实例介绍
【实例简介】
随机有限集理论系统介绍及其在多目标多传感器中的应用和相关算法
Statistical Multisource-Multitarget Information Fusion Ronald p s. mahler ARTECH HOUSE BOSTON LONDON rtechhouse.c Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the U.S. Library of Congress British Library cataloguing in Publication Data A catalogue record for this book is available from the british library ISBN13:978-1-59693-092-6 Cover design by Yekaterina Ratner O 2007 ARTECH HOUSE, INC 685 Canton Street Norwood. MA 02062 All rights reserved Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including pho- tocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark 10987654321 ToIR Goodman Contents Preface Acknowledgments Chapter 1 Introduction to the book 1.1 What Is the Purpose of This Book? 1.2 Major Challenges in Information Fusion 7 1.3 Why Random Sets--or FISST? 1.3.1 Why Isnt Multitarget Filtering Straightforward? 1.3.2 Beyond heuristics 10 1.3.3 How Do Single-Target and Multitarget Statistics Differ? 1.3.5 What Is Formal Bayes Mouang ous Data 1.3.4 How Do Conventional and biguous Data Differ? 11 1.3.6 How Is Ambiguous Information Modeled? 1.3.7 What Is Multisource-Multitarget Formal Modeling? 1 1. 4 Random sets in Information fusion 15 1.4.1 Statistics of Multiobject Systems 1.4.2 Statistics of Expert Systems 16 1.4.3 Finite Set statistics 1. 5 Organization of the Book 1.5.1 Part I: Unified Single-Target Multisource Integration 17 1.5.2 Part II: Unified Multitarget -Multisource Integration 20 1.5.3 Part Ill: Approximate Multitarget Filtering 21 1.5.4 Appendixes 22 Contents I Unified Single-Target Multisource Integration Chapter 2 Single-Target Filtering 2. 1 Introduction to the chapte 2.1.1 Summary of Major Lessons Learned 26 2.1.2 Organization of the Chapter 2.2 The Kalman filter 2.2.1 Kalman filter initializatio 28 2.2.2 Kalman filter predictor 28 2.2.3 Kalman Filter Corrector 29 2. 2. 4 Derivation of the kalman filter 30 2.2.5 Measurement Fusion Using the Kalman filter 32 2.2.6 Constant-Gain Kalman Filters 2.3 Bayes Formulation of the Kalman Filter 2.3. 1 Some Mathematical Preliminaries 2.3.2 Bayes Formulation of the KF: Predictor 2.3.3 Bayes Formulation of the KF: Corrector 2.3.4 Bayes Formulation of the KF: Estimation 40 2. 4 The Single-Target Bayes Filter 42 2.4.1 Single-Target Bayes Filter: An Illustration 2.4.2 Relationship Between the Bayes and Kalman Filters 45 2.4.3 Single-Target Bayes Filter: Modeling 51 2.4.4 Single-Target Bayes Filter: Formal Bayes Modeling 56 2.4.5 Single-Target Bayes Filter: Initialization 61 2.4.6 Single-Target Bayes Filter: Predictor 2.4.7 Single- Target Bayes Filter: Corrector 62 2.4.8 Single-Target Bayes Filter: State Estimation 2. 4.9 Single- Target Bayes Filter: Error Estimation 2.4.10 Single-Target Bayes Filter: Data Fusion 2.4.11 Single-Target Bayes Filter: Computation 68 2.5 Single-Target Bayes Filter: Implementation 70 2.5.1 Taylor Series Approximation: The EKF 2.5.2 Gaussian-Mixture Approximation 72 2.5.3 Sequential Monte Carlo Approximation 2.6 Chapter exercises 87 Chapter 3 General Data Modeling 89 3.1 Introduction to the chapte 3.1.1 Summary of Major Lessons Learned Contents 3.1.2 Organization of the Chapter 3.2 Issues in Modeling Uncertainty 3.3 Issues in Modeling Uncertainty in Data 3.4 Examples 3.4.1 Random, Slightly Imprecise Measurements 97 3.4.2 Imprecise, Slightly Random Measurements 101 3.4.3 Nonrandom Vague measurements 102 3.4.4 Nonrandom Uncertain Measurements 103 3.4.5 Ambiguity Versus Randomness 3.5 The Core Bayesian Approach 3.5.1 Formal Bayes Modeling in General 109 3.5.2 The Bayes Filter in General 110 3.5.3 Bayes Combination Operators 3.5.4 Bayes-Invariant Measurement Conversion 3.6 Formal Modeling of Generalized Data 114 3.7 Chapter Exercise 117 Chapter 4 Random Set Uncertainty Representations 119 4.1 Introduction to the Chapter l19 4.1.1 Summary of Major Lessons Learned 119 4.1.2 Organization of the Chapter 120 4.2 Universes, Events, and the logic of events 120 4.3 Fuzzy Set Theory 121 4.3.1 Fuzzy logics 122 4.3.2 Random Set representation of Fuzzy events 4.3.3 Finite-Level Fuzzy Sets 126 4.3. 4 Copula Fuzzy Logic 129 4.3.5 General Random Set Representations of Fuzzy Sets 131 4. 4 Generalized Fuzzy Set Theory 133 4.4.1 Random Set Representation of Generalized Fuzzy Events 134 4.5 Dempster-Shafer Theory 134 4.5. 1 Dempster,s Combinatie 136 4.5.2 "Zadeh's Paradox" and Its Misinterpretation 138 4.5.3 Converting b.m. as to probability distributions 141 4.5.4 Random Set Representation of Uncertain events 143 4.6 Fuzzy Dempster-Shafer Theor 4.6.1 Random Set Representation of Fuzzy ds Evidence 145 Contents 4.7 Inference rules 147 4.7.1 What Are rules? 147 4.7.2 Combining Rules Using Conditional Event Algebra 148 4.7.3 Random Set Representation of First-Order rules 150 4.7.4 Random Set Representation of Composite rules 151 4.7.5 Random Set Representation of Second-Order Rules 152 4.8 Is Bayes Subsumed by Other Theories? 4.9 Chapter Exercises 154 Chapter 5 UGA Measurements 57 5.1 Introduction to the chapte 157 5.1.1 Notation 158 5.1.2 Summary of Major Lessons Learned 159 5.1.3 Organization of the chapter 161 5.2 What Is a uGA Measurement? 162 5.2.1 Modeling UGA Measurement 5.2.2 Modeling the Generation of UGA Measurements 1 5.3 Likelihoods for UGA Measurements l64 5.3.1 Special Case: 0 Is Statistical 165 5.3.2 Special Case: e Is Fuzzy 166 5.3.3 Special Case: e Is Generalized Fuzzy 5.3.4 Special Case: e Is Discrete/ Dempster-Shafer 5.3.5 Special Case: e Is Fuzzy Dempster-Shafer 173 5.3.6 Special Case: O Is a First-Order Fuzzy rule 174 5.3.7 Special Case: e Is a Composite Fuzzy rule l79 5.3.8 Special Case: 0 Is a Second-Order Fuzzy rule 5. 4 Bayes Unification of UGA Fusion 181 5.4.1 Bayes Unification of UGA Fusion Using Normal alized d ter's combinatie 185 5.4.2 Bayes Unification of UGA Fusion Using Normal ized and Unnormalized fuzzy dempsters combi- nations 186 5.4.3 Bayes Unification of UGA Fusion Using Copula 186 5.4.4 Bayes Unification of UGa Rule-Firin 187 5.4.5 If 3o Is Finite, Then Generalized Likelihoods are Strict likelihoods 188 【实例截图】
【核心代码】
随机有限集理论系统介绍及其在多目标多传感器中的应用和相关算法
Statistical Multisource-Multitarget Information Fusion Ronald p s. mahler ARTECH HOUSE BOSTON LONDON rtechhouse.c Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the U.S. Library of Congress British Library cataloguing in Publication Data A catalogue record for this book is available from the british library ISBN13:978-1-59693-092-6 Cover design by Yekaterina Ratner O 2007 ARTECH HOUSE, INC 685 Canton Street Norwood. MA 02062 All rights reserved Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including pho- tocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark 10987654321 ToIR Goodman Contents Preface Acknowledgments Chapter 1 Introduction to the book 1.1 What Is the Purpose of This Book? 1.2 Major Challenges in Information Fusion 7 1.3 Why Random Sets--or FISST? 1.3.1 Why Isnt Multitarget Filtering Straightforward? 1.3.2 Beyond heuristics 10 1.3.3 How Do Single-Target and Multitarget Statistics Differ? 1.3.5 What Is Formal Bayes Mouang ous Data 1.3.4 How Do Conventional and biguous Data Differ? 11 1.3.6 How Is Ambiguous Information Modeled? 1.3.7 What Is Multisource-Multitarget Formal Modeling? 1 1. 4 Random sets in Information fusion 15 1.4.1 Statistics of Multiobject Systems 1.4.2 Statistics of Expert Systems 16 1.4.3 Finite Set statistics 1. 5 Organization of the Book 1.5.1 Part I: Unified Single-Target Multisource Integration 17 1.5.2 Part II: Unified Multitarget -Multisource Integration 20 1.5.3 Part Ill: Approximate Multitarget Filtering 21 1.5.4 Appendixes 22 Contents I Unified Single-Target Multisource Integration Chapter 2 Single-Target Filtering 2. 1 Introduction to the chapte 2.1.1 Summary of Major Lessons Learned 26 2.1.2 Organization of the Chapter 2.2 The Kalman filter 2.2.1 Kalman filter initializatio 28 2.2.2 Kalman filter predictor 28 2.2.3 Kalman Filter Corrector 29 2. 2. 4 Derivation of the kalman filter 30 2.2.5 Measurement Fusion Using the Kalman filter 32 2.2.6 Constant-Gain Kalman Filters 2.3 Bayes Formulation of the Kalman Filter 2.3. 1 Some Mathematical Preliminaries 2.3.2 Bayes Formulation of the KF: Predictor 2.3.3 Bayes Formulation of the KF: Corrector 2.3.4 Bayes Formulation of the KF: Estimation 40 2. 4 The Single-Target Bayes Filter 42 2.4.1 Single-Target Bayes Filter: An Illustration 2.4.2 Relationship Between the Bayes and Kalman Filters 45 2.4.3 Single-Target Bayes Filter: Modeling 51 2.4.4 Single-Target Bayes Filter: Formal Bayes Modeling 56 2.4.5 Single-Target Bayes Filter: Initialization 61 2.4.6 Single-Target Bayes Filter: Predictor 2.4.7 Single- Target Bayes Filter: Corrector 62 2.4.8 Single-Target Bayes Filter: State Estimation 2. 4.9 Single- Target Bayes Filter: Error Estimation 2.4.10 Single-Target Bayes Filter: Data Fusion 2.4.11 Single-Target Bayes Filter: Computation 68 2.5 Single-Target Bayes Filter: Implementation 70 2.5.1 Taylor Series Approximation: The EKF 2.5.2 Gaussian-Mixture Approximation 72 2.5.3 Sequential Monte Carlo Approximation 2.6 Chapter exercises 87 Chapter 3 General Data Modeling 89 3.1 Introduction to the chapte 3.1.1 Summary of Major Lessons Learned Contents 3.1.2 Organization of the Chapter 3.2 Issues in Modeling Uncertainty 3.3 Issues in Modeling Uncertainty in Data 3.4 Examples 3.4.1 Random, Slightly Imprecise Measurements 97 3.4.2 Imprecise, Slightly Random Measurements 101 3.4.3 Nonrandom Vague measurements 102 3.4.4 Nonrandom Uncertain Measurements 103 3.4.5 Ambiguity Versus Randomness 3.5 The Core Bayesian Approach 3.5.1 Formal Bayes Modeling in General 109 3.5.2 The Bayes Filter in General 110 3.5.3 Bayes Combination Operators 3.5.4 Bayes-Invariant Measurement Conversion 3.6 Formal Modeling of Generalized Data 114 3.7 Chapter Exercise 117 Chapter 4 Random Set Uncertainty Representations 119 4.1 Introduction to the Chapter l19 4.1.1 Summary of Major Lessons Learned 119 4.1.2 Organization of the Chapter 120 4.2 Universes, Events, and the logic of events 120 4.3 Fuzzy Set Theory 121 4.3.1 Fuzzy logics 122 4.3.2 Random Set representation of Fuzzy events 4.3.3 Finite-Level Fuzzy Sets 126 4.3. 4 Copula Fuzzy Logic 129 4.3.5 General Random Set Representations of Fuzzy Sets 131 4. 4 Generalized Fuzzy Set Theory 133 4.4.1 Random Set Representation of Generalized Fuzzy Events 134 4.5 Dempster-Shafer Theory 134 4.5. 1 Dempster,s Combinatie 136 4.5.2 "Zadeh's Paradox" and Its Misinterpretation 138 4.5.3 Converting b.m. as to probability distributions 141 4.5.4 Random Set Representation of Uncertain events 143 4.6 Fuzzy Dempster-Shafer Theor 4.6.1 Random Set Representation of Fuzzy ds Evidence 145 Contents 4.7 Inference rules 147 4.7.1 What Are rules? 147 4.7.2 Combining Rules Using Conditional Event Algebra 148 4.7.3 Random Set Representation of First-Order rules 150 4.7.4 Random Set Representation of Composite rules 151 4.7.5 Random Set Representation of Second-Order Rules 152 4.8 Is Bayes Subsumed by Other Theories? 4.9 Chapter Exercises 154 Chapter 5 UGA Measurements 57 5.1 Introduction to the chapte 157 5.1.1 Notation 158 5.1.2 Summary of Major Lessons Learned 159 5.1.3 Organization of the chapter 161 5.2 What Is a uGA Measurement? 162 5.2.1 Modeling UGA Measurement 5.2.2 Modeling the Generation of UGA Measurements 1 5.3 Likelihoods for UGA Measurements l64 5.3.1 Special Case: 0 Is Statistical 165 5.3.2 Special Case: e Is Fuzzy 166 5.3.3 Special Case: e Is Generalized Fuzzy 5.3.4 Special Case: e Is Discrete/ Dempster-Shafer 5.3.5 Special Case: e Is Fuzzy Dempster-Shafer 173 5.3.6 Special Case: O Is a First-Order Fuzzy rule 174 5.3.7 Special Case: e Is a Composite Fuzzy rule l79 5.3.8 Special Case: 0 Is a Second-Order Fuzzy rule 5. 4 Bayes Unification of UGA Fusion 181 5.4.1 Bayes Unification of UGA Fusion Using Normal alized d ter's combinatie 185 5.4.2 Bayes Unification of UGA Fusion Using Normal ized and Unnormalized fuzzy dempsters combi- nations 186 5.4.3 Bayes Unification of UGA Fusion Using Copula 186 5.4.4 Bayes Unification of UGa Rule-Firin 187 5.4.5 If 3o Is Finite, Then Generalized Likelihoods are Strict likelihoods 188 【实例截图】
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