Mathematics of data fusion:
Gespeichert in:
Beteiligte Personen: | , , |
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Format: | Buch |
Sprache: | Englisch |
Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1997
|
Schriftenreihe: | [Theory and decision library / B]
37 |
Schlagwörter: | |
Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007845052&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
Umfang: | XII, 507 S. |
ISBN: | 0792346742 |
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adam_text | MATHEMATICS OF DATA FUSION BY I. R. GOODMAN NCCOSC RDTE DTV, SAN DIEGO,
CALIFORNIA, U.S.A. RONALD P. S. MAHLER LOCKHEED MARTIN TACTICAL DEFENCES
SYSTEMS, SAINT PAUL, MINNESOTA, U.S.A. AND HUNG T. NGUYEN DEPARTMENT OF
MATHEMATICAL SCIENCES, NEW MEXICO STATE UNIVERSITY, LAS CRUCES, NEW
MEXICO, U.S.A. KLUWER ACADEMIC PUBLISHERS DORDRECHT/ BOSTON / LONDON
CONTENTS PREFACE XI 1 INTRODUCTION 1 1.1 WHAT IS DATA FUSION? 3 1.2
RANDOM SET THEORY 7 1.3 CONDITIONAL AND RELATIONAL EVENT ALGEBRA 10 1
INTRODUCTION TO DATA FUSION 15 2 DATA FUSION AND STANDARD TECHNIQUES 17
2.1 DATA FUSION 17 2.1.1 CHAPTER SUMMARY 18 2.1.2 WHAT IS DATA FUSION?
18 2.1.3 THE SUBDISCIPLINES OF DATA FUSION 20 2.1.4 CENTRAL VS.
DISTRIBUTED FUSION 22 2.1.5 SOME MAJOR PROBLEMS OF DATA FUSION 23 2.1.6
HOW DOES ONE FUSE DATA? 26 2.2 MULTISENSOR, MULTITARGET ESTIMATION 27
2.2.1 INDIRECT ESTIMATION 27 2.2.2 DIRECT ESTIMATION 37 2.3 EXPERT
SYSTEMS . . . 43 2.3.1 IMPRECISE EVIDENCE . 45 2.3.2 VAGUE EVIDENCE:
FUZZY LOGIC 48 2.3.3 CONTINGENT EVIDENCE: CONDITIONAL EVENT ALGEBRA 50
2.3.4 PARTIAL-PROBABILISTIC EVIDENCE 54 2.4 RANDOM SETS ; 54 2.5
FINITE-SET STATISTICS 58 2.5.1 RANDOM SET FORMULATION OF DATA FUSION
PROBLEMS . . . . 61 2.5.2 AN INTEGRAL AND DIFFERENTIAL CALCULUS FOR DATA
FUSION . . 62 2.5.3 THE GLOBAL DENSITY OF A SENSOR SUITE 62 2.5.4 A
SIMPLE ILLUSTRATION 63 2.5.5 THE PARALLELISM BETWEEN POINT- AND
FINITE-SET STATISTICS . 65 2.5.6 DATA FUSION USING AMBIGUOUS EVIDENCE 68
VI - CONTENTS 2.5.7 POSSIBLE OBJECTIONS TO FINITE-SET STATISTICS 71
2.6 CONDITIONAL AND RELATIONAL EVENT ALGEBRA 73 2.7 BIBLIOGRAPHY 79 II
THE RANDOM SET APPROACH TO DATA FUSION 91 3 FOUNDATIONS OF RANDOM SETS
93 3.1 DISTRIBUTIONS OF RANDOM SETS 93 3.2 RADON-NIKODYM DERIVATIVES 100
3.3 MOBIUS TRANSFORMS OF SET-FUNCTIONS 112 3.4 RANDOM SETS IN
DECISION-MAKING 116 3.4.1 CONFIDENCE REGION ESTIMATION 116 3.4.2
IMPRECISE PROBABILITIES 117 3.4.3 UNCERTAINTY MODELING 125 3.5
BIBLIOGRAPHY 127 4 FINITE RANDOM SETS 131 4.1 MATHEMATICAL PRELIMINARIES
131 4.1.1 RELATIONSHIP BETWEEN THE EUCLIDEAN-SPACE AND HIT-OR-MISS
TOPOLOGIES 131 4.1.2 HYBRID SPACES 135 4.1.3 THE HAUSDORFF METRIC 137
4.2 A CALCULUS OF SET FUNCTIONS 138 4.2.1 DISCRETE CASE: DIFFERENCE
CALCULUS ON FINITE SETS 139 4.2.2 THE SET INTEGRAL 141 4.2.3 THE
GENERALIZED RADON-NIKODYM DERIVATIVE 144 4.2.4 SET DERIVATIVES 150 4.3
BASIC PROPERTIES OF FINITE RANDOM SUBSETS 152 - 4.3.1 BELIEF MEASURES OF
FINITE RANDOM SUBSETS 152 4.3.2 EXISTENCE OF SET DERIVATIVES 157 4.3.3
GLOBAL PROBABILITY DENSITY FUNCTIONS 162 4.3.4 GLOBAL COVERING DENSITIES
168 4.3.5 RELATIONSHIP TO OTHER APPROACHES 170 4.4 BIBLIOGRAPHY 171 5
FINITE-SET STATISTICS 175 5.1 BASIC STATISTICAL CONCEPTS 175 5.1.1
EXPECTED VALUES 175 5.1.2 COVARIANCES 183 5.1.3 PRIOR AND POSTERIOR
GLOBAL DENSITIES 184 5.2 GLOBAL PARAMETRIC ESTIMATION 188 5.2.1 GLOBAL
ESTIMATORS OF VECTOR-VALUED FUNCTIONS 189 5.2.2 THE GLOBAL ML AND MAP
ESTIMATORS 190 5.2.3 SET PARAMETERS AND THE STATISTICAL CONSISTENCY OF
THE GLOBAL ML AND MAP ESTIMATORS 194 CONTENTS VII 5.3 INFORMATION THEORY
AND INFORMATION FUSION 205 5.3.1 GLOBAL INFORMATION THEORY 205 5.3.2
GLOBAL BEST-PERFORMANCE INEQUALITIES 209 5.4 BIBLIOGRAPHY 217 6 FUSION
OF UNAMBIGUOUS OBSERVATIONS 219 6.1 THE CENTRAL-FUSION PROBLEM 219 6.2
RANDOM SET MEASUREMENT MODELS 221 6.2.1 SINGLE-SENSOR, SINGLE-TARGET
MEASUREMENT MODELS . . . . 221 6.2.2 MULTISENSOR, MULTITARGET
MEASUREMENT MODELS 225 6.2.3 CONVENTIONAL INTERPRETATION OF GLOBAL
MEASUREMENT MODELS228 6.3 MODELING PRIOR KNOWLEDGE 235 6.4 RANDOM SET
MOTION MODELS 236 6.4.1 BAYESIAN RECURSIVE NONLINEAR FILTERING 237 6.4.2
GLOBAL NONLINEAR FILTERING 238 6.4.3 CONSTRUCTING GLOBAL MOTION MODELS
239 6.4.4 CLOSURE PROPERTIES OF CANONICAL GLOBAL DENSITIES 243 6.5
RANDOM SET OUTPUTS OF ESTIMATORS 244 6.6 SIMPLE EXAMPLES 247- 6.6.1 TWO
TARGETS IN ONE DIMENSION 247 6.6.2 MULTIPLE TARGETS IN TWO DIMENSIONS
256 6.7 BIBLIOGRAPHY 261 7 FUSION OF AMBIGUOUS OBSERVATIONS 263 7.1
OVERVIEW OF THE APPROACH: THE FINITE UNIVERSE CASE 264 7.1.1 EVIDENCE AS
A CONSTRAINT ON DATA 266 7.1.2 MEASUREMENT MODELS FOR DATA AND EVIDENCE
269 7.1.3 THE STRONG-CONSISTENCY MEASUREMENT MODEL 270 7.1.4 THE
DATA-DEPENDENT MEASUREMENT MODEL 272 7.1.5 WEAK-CONSISTENCY MEASUREMENT
MODELS 274 7.1.6 SIGNATURE-BASED MEASUREMENT JVIODELS FOR EVIDENCE . . .
. 275 7.2 UNIFIED DATA FUSION 279 7.2.1 MODELING AMBIGUOUS EVIDENCE
USING DRACS 279 7.2.2 CONDITIONING ON AMBIGUOUS EVIDENCE: SINGLE SENSOR,
SIN- GLE TARGET CASE 280 7.2.3 CONDITIONING ON AMBIGUOUS EVIDENCE:
SINGLE SENSOR, MUL- TITARGET CASE . -. V 284 7.2.4 MULTISENSOR,
MULTITARGET CASE 289 7.2.5 BAYESIAN CHARACTERIZATION OF RULES OF
EVIDENTIAL COMBI- NATION 289 7.2.6 NONLINEAR FILTERING WITH DATA AND
EVIDENCE 290 7.3 BIBLIOGRAPHY 293 VIII CONTENTS 8 OUTPUT MEASUREMENT 295
8.1 PERFORMANCE EVALUATION 297 8.1.1 INFORMATION MEASURED WITH RESPECT
TO GROUND TRUTH . . 297 8.1.2 RELATIVE INFORMATION 302 8.1.3 COMPONENTS
OF INFORMATION 304 8.1.4 INFORMATION WITH CONSTRAINTS 307 8.2
NONPARAMETRIC ESTIMATION 312 8.2.1 REVIEW OF NONPARAMETRIC ESTIMATION
313 8.2.2 GLOBAL NONPARAMETRIC ESTIMATION 318 8.2.3 GLOBAL
REPRODUCING-KERNEL ESTIMATION 319 8.3 BIBLIOGRAPHY 337 III USE OF
CONDITIONAL AND RELATIONAL EVENTS IN DATA FUSION 339 SCOPE OF WORK 341 9
INTRODUCTION TO THE CONDITIONAL AND RELATIONAL EVENT ALGEBRA ASPECTS OF
DATA FUSION 345 9.1 PHILOSOPHY OF APPROACH 345 9.2 OVERVIEW OF THE
PROBLEM AND THE NEED FOR AN ALGEBRAIC BASIS PRECEDING NUMERICAL
CALCULATIONS 346 9.3 ALGEBRAIC APPROACH TO TREATING INFORMATION 348
9.3.1 PARTITIONING OF INFORMATION 348 9.3.2 BOOLEAN ALGEBRA, PROBABILITY
SPACES, AND DEDUCTION AND ENDUCTION 349 9.3.3 ALGEBRAIC COMBINING OF
INFORMATION 351 9.4 THE ALGEBRAIC DECISION THEORY PROBLEM, RELATIONAL
EVENT ALGE- BRA, AND INTRODUCTION TO MEASURES OF SIMILARITY 353 9.5
BIBLIOGRAPHY 357 10 POTENTIAL APPLICATION OF CONDITIONAL EVENT ALGEBRA
TO COMBIN- ING CONDITIONAL INFORMATION 359 10.1 MODELING INFERENCE RULES
. . : 359 10.2 CONDITIONAL EVENT ALGEBRA PROBLEM AND CONNECTIONS WITH
SIMI- LARITY MEASURES 362 10.3 APPLICATION OF CONDITIONAL EVENT ALGEBRA
TO THE DETERMINATION OF CONSTANT-PROBABILITY EVENTS 364 10.4
BIBLIOGRAPHY -. 367 11 THREE PARTICULAR CONDITIONAL EVENT ALGEBRAS 369
11.1 GENERAL REMARKS ON CONDITIONAL EVENT ALGEBRA 369 11.2
DEFINETTI-GOODMAN-NGUYEN-WALKER CONDITIONAL EVENT ALGEBRA . 369 11.3
ADAMS-CALABRESE (AC) CONDITIONAL EVENT ALGEBRA 373 11.4 SOME COMPARISONS
OF DGNW AND AC CONDITIONAL EVENT ALGEBRAS376 CONTENTS IX 11.5 LEWIS
NEGATIVE RESULT CONCERNING FORCED BOOLEAN CONDITIONAL EVENT ALGEBRAS 377
11.6 INTRODUCTION TO PRODUCT SPACE CONDITIONAL EVENT ALGEBRA . . . . 378
11.7 BIBLIOGRAPHY 381 12 FURTHER DEVELOPMENT OF PRODUCT SPACE
CONDITIONAL EVENT AL- GEBRA 383 12.1 EQUIVALENCE, PARTIAL ORDERING, AND
CALCULUS OF LOGICAL OPERATIONS 383 12.2 ADDITIONAL IMPORTANT PROPERTIES
OF PS 393 12.2.1 COMPARISON OF [.|..] AND (.|..) TYPE OF EVENTS 393
12.2.2 LEWIS THEOREM AND PS 395 12.2.3 HIGHER ORDER CONDITIONALS FOR PS
395 12.2.4 OTHER PROPERTIES OF PS 396 12.3 CONDITIONAL EVENTS AND THEIR
RELATION TO CONDITIONING OF RAN- DOM VARIABLES FOR PS 397 12.4 BOOLEAN
CONDITIONAL EVENT ALGEBRAS DISTINCT FROM PS 399 12.5 FUNDAMENTAL
CHARACTERIZATION OF PS 401 12.6 BIBLIOGRAPHY 403 13 PRODUCT SPACE
CONDITIONAL EVENT ALGEBRA AS A TOOL FOR FURTHER ANALYSIS OF CONDITIONAL
EVENT ALGEBRA ISSUES 405 13.1 DIRECT CONNECTIONS BETWEEN PS AND BOTH
DGNW AND AC VIA PARTIAL ORDERING AND DEDUCTION-ENDUCTION RELATIONS 405
13.2 DIRECT APPLICATION OF PS TO MOTIVATING EXAMPLE 1 415 13.3 RIGOROUS
FORMULATION OF CONSTANT PROBABILITY EVENTS AND INTER- VALS WITHIN A PS
FRAMEWORK 417 13.4 BIBLIOGRAPHY 423 14 TESTING OF HYPOTHESES FOR
DISTINCTNESS OF EVENTS AND EVENT SIMILARITY ISSUES 425 GENERAL REMARKS
425 14.1 CLASSICAL TESTING OF STATISTICAL HYPOTHESES AND ESTIMATION /
RE- GRESSION APPLIED TO THE COMPARISON OF DIFFERENT PROBABILITY DIS-
TRIBUTIONS 426 14.2 TESTING HYPOTHESES OF DIFFERENT EVENTS RELATIVE TO A
COMMON PROBABILITY MEASURE 426 14.3 TESTING HYPOTHESES UNDER A HIGHER
ORDER PROBABILITY ASSUMP- TION ON THE RELATIVE ATOMS 428 14.4
PROBABILITY DISTANCE FUNCTIONS AND PS CONDITIONAL EVENT ALGEBRA432 14.5
NUMERICAL-VALUED METRICS ON A PROBABILITY SPACE 434 14.6 ALGEBRAIC
METRICS ON A PROBABILITY SPACE 436 14.7 DEVELOPMENT OF PROBABILITY
DISTANCE FUNCTIONS USING ALGEBRAIC METRICS 440 X CONTENTS 14.8
ADDITIONAL RELATIONS AMONG THE BASIC PROBABILITY DISTANCE FUNC- TIONS
AND OPEN ISSUES 448 14.9 BIBLIOGRAPHY 453 15 TESTING HYPOTHESES AND
ESTIMATION RELATIVE TO NATURAL LAN- GUAGE DESCRIPTIONS 455 15.1
MOTIVATING EXAMPLE 4 455 15.2 COPULAS, COCOPULAS, AND FUZZY LOGIC
OPERATORS 457 15.3 NUMERICALLY-BASED MEASURES OF SIMILARITY AND METRICS
FOR THE PROBLEM 458 15.4 ONE-POINT RANDOM SET COVERAGE REPRESENTATIONS
OF FUZZY SETS AND FUZZY LOGIC 460 15.5 USE OF ONE-POINT COVERAGES WITH
PROBABILITY DISTANCE FUNCTIONS 465 15.6 INCORPORATION OF FUZZY LOGIC
MODIFIERS AND USE OF RELATIONAL EVENT ALGEBRA IN EXAMPLE 4 466 15.7
ADDITIONAL ANALYSIS OF EXAMPLE 4 474 15.8 BIBLIOGRAPHY 479 16
DEVELOPMENT OF RELATIONAL EVENT ALGEBRA PROPER TO ADDRESS DATA FUSION
PROBLEMS 481 OVERVIEW 481 16.1 USE OF RELATIONAL EVENT ALGEBRA AND
PROBABILITY DISTANCES IN COMPARING OPINIONS OF TWO EXPERTS WEIGHTED
COMBINATIONS OF PROBABILITIES 482 16.2 COMPARING AND COMBINING
POLYNOMIALS OR ANALYTIC FUNCTIONS OF PROBABILITIES WITH WEIGHTED
COEFFICIENTS USING RELATIONAL EVENT ALGEBRA AND PROBABILITY DISTANCES
485 16.3 COMPARISON OF MODELS WHOSE UNCERTAINTIES ARE TWO ARGUMENT
QUADRATIC FUNCTIONS 489 16.4 GENERAL RELATIONAL EVENT ALGEBRA PROBLEM
AND A MODIFICATION - FOR RELATIONAL EVENTS HAVING CONSTANT-PROBABILITY
EVENT COEFFI- CIENTS POSSIBLY DEPENDENT UPON PROBABILITIES 492 16.5
CONCLUDING REMARKS 499 16.6 BIBLIOGRAPHY 501 INDEX 503
|
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author | Goodman, Irwin R. Mahler, Ronald P. S. Nguyen, Hung T. 1944- |
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id | DE-604.BV011640719 |
illustrated | Not Illustrated |
indexdate | 2024-12-20T10:16:07Z |
institution | BVB |
isbn | 0792346742 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007845052 |
oclc_num | 37269146 |
open_access_boolean | |
owner | DE-739 DE-12 DE-29T DE-91G DE-BY-TUM DE-521 DE-706 |
owner_facet | DE-739 DE-12 DE-29T DE-91G DE-BY-TUM DE-521 DE-706 |
physical | XII, 507 S. |
publishDate | 1997 |
publishDateSearch | 1997 |
publishDateSort | 1997 |
publisher | Kluwer |
record_format | marc |
series2 | [Theory and decision library / B] |
spellingShingle | Goodman, Irwin R. Mahler, Ronald P. S. Nguyen, Hung T. 1944- Mathematics of data fusion Fusion multicapteurs - Mathématiques Systèmes experts (Informatique) Mathematik Expert systems (Computer science) Multisensor data fusion -- Mathematics Datenintegration (DE-588)4197730-0 gnd Informationstheorie (DE-588)4026927-9 gnd |
subject_GND | (DE-588)4197730-0 (DE-588)4026927-9 |
title | Mathematics of data fusion |
title_auth | Mathematics of data fusion |
title_exact_search | Mathematics of data fusion |
title_full | Mathematics of data fusion by I. R. Goodman ; Ronald P. S. Mahler and Hung T. Nguyen |
title_fullStr | Mathematics of data fusion by I. R. Goodman ; Ronald P. S. Mahler and Hung T. Nguyen |
title_full_unstemmed | Mathematics of data fusion by I. R. Goodman ; Ronald P. S. Mahler and Hung T. Nguyen |
title_short | Mathematics of data fusion |
title_sort | mathematics of data fusion |
topic | Fusion multicapteurs - Mathématiques Systèmes experts (Informatique) Mathematik Expert systems (Computer science) Multisensor data fusion -- Mathematics Datenintegration (DE-588)4197730-0 gnd Informationstheorie (DE-588)4026927-9 gnd |
topic_facet | Fusion multicapteurs - Mathématiques Systèmes experts (Informatique) Mathematik Expert systems (Computer science) Multisensor data fusion -- Mathematics Datenintegration Informationstheorie |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007845052&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000021513 |
work_keys_str_mv | AT goodmanirwinr mathematicsofdatafusion AT mahlerronaldps mathematicsofdatafusion AT nguyenhungt mathematicsofdatafusion |
Inhaltsverzeichnis
Paper/Kapitel scannen lassen
Paper/Kapitel scannen lassen
Teilbibliothek Mathematik & Informatik
Signatur: |
0102 SOZ 200f 2001 A 888-37 Lageplan |
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Exemplar 1 | Ausleihbar Am Standort |