Kalman Filtering Techniques for Radar Tracking

252 Pages·2016·3.94 MB·English

by  Ramachandra K.V.

Kalman Filtering Techniques
for Radar Tracking
K. V. Ramachandra
Elecf ronics and Radar Developmenf Esf ablis hmenf
Ba ng a lore, India
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Preface
The Kalman filter theory published in 1960 significantly boosted the devel-
opment of sophisticated digital filter algorithms for tracking space vehicles.
As a result, a large number of tracking filters have been developed and their
algorithms published in journals.
Tracking of objects based on Kalman filter theory has become an
established technique of fundamental importance in both engineering
applications and scientific investigations. The central problem is that radar
and sonar systems, optical telescopes, and infrared sensors used in civil
and defense applications require updated information obtained continu-
ously on the parameters that describe the dynamics of such targets as
satellites, missiles, aircraft, ships, submarines, RPVs, and other objects
having a significant relative motion with respect to the sensor.
Recent developments such as track-while-scan systems, phased array
radar tracking, airborne radar tracking, multitarget tracking, multisensor
tracking, and multitarget multisensor tracking have not only increased
the scope of tracking technology but also added new dimensions to it.
Specifically, the position of a target such as an aircraft or similar
vehicle is measured at discrete intervals of time by an automatic
track-while-scan radar sensor, and the measurements are reported to a radar
data processor (RDP).The reports obtained from successive radar scans are
processed by the RDP and suitable tracks are formed.
A computer tracking filter is used to smooth the report data corrupted
by range noise and angular noise caused by the electronic and mechanical
components of the measuring device.
The tracking filter is the most important component of an
RDP/ surveillance system. It processes the target radar measurements,
reduces the measurement errors, estimates the position, velocity, and/ or
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vi Preface
acceleration of the target at any instant of time, and predicts the future
position of the target. Hence the tracking filter is the heart and soul of
a radar data processing system.
This book deals with the development of different types of tracking
filters based on the Kalman filtering techniques for radar tracking
applications.
Chapter 1 presents the discrete-time formulation of Kalman filter, the
continuous-time and continuous-discrete-time formulations of Kalman-
Bucy filters, and the extended Kalman filter.
Chapter 2 deals with the application of Kalman filter theory for
developing one-dimensional trackers for tracking targets such as an aircraft
moving with constant velocity or constant acceleration motion when pos-
ition measurements are obtained by a track-while-scan radar sensor through
random noise. Three models are discussed and their steady state results
obtained analytically.
Chapter 3 deals with the extension of one-dimensional models to two
dimensions for tracking an aircraft or any other space vehicle by a
two-dimensional track-while-scan radar that measures the range and bear-
ing of the target. The tracking operation is assumed to be done in the
cartesian coordinate system, and the coupling between the quantities
measured by the radar and the cartesian coordinate system is explicitly con-
sidered in the development of two-dimensional models.
Chapter 4 deals with the extension of one-dimensional models to three
dimensions for tracking an aircraft or any other target with range, bearing,
and elevation measurements obtained by a three-dimensional
track-while-scan radar sensor. The tracking operation is assumed to be
performed in cartesian coordinates and the coupling is explicitly considered.
Chapter 5 deals with the continuous-time Kalman tracking filters with
position measurements. Fitzgerald’s steady state solutions of ECV and ECA
models are discussed. The general solution of the second-order ECV model
of Nash is given. The random walk velocity model and the random walk
acceleration model are also presented.
Chapter 6 deals with the continuous-discrete-time Kalman tracking
filters with position measurements. Singer’s ECA model and Fitzgerald’s
steady state performance analysis are discussed. Vaughan’s nonrecursive
algorithm is briefly described. The steady state results of ECV and ECA
filters based on Vaughan’s nonrecursive algorithm are presented. Finally,
Beuzit’s steady state results of the ECA filter obtained by a comparison
of Kalman and Wiener filter theories are presented.
Preface vii
Chapter 7 deals with con tin uous-discrete-time one-dimensional
models with position and velocity measurements. A two-state model, an
ECV target tracking filter, Fitzgerald’s steady state analysis of the ECA
model, and a three-state filter are discussed and their steady state solutions
are presented.
Chapter 8 deals with continuous-time one-dimensional tracking filters
with position and velocity measurements. A two-state model and a
three-state model are discussed.
Chapter 9 deals with maneuvering target tracking filters.
Bar-Shalom-Birmiwal’s model is discussed and Blom-Bar-Shalom’s
interacting multiple model is presented.
Chapter 10 deals with tracking a maneuvering target in clutter.
Validation region or gate, the probabilistic data association filter, and Bar-
Shalom-Chang-Blom’s model for automatic track formation are discussed.
Chapter 11 deals with an introduction to multitarget tracking. The
JPDAF and Reid’s algorithm are mentioned.
This book provides enough information in the selection of trackers to
meet the requirements of practicing engineers. It also provides sufficient
material for advanced students to take up further work in the field.
K. V. Ramachandra
Acknowledgments
I wish to express my gratitude to Dr. A. P. J. Abdul Kalam, Scientific
Adviser to the Minister for Defence, and Dr. V. K. Aatre, Chief Controller
of Research & Development, DRDO, New Delhi, and Dr. G. M. Cleetus,
Director, Mr. N. P. Ramasubba Rao, former Director, Mr. K. U. Limaye,
Associate Director, Dr. S. Christopher, Divisional Officer of “C” Radar
Division, Mr. K. N. Dinesh Kumar, Scientist “D,” Mr. J. Paramashivan,
Technical Officer “B,” and other colleagues at the Electronics and Radar
Development Establishment, Bangalore, India, for their help and encour-
agement in the development of the book. Credit goes to Miss S. Sukanya
for the cover artwork.
I am also grateful to Mr. R. P. Mohan of Bharath Electronics Ltd.,
Bangalore; Mr. B. N. Ramesh of Metabyte, Fremont, California; Mr.
B. R. Mohan and Mrs. B. R. Geetha of National College, Bangalore;
and Mrs. B. R. Gayathri of Fremont, California, for their invaluable
interest and help in the development of the book.
I am deeply indebted to Mrs. Chaya Ramachandra for her patience
and perseverance during the preparation of the book.
Finally, I wish to thank Dr. Y. Bar-Shalom, Distinguished Professor,
University of Connecticut, Storrs, Connecticut, for his help in the develop-
ment of the book.
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Contents
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1. Kalman Filter 1
2. Discrete-Time One-Dimensional Tracking Filters 9
3. Discrete-Time Two-Dimensional Tracking Filters 45
4, Discrete-Time Three-Dimensional Tracking Filters 61
5. Continuous-Time One-Dimensional Tracking Filters
with Position Measurements 75
6, Contiii uo us- Discre te-Time One- Dimensional Tracking
Filters with Position Measurements 87
7. Continuous-Discrete-Time One-Dimensional Tracking
Filters with Position and Rate Measurements 117
8. Continuous-Time One-Dimensional Kalman Tracking
Filters with Posit ion and Velocity Measurements 167
9. Maneuvering Target Tracking 191
10. Tracking a Maneuvering Target in Clutter 209
1I. Introduction to Multitarget Tracking 227
Index 23I
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