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TRACKING AND KALMAN FILTERING
MADE EASY
Tracking and Kalman Filtering Made Easy. Eli Brookner
Copyright # 1998 John Wiley & Sons, Inc.
ISBNs: 0-471-18407-1 (Hardback); 0-471-22419-7 (Electronic)
TRACKING AND
KALMAN FILTERING
MADE EASY
ELI BROOKNER
Consulting Scientist
Raytheon Comp.
Sudbury, MA
A Wiley-Interscience Publication
JOHN WILEY & SONS, INC
New York
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Chichester
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Weinheim
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Designations used by companies to distinguish their products are often claimed as trademarks.
In all instances where John Wiley & Sons, Inc., is aware of a claim, the product names appear
in initial capital or
ALL CAPITAL LETTERS. Readers, however, should contact the appropriate
companies for more complete information regarding trademarks and registration.
Copyright # 1998 by John Wiley & Sons, Inc. All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system or transmitted
in any form or by any means, electronic or mechanical, including uploading, downloading,
printing, decompiling, recording or otherwise, except as permitted under Sections 107 or 108
of the 1976 United States Copyright Act, without the prior written permission of the Publisher.
Requests to the Publisher for permission should be addressed to the Permissions Department,
John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011,
fax (212) 850-6008, E-Mail: PERMREQ @ WILEY.COM.
This publication is designed to provide accurate and authoritative information in regard to the
subject matter covered. It is sold with the understanding that the publisher is not engaged in
rendering professional services. If professional advice or other expert assistance is required,
the services of a competent professional person should be sought.
ISBN 0-471-22419-7
This title is also available in print as ISBN 0-471-18407-1.
For more information about Wiley products, visit our web site at www.Wiley.com.
To Larry and Vera,
Richard and Connie,
and Daniel, the little miracle
CONTENTS
PREFACE xiii
ACKNOWLEDGMENT xxi
PART I TRACKING, PREDICTION, AND SMOOTHING BASICS
1 g–h and g–h–k Filters 3
1.1 Why Tracking and Prediction are Needed in a Radar 3
1.2 g–h Filters 14
1.2.1 Simple Heruistic Derivation of g–h Tracking and
Prediction Equations 14
1.2.2 – Filter 23
1.2.3 Other Special Types of Filters 23
1.2.4 Important Properties of g–h Tracking Filters 24
1.2.4.1 Steady-State Performance for Constant-
Velocity Target 24
1.2.4.2 For What Conditions is the Constant-
Velocity Assumption Reasonable 24
1.2.4.3 Steady-State Response for Target with
Constant Acceleration 25
1.2.4.4 Tracking Errors due to Random Range
Measurement Error 27
1.2.4.5 Balancing of Lag Error and rms
Prediction Error 27
vii
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