - its predictability - and the sensor measurement uncertainty - the sensor errors.
This is particularly important when KFs are used as modules in an adaptive estimator, like the
Interacting Multiple Model (IMM) estimator. Another contribution is providing guidelines as to
what estimator should be used in specific problems, namely, when an (adaptive) IMM estimator
is preferable over a KF.
The Text and Hyperlinked Viewgraph Format
The format of this text is also unique - teztgraphTM - in that it dares to attempt to accomplish
two goals in one format: to serve as a self-contained concise text, without excess verbosity, and,
at the same time, to enable the lecturer to use the pages of this text as viewgraphs for lectures. To
this purpose, a double-spaced version of all the pages of this text (with appropriate page breaks)
‘The authors disclaim any responsibility for severe damage readers might suffer when falling asleep face forward
while reading this book.
2As Ben Fran klin said, the goal in his life was “to rise to an (sic) happy mediocrity and secure competency.” Our
objective is to provide the tools for future successful applications.