This is the sequel to the 2007 Artech House bestselling title, Statistical Multisource-Multitarget Information Fusion. That earlier book was a comprehensive resource for an in-depth understanding of finite-set statistics (FISST), a unified, systematic, and Bayesian approach to information fusion. The cardinalized probability hypothesis density (CPHD) filter, which was first systematically described in the earlier book, has since become a standard multitarget detection and tracking technique, especially in research and development.
Since 2007, FISST has inspired a considerable amount of research, conducted in more than a dozen nations, and reported in nearly a thousand publications. This sequel addresses the most intriguing practical and theoretical advances in FISST, for the first time aggregating and systematizing them into a coherent, integrated, and deep-dive picture. Special emphasis is given to computationally fast exact closed-form implementation approaches. The book also includes the first complete and systematic description of RFS-based sensor/platform management and situation assessment.
Author(s): Mahler, R.
Publisher: Artech House
Year: 2014
Language: English
Pages: 1167
Contents
Preface
Acknowledgments
Chapter 1 Introduction to the Book
1.1 OVERVIEW OF FINITE-SET STATISTICS
1.2 RECENT ADVANCES IN FINITE-SET STATISTICS
1.3 ORGANIZATION OF THE BOOK
Part I Elements of Finite-Set Statistics
Chapter 2 Random Finite Sets
2.1 INTRODUCTION
2.2 SINGLE-SENSOR, SINGLE-TARGET STATISTICS
2.3 RANDOM FINITE SETS (RFSs)
2.4 MULTIOBJECT STATISTICS IN A NUTSHELL
Chapter 3 Multiobject Calculus
3.1 INTRODUCTION
3.2 BASIC CONCEPTS
3.3 SET INTEGRALS
3.4 MULTIOBJECT DIFFERENTIAL CALCULUS
3.5 KEY FORMULAS OF MULTIOBJECT CALCULUS
Chapter 4 Multiobject Statistics
4.1 INTRODUCTION
4.2 BASIC MULTIOBJECT STATISTICAL DESCRIPTORS
4.3 IMPORTANT MULTIOBJECT PROCESSES
4.4 BASIC DERIVED RFSs
Chapter 5 Multiobject Modeling and Filtering
5.1 INTRODUCTION
5.2 THE MULTISENSOR-MULTITARGET BAYES FILTER
5.3 MULTITARGET BAYES OPTIMALITY
5.4 RFS MULTITARGET MOTION MODELS
5.5 RFS MULTITARGET MEASUREMENT MODELS
5.6 MULTITARGET MARKOV DENSITIES
5.7 MULTISENSOR-MULTITARGET LIKELIHOOD FUNCTIONS
5.8 THE MULTITARGET BAYES FILTER IN p.g.fl. FORM
5.9 THE FACTORED MULTITARGET BAYES FILTER
5.10 APPROXIMATE MULTITARGET FILTERS
Chapter 6 Multiobject Metrology
6.1 INTRODUCTION
6.2 MULTIOBJECT MISS DISTANCE
6.3 MULTIOBJECT INFORMATION FUNCTIONALS
Part II RFS Filters: StandardMeasurement Model
Chapter 7 Introduction to Part II
7.1 SUMMARY OF MAJOR LESSONS LEARNED
7.2 STANDARD MULTITARGET MEASUREMENT MODEL
7.3 AN APPROXIMATE STANDARD LIKELIHOOD FUNCTION
7.4 STANDARD MULTITARGET MOTION MODEL
7.5 STANDARD MOTION MODEL WITH TARGET SPAWNING
7.6 ORGANIZATION OF PART II
Chapter 8 Classical PHD and CPHD Filters
8.1 INTRODUCTION
8.2 A GENERAL PHD FILTER
8.3 ARBITRARY-CLUTTER PHD FILTER
8.4 CLASSICAL PHD FILTER
8.5 CLASSICAL CARDINALIZED PHD (CPHD) FILTER
8.6 ZERO FALSE ALARMS (ZFA) CPHD FILTER
8.7 PHD FILTER FOR STATE-DEPENDENT POISSON CLUTTER
Chapter 9 Implementing Classical PHD/CPHDFilters
9.1 INTRODUCTION
9.2 “SPOOKY ACTION AT A DISTANCE”
9.3 MERGING AND SPLITTING FOR PHD FILTERS
9.4 MERGING AND SPLITTING FOR CPHD FILTERS
9.5 GAUSSIAN MIXTURE (GM) IMPLEMENTATION
9.6 SEQUENTIAL MONTE CARLO (SMC) IMPLEMENTATION
Chapter 10 Multisensor PHD and CPHD Filters
10.1 INTRODUCTION
10.2 THE MULTISENSOR-MULTITARGET BAYES FILTER
10.3 THE GENERAL MULTISENSOR PHD FILTER
10.4 THE MULTISENSOR CLASSICAL PHD FILTER
10.5 ITERATED-CORRECTOR MULTISENSOR PHD/CPHD FILTERS
10.6 PARALLEL COMBINATION MULTISENSOR PHD AND CPHD FILTERS
10.7 AN ERRONEOUS “AVERAGED” MULTISENSOR PHD FILTER
10.8 PERFORMANCE COMPARISONS
Chapter 11 Jump-Markov PHD/CPHD Filters
11.1 INTRODUCTION
11.2 JUMP-MARKOV FILTERS: A REVIEW
11.3 MULTITARGET JUMP-MARKOV SYSTEMS
11.4 JUMP-MARKOV PHD FILTER
11.5 JUMP-MARKOV CPHD FILTER
11.6 VARIABLE STATE SPACE JUMP-MARKOV CPHD FILTERS
11.7 IMPLEMENTING JUMP-MARKOV PHD/CPHD FILTERS
11.8 IMPLEMENTED JUMP-MARKOV PHD/CPHD FILTERS
Chapter 12 Joint Tracking and Sensor-Bias Estimation
12.1 INTRODUCTION
12.2 MODELING SENSOR BIASES
12.3 OPTIMAL JOINT TRACKING AND REGISTRATION
12.4 THE BURT-PHD FILTER
12.5 SINGLE-FILTER BURT-PHD FILTERS
12.6 IMPLEMENTED BURT-PHD FILTERS
Chapter 13 Multi-Bernoulli Filters
13.1 INTRODUCTION
13.2 THE BERNOULLI FILTER
13.3 THE MULTISENSOR BERNOULLI FILTER
13.4 THE CBMEMBER FILTER
13.5 JUMP-MARKOV CBMEMBER FILTER
Chapter 14 RFS Multitarget Smoothers
14.1 INTRODUCTION
14.2 SINGLE-TARGET FORWARD-BACKWARD SMOOTHER
14.3 GENERAL MULTITARGET FORWARD-BACKWARD SMOOTHER
14.4 BERNOULLI FORWARD-BACKWARD SMOOTHER
14.5 PHD FORWARD-BACKWARD SMOOTHER
14.6 ZTA-CPHD SMOOTHER
Chapter 15 Exact Closed-Form Multitarget Filter
15.1 INTRODUCTION
15.2 LABELED RFSS
15.3 EXAMPLES OF LABELED RFSS
15.4 MODELING FOR THE VO-VO FILTER
15.5 CLOSURE OF MULTITARGET BAYES FILTER
15.6 IMPLEMENTATION OF THE VO-VO FILTER: SKETCH
15.7 PERFORMANCE RESULTS
Part III RFS Filters for UnknownBackgrounds
Chapter 16 Introduction to Part III
16.1 INTRODUCTION
16.2 OVERVIEW OF THE APPROACH
16.3 MODELS FOR UNKNOWN BACKGROUNDS
16.4 ORGANIZATION OF PART III
Chapter 17 RFS Filters for Unknown pD
17.1 INTRODUCTION
17.2 THE PD-CPHD FILTER
17.3 BETA-GAUSSIAN MIXTURE (BGM) APPROXIMATION
17.4 BGM IMPLEMENTATION OF THE PD-PHD FILTER
17.5 BGM IMPLEMENTATION OF THE PD-CPHD FILTER
17.6 THE PD-CBMEMBER FILTER
17.7 IMPLEMENTATIONS OF PD-AGNOSTIC RFS FILTERS
Chapter 18 RFS Filters for Unknown Clutter
18.1 INTRODUCTION
18.2 A GENERAL MODEL FOR UNKNOWN BERNOULLI CLUTTER
18.3 CPHD FILTER FOR GENERAL BERNOULLI CLUTTER
18.4 THE λ-CPHD FILTER
18.5 THE κ-CPHD FILTER
18.6 MULTISENSOR κ-CPHD FILTERS
18.7 THE κ-CBMEMBER FILTER
18.8 IMPLEMENTED CLUTTER-AGNOSTIC RFS FILTERS
18.9 CLUTTER-AGNOSTIC PSEUDOFILTERS
18.10 CPHD/PHD FILTERS WITH POISSON-MIXTURE CLUTTER
18.11 RELATED WORK
Part IV RFS Filters for Nonstandard Measurement Models
Chapter 19 RFS Filters for Superpositional Sensors
19.1 INTRODUCTION
19.2 EXACT SUPERPOSITIONAL CPHD FILTER
19.3 HAUSCHILDT’S APPROXIMATION
19.4 THOUIN-NANNURU-COATES (TNC) APPROXIMATION
Chapter 20 RFS Filters for Pixelized Images
20.1 INTRODUCTION
20.2 THE IO MULTITARGET MEASUREMENT MODEL
20.3 IO MOTION MODEL
20.4 IO-CPHD FILTER
20.5 IO-MEMBER FILTER
20.6 IMPLEMENTATIONS OF IO-MEMBER FILTERS
Chapter 21 RFS Filters for Cluster-Type Targets
21.1 INTRODUCTION
21.2 EXTENDED-TARGET MEASUREMENT MODELS
21.3 EXTENDED-TARGET BERNOULLI FILTERS
21.4 EXTENDED-TARGET PHD/CPHD FILTERS
21.5 EXTENDED-TARGET CPHD FILTER: APB MODEL
21.6 CLUSTER-TARGET MEASUREMENT MODEL
21.7 CLUSTER-TARGET PHD AND CPHD FILTERS
21.8 MEASUREMENT MODELS FOR LEVEL-1 GROUP TARGETS
21.9 PHD/CPHD FILTERS FOR LEVEL-1 GROUP TARGETS
21.10 MEASUREMENT MODELS FOR GENERAL GROUP TARGETS
21.11 PHD/CPHD FILTERS FOR LEVEL-ℓ GROUP TARGETS
21.12 A MODEL FOR UNRESOLVED TARGETS
21.13 MOTION MODEL FOR UNRESOLVED TARGETS
21.14 THE UNRESOLVED-TARGET PHD FILTER
21.15 APPROXIMATE UNRESOLVED-TARGET PHD FILTER
21.16 APPROXIMATE UNRESOLVED-TARGET CPHD FILTER
Chapter 22 RFS Filters for Ambiguous Measurements
22.1 INTRODUCTION
22.2 RANDOM SET MODELS OF AMBIGUOUS MEASUREMENTS
22.3 GENERALIZED LIKELIHOOD FUNCTIONS (GLFS)
22.4 UNIFICATION OF EXPERT-SYSTEM THEORIES
22.5 GLFS FOR IMPERFECTLY CHARACTERIZED TARGETS
22.6 GLFS FOR UNKNOWN TARGET TYPES
22.7 GLFS FOR INFORMATION WITH UNKNOWN CORRELATIONS
22.8 GLFS FOR UNRELIABLE INFORMATION SOURCES
22.9 USING GLFS IN MULTITARGET FILTERS
22.10 GLFS IN RFS MULTITARGET FILTERS
22.11 USING GLFS WITH CONVENTIONAL MULTITARGET FILTERS
Part V Sensor, Platform, and Weapons Management
Chapter 23 Introduction to Part V
23.1 BASIC ISSUES IN SENSOR MANAGEMENT
23.2 INFORMATION THEORY AND INTUITION: AN EXAMPLE
23.3 SUMMARY OF RFS SENSOR CONTROL
23.4 ORGANIZATION OF PART V
Chapter 24 Single-Target Sensor Management
24.1 INTRODUCTION
24.2 EXAMPLE: MISSILE-TRACKING CAMERAS
24.3 SINGLE-SENSOR, SINGLE-TARGET CONTROL: MODELING
24.4 SINGLE-SENSOR, SINGLE-TARGET CONTROL: SINGLE-STEP
24.5 SINGLE-SENSOR, SINGLE-TARGET CONTROL: OBJECTIVE
24.6 SINGLE-SENSOR, SINGLE-TARGET CONTROL: HEDGING
24.7 SINGLE–SENSOR, SINGLE-TARGET CONTROL: OPTIMIZATION
24.8 SPECIAL CASE 1: IDEAL SENSOR DYNAMICS
24.9 SIMPLE EXAMPLE: LINEAR-GAUSSIAN CASE
24.10 SPECIAL CASE 2: SIMPLIFIED NONIDEAL DYNAMICS
Chapter 25 Multitarget Sensor Management
25.1 INTRODUCTION
25.2 MULTITARGET CONTROL: TARGET AND SENSOR STATE SPACES
25.3 MULTITARGET CONTROL: CONTROL SPACES
25.4 MULTITARGET CONTROL: MEASUREMENT SPACES
25.5 MULTITARGET CONTROL: MOTION MODELS
25.6 MULTITARGET CONTROL: MEASUREMENT MODELS
25.7 MULTITARGET CONTROL: SUMMARY OF NOTATION
25.8 MULTITARGET CONTROL: SINGLE STEP
25.9 MULTITARGET CONTROL: OBJECTIVE FUNCTIONS
25.10 MULTISENSOR-MULTITARGET CONTROL: HEDGING
25.11 MULTISENSOR-MULTITARGET CONTROL: OPTIMIZATION
25.12 SENSOR MANAGEMENT WITH IDEAL SENSOR DYNAMICS
25.13 SIMPLIFIED NONIDEAL MULTISENSOR DYNAMICS
25.14 TARGET PRIORITIZATION
Chapter 26 Approximate Sensor Management
26.1 INTRODUCTION
26.2 SENSOR MANAGEMENT WITH BERNOULLI FILTERS
26.3 SENSOR MANAGEMENT WITH PHD FILTERS
26.4 SENSOR MANAGEMENT WITH CPHD FILTERS
26.5 SENSOR MANAGEMENT WITH CBMEMBER FILTERS
26.6 RFS SENSOR MANAGEMENT IMPLEMENTATIONS
Appendix A Glossary of Notation and Terminology
A.1 TRANSPARENT NOTATIONAL SYSTEM
A.2 GENERAL MATHEMATICS
A.3 SET THEORY
A.4 FUZZY LOGIC AND DEMPSTER-SHAFER THEORY
A.5 PROBABILITY AND STATISTICS
A.6 RANDOM SETS
A.7 MULTITARGET CALCULUS
A.8 FINITE-SET STATISTICS
A.9 GENERALIZED MEASUREMENTS
Appendix B Bayesian Analysis of Dynamic Systems
B.1 FORMAL BAYES MODELING IN GENERAL
B.2 THE BAYES FILTER IN GENERAL
Appendix C Rigorous Functional Derivatives
C.1 NONCONSTRUCTIVE DEFINITION OF THE FUNCTIONAL DERIVATIVE
C.2 THE CONSTRUCTIVE RADON-NIKOD´YM DERIVATIVE
C.3 CONSTRUCTIVE DEFINITION OF THE FUNCTIONAL DERIVATIVE
Appendix D Partitions of Finite Sets
D.1 COUNTING PARTITIONS
D.2 RECURSIVE CONSTRUCTION OF PARTITIONS
Appendix E Beta Distributions
Appendix F Markov Time Update of Beta Distributions
Appendix G Normal-Wishart Distributions
G.1 PROOF OF (G.8)
G.2 PROOF OF (G.22)
G.3 PROOF OF (G.23)
G.4 PROOF OF (G.29)
Appendix H Complex-Number Gaussian Distributions
Appendix I Statistics of Level-1 Group Targets
Appendix J FISST Calculus and Moyal’s Calculus
J.1 A “POINT PROCESS” FUNCTIONAL CALCULUS
J.2 VOLTERRA FUNCTIONAL DERIVATIVES
J.3 MOYAL’S FUNCTIONAL CALCULUS OF p.g.fl.s
Appendix K Mathematical Derivations
References
About the Author
Index
