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E-raamat: Advances in Statistical Multisource-Multitarget Information Fusion

  • Formaat: 1174 pages
  • Ilmumisaeg: 31-Jan-2014
  • Kirjastus: Artech House Publishers
  • ISBN-13: 9781608077991
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Advances in Statistical Multisource-Multitarget Information FusionSuurem pilt
  • Formaat: 1174 pages
  • Ilmumisaeg: 31-Jan-2014
  • Kirjastus: Artech House Publishers
  • ISBN-13: 9781608077991
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Mahler describes random set information fusion for signal processing for graduate students, researchers, and engineers and for mathematicians and statisticians interested in tracking, information fusion, robotics, and related areas. He covers elements of finite-set statistics; random finite set filters: standard measurement model; random finite set filters for unknown backgrounds; random finite set filters for nonstandard measurement models; and sensor, platform, and weapons management. The topics include multi-object modeling and filtering, implementing classical probability hypothesis density and cardinalized probability hypothesis density filters, joint tracking and sensor-bias estimation, exact closed-form multi-target filter, random finite set filters for superpositional sensors, and single-target sensor management. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Preface xxix
Acknowledgments xxxv
Chapter 1 Introduction to the Book 1(40)
1.1 Overview of Finite-Set Statistics
4(21)
1.1.1 The Philosophy of Finite-Set Statistics
4(6)
1.1.2 Misconceptions About Finite-Set Statistics
10(6)
1.1.3 The Measurement-to-Track Association Approach
16(2)
1.1.4 The Random Finite Set (RFS) Approach
18(6)
1.1.5 Extension to Nontraditional Measurements
24(1)
1.2 Recent Advances in Finite-Set Statistics
25(11)
1.2.1 Advances in Conventional PHD and CPHD Filters
26(1)
1.2.2 Multitarget Smoothers
26(1)
1.2.3 PHD and CPHD Filters for Unknown Backgrounds
27(1)
1.2.4 PHD Filters for Nonpoint Targets
28(1)
1.2.5 Advances in Classical Multi-Bernoulli Filters
29(1)
1.2.6 RFS Filters for "Raw-Data" Sensors
30(1)
1.2.7 Theoretical Advances
31(1)
1.2.8 Advances in Fusing Nontraditional Measurements
32(1)
1.2.9 Advances Toward Fully Unified Systems
33(3)
1.3 Organization of the Book
36(5)
I Elements of Finite-Set Statistics 41(120)
Chapter 2 Random Finite Sets
43(16)
2.1 Introduction
43(1)
2.1.1 Organization of the
Chapter
43(1)
2.2 Single-Sensor, Single-Target Statistics
44(6)
2.2.1 Basic Notation
44(1)
2.2.2 State Spaces and Measurement Spaces
45(1)
2.2.3 Random States and Measurements, Probability-Mass Functions, and Probability Densities
46(1)
2.2.4 Target Motion Models and Markov Densities
47(1)
2.2.5 Measurement Models and Likelihood Functions
47(1)
2.2.6 Nontraditional Measurements
48(1)
2.2.7 The Single-Sensor, Single-Target Bayes Filter
48(2)
2.3 Random Finite Sets (RFSs)
50(5)
2.3.1 RFSs and Point Processes
51(2)
2.3.2 Examples of RFSs
53(1)
2.3.3 Algebraic Properties of RFSs
54(1)
2.4 Multiobject Statistics in a Nutshell
55(4)
Chapter 3 Multiobject Calculus
59(22)
3.1 Introduction
59(1)
3.2 Basic Concepts
60(2)
3.2.1 Set Functions
60(1)
3.2.2 Functionals
60(1)
3.2.3 Functional Transformations
61(1)
3.2.4 Multiobject Density Functions
62(1)
3.3 Set Integrals
62(2)
3.4 Multiobject Differential Calculus
64(5)
3.4.1 Gateaux Directional Derivatives
65(1)
3.4.2 Volterra Functional Derivatives
66(1)
3.4.3 Set Derivatives
67(2)
3.5 Key Formulas of Multiobject Calculus
69(12)
3.5.1 Fundamental Theorem of Multiobject Calculus
70(1)
3.5.2 Change of Variables Formula for Set Integrals
71(1)
3.5.3 Set Integrals on Joint Spaces
71(2)
3.5.4 Constant Rule
73(1)
3.5.5 Sum Rule
73(1)
3.5.6 Linear Rule
73(1)
3.5.7 Monomial Rule
73(1)
3.5.8 Power Rule
74(1)
3.5.9 Product Rules
74(1)
3.5.10 First Chain Rule
75(1)
3.5.11 Second Chain Rule
76(1)
3.5.12 Third Chain Rule
76(1)
3.5.13 Fourth Chain Rule
77(1)
3.5.14 Clark's General Chain Rule
78(3)
Chapter 4 Multiobject Statistics
81(26)
4.1 Introduction
81(1)
4.2 Basic Multiobject Statistical Descriptors
81(17)
4.2.1 Belief-Mass Functions
83(1)
4.2.2 Multiobject Probability Density Functions
84(1)
4.2.3 Convolution and Deconvolution
85(1)
4.2.4 Probability Generating Functionals (p.g.fl.'s)
86(2)
4.2.5 Multivariate p.g.fl.'s
88(4)
4.2.6 Cardinality Distributions
92(1)
4.2.7 Probability Generating Functions (p.g.f.'s)
92(1)
4.2.8 Probability Hypothesis Densities (PHDs)
93(2)
4.2.9 Factorial Moment Density
95(1)
4.2.10 Equivalence of the Fundamental Descriptors
95(1)
4.2.11 Radon-NikodSim Formulas
96(1)
4.2.12 Campbell's Theorems
96(2)
4.3 Important Multiobject Processes
98(5)
4.3.1 Poisson RFSs
98(1)
4.3.2 Identical, Independently Distributed Cluster (i.i.d.c.) RFSs
99(1)
4.3.3 Bernoulli RFSs
100(1)
4.3.4 Multi-Bernoulli RFSs
101(2)
4.4 Basic Derived RFSs
103(4)
4.4.1 Censored RFSs
103(1)
4.4.2 Cluster RFSs
104(3)
Chapter 5 Multiobject Modeling and Filtering
107(32)
5.1 Introduction
107(1)
5.2 The Multisensor-Multitarget Bayes Filter
108(2)
5.3 Multitarget Bayes Optimality
110(2)
5.4 RFS Multitarget Motion Models
112(1)
5.5 RFS Multitarget Measurement Models
113(4)
5.6 Multitarget Markov Densities
117(1)
5.7 Multisensor-Multitarget Likelihood Functions
118(2)
5.8 The Multitarget Bayes Filter in p.g.fl. Form
120(2)
5.8.1 The p.g.fl. Time Update Equation
120(1)
5.8.2 The p.g.fl. Measurement Update Equation
121(1)
5.9 The Factored Multitarget Bayes Filter
122(3)
5.10 Approximate Multitarget Filters
125(14)
5.10.1 The p.g.fl. Time Update for Independent Targets
126(2)
5.10.2 The p.g.fl. Measurement Update for Independent Measurements
128(1)
5.10.3 A Principled Approximation Methodology
129(1)
5.10.4 Poisson Approximation: PHD Filters
130(2)
5.10.5 i.i.d.c. Approximation: CPHD Filters
132(2)
5.10.6 Multi-Bernoulli Approximation: Multi-Bernoulli Filters
134(2)
5.10.7 Bernoulli Approximation: Bernoulli Filters
136(3)
Chapter 6 Multiobject Metrology
139(22)
6.1 Introduction
139(1)
6.2 Multiobject Miss Distance
140(13)
6.2.1 Multiobject Miss Distance: A History
141(3)
6.2.2 The Optimal Sub-Pattern Assignment (OSPA) Metric
144(3)
6.2.3 Extension of OSPA to Covariance (COSPA)
147(2)
6.2.4 OSPA for Labeled Tracks (LOSPA)
149(3)
6.2.5 Temporal OSPA (TOSPA)
152(1)
6.3 Multiobject Information Functionals
153(10)
6.3.1 Csiszar Information Functionals
154(3)
6.3.2 Csiszar Functionals for Poisson Processes
157(1)
6.3.3 Csiszar Functionals for i.i.d.c. Processes
158(3)
II RFS Filters: Standard Measurement Model 161(340)
Chapter 7 Introduction to Part II
163(18)
7.1 Summary of Major Lessons Learned
164(1)
7.2 Standard Multitarget Measurement Model
165(8)
7.2.1 Standard Multitarget Measurement Submodels
166(1)
7.2.2 Standard Multitarget Measurement Model: p.g.fl. and Likelihood
167(1)
7.2.3 Standard Multitarget Measurement Model: Special Cases
168(1)
7.2.4 Measurement-to-Track Association (MTA)
169(4)
7.2.5 Relationship Between the MTA and RFS Approaches
173(1)
7.3 An Approximate Standard Likelihood Function
173(1)
7.4 Standard Multitarget Motion Model
174(4)
7.5 Standard Motion Model with Target Spawning
178(1)
7.6 Organization of Part II
178(3)
Chapter 8 Classical PHD and CPHD Filters
181(36)
8.1 Introduction
181(2)
8.1.1 Summary of Major Lessons Learned
181(2)
8.1.2 Organization of the
Chapter
183(1)
8.2 A General PHD Filter
183(6)
8.2.1 General PHD Filter: Motion Modeling
185(1)
8.2.2 General PHD Filter: Predictor
186(1)
8.2.3 General PHD Filter: Measurement Modeling
187(1)
8.2.4 General PHD Filter: Corrector
188(1)
8.3 Arbitrary-Clutter PHD Filter
189(2)
8.3.1 Time Update Equations for the Arbitrary-Clutter Classical PHD Filter
189(1)
8.3.2 Measurement Modeling for the Arbitrary-Clutter Classical PHDFilter
189(1)
8.3.3 Arbitrary-Clutter PHD Filter: Corrector
190(1)
8.4 Classical PHD Filter
191(10)
8.4.1 Classical PHD Filter: Predictor
192(1)
8.4.2 Classical PHD Filter: Measurement Modeling
192(1)
8.4.3 Classical PHD Filter: Corrector
193(1)
8.4.4 Classical PHD Filter: State Estimation
194(1)
8.4.5 Classical PHD Filter: Uncertainty Estimation
195(1)
8.4.6 Classical PHD Filter: Characteristics
195(6)
8.5 Classical Cardinalized PHD (CPHD) Filter
201(11)
8.5.1 Classical CPHD Filter Motion Modeling
202(1)
8.5.2 Classical CPHD Filter: Predictor
202(2)
8.5.3 Classical CPHD Filter: Measurement Modeling
204(1)
8.5.4 Classical CPHD Filter: Corrector
205(3)
8.5.5 Classical CPHD Filter: State Estimation
208(1)
8.5.6 Classical CPHD Filter: Characteristics
208(2)
8.5.7 Approximate Classical CPHD Filter
210(2)
8.6 Zero False Alarms (ZFA) CPHD Filter
212(3)
8.6.1 Comparison of the PHD and ZFA-CPHD Filters
213(2)
8.7 PHD Filter for State-Dependent Poisson Clutter
215(2)
Chapter 9 Implementing Classical PHD/CPHD Filters
217(60)
9.1 Introduction
217(2)
9.1.1 Summary of Major Lessons Learned
217(1)
9.1.2 Organization of the
Chapter
218(1)
9.2 "Spooky Action at a Distance"
219(2)
9.3 Merging and Splitting for PHD Filters
221(2)
9.3.1 Merging for PHD Filters
221(1)
9.3.2 Splitting for PHD Filters
222(1)
9.4 Merging and Splitting for CPHD Filters
223(3)
9.4.1 Merging for CPHD Filters
223(1)
9.4.2 Splitting for CPHD Filters
224(2)
9.5 Gaussian Mixture (GM) Implementation
226(35)
9.5.1 Standard GM Implementation
227(1)
9.5.2 Pruning Gaussian Components
228(1)
9.5.3 Merging Gaussian Components
229(2)
9.5.4 GM-PHD Filter
231(13)
9.5.5 GM-CPHD Filter
244(6)
9.5.6 Implementation with Nonconstant pp
250(1)
9.5.7 Implementation with Partially Uniform Target Births
251(6)
9.5.8 Implementation with Target Identity
257(4)
9.6 Sequential Monte Carlo (SMC) Implementation
261(16)
9.6.1 SMC Approximation
262(1)
9.6.2 SMC-PHD Filter
263(4)
9.6.3 SMC-CPHD Filter
267(2)
9.6.4 Using Measurements to Choose New Particles
269(6)
9.6.5 Implementation with Target Identity
275(2)
Chapter 10 Multisensor PHD and CPHD Filters
277(34)
10.1 Introduction
277(2)
10.1.1 Summary of Major Lessons Learned
277(1)
10.1.2 Organization of the
Chapter
278(1)
10.2 The Multisensor-Multitarget Bayes Filter
279(2)
10.3 The General Multisensor PHD Filter
281(2)
10.3.1 General Multisensor PHD Filter: Modeling
281(1)
10.3.2 General Multisensor PHD Filter: Update
282(1)
10.4 The Multisensor Classical PHD Filter
283(4)
10.4.1 Implementations of the Exact Classical Multisensor PHD Filter
287(1)
10.5 Iterated-Corrector Multisensor PHD/CPHD Filters
287(2)
10.5.1 Limitations of the Iterated-Corrector Approach
288(1)
10.6 Parallel Combination Multisensor PHD and CPHD Filters
289(11)
10.6.1 Parallel Combination Multisensor CPHD Filter
293(3)
10.6.2 Parallel Combination Multisensor PHD Filter
296(3)
10.6.3 Simplified PCAM-PHD Filter
299(1)
10.7 An Erroneous "Averaged" Multisensor PHD Filter
300(6)
10.8 Performance Comparisons
306(5)
Chapter 11 Jump-Markov PHD/CPHD Filters
311(40)
11.1 Introduction
311(4)
11.1.1 Summary of Major Lessons Learned
313(1)
11.1.2 Organization of the
Chapter
314(1)
11.2 Jump-Markov Filters: A Review
315(3)
11.2.1 The Jump-Markov Bayes Recursive Filter
316(1)
11.2.2 State Estimation for Jump-Markov Filters
317(1)
11.3 Multitarget Jump-Markov Systems
318(2)
11.3.1 What Is a Multitarget Jump-Markov System?
318(2)
11.3.2 The Multitnrget Jump-Markov Filter
320(1)
11.4 Jump-Markov PHD Filter
320(4)
11.4.1 Jump-Markov PHD Filter: Models
321(1)
11.4.2 Jump-Markov PHD Filter: Time Update
322(1)
11.4.3 Jump-Markov PHD Filter: Measurement Update
323(1)
11.4.4 Jump-Markov PHD Filter: State Estimation
324(1)
11.5 Jump-Markov CPHD Filter
324(5)
11.5.1 Jump-Markov CPHD Filter: Modeling
325(1)
11.5.2 Jump-Markov CPHD Filter: Time Update
325(1)
11.5.3 Jump-Markov CPHD Filter: Measurement Update
326(3)
11.5.4 Jump-Markov CPHD Filter: State Estimation
329(1)
11.6 Variable State Space Jump-Markov CPHD Filters
329(11)
11.6.1 Variable State Space CPHD Filters: Modeling
331(2)
11.6.2 Variable State Space CPHD Filters: Time Update
333(2)
11.6.3 Variable State Space CPHD Filters: Measurement Update
335(3)
11.6.4 Variable State Space CPHD Filters: State Estimation
338(2)
11.7 Implementing Jump-Markov PHD/CPHD Filters
340(6)
11.7.1 Gaussian Mixture Jump-Markov PHD/CPHD Filters
340(6)
11.7.2 Particle Implementation of Jump-Markov PHD and CPHD Filters
346(1)
11.8 Implemented Jump-Markov PHD/CPHD Filters
346(5)
11.8.1 Jump-Markov PHD Filter of Pasha et al.
347(1)
11.8.2 IMM-Type JM-PHD Filter of Punithakumar et al.
347(1)
11.8.3 Best-Fitting-Gaussian PHD Filter of Wenling Li and Yingmin Jia
348(1)
11.8.4 JM-CPHD Filter of Georgescu et al.
349(1)
11.8.5 Current Statistical Model (CSM) PHD Filter of Mengjun et al.
349(1)
11.8.6 The Variable State Space CPHD Filter of Chen et al.
350(1)
Chapter 12 Joint Tracking and Sensor-Bias Estimation
351(28)
12.1 Introduction
351(7)
12.1.1 Example: "Gridlocking" of Sensor Platforms
352(4)
12.1.2 Gridlocking in General
356(1)
12.1.3 Summary of Major Lessons Learned
356(1)
12.1.4 Organization of the
Chapter
357(1)
12.2 Modeling Sensor Biases
358(1)
12.3 Optimal Joint Tracking and Registration
359(6)
12.3.1 Optimal BURT Filter: Single-Filter Version
360(2)
12.3.2 Optimal BURT Filter: Two-Filter Version
362(2)
12.3.3 Optimal BURT Procedure
364(1)
12.4 The BURT-PHD Filter
365(7)
12.4.1 BURT-PHD Filter: Single-Sensor Case
366(5)
12.4.2 BURT-PHD Filter: Multisensor Case Using Iterated Corrector
371(1)
12.4.3 BURT-PHD Filter: Multisensor Case Using Parallel Combination
372(1)
12.5 Single-Filter BURT-PHD Filters
372(4)
12.5.1 Single-Filter BURT-PHD Filter for Static Biases
372(3)
12.5.2 A Heuristic Single-Filter BURT-PHD Filter
375(1)
12.6 Implemented BURT-PHD Filters
376(3)
12.6.1 The BURT-PHD Filter of Ristic and Clark
377(1)
12.6.2 The BURT-PHD Filter of Lian et al.
377(2)
Chapter 13 Multi-Bernoulli Filters
379(26)
13.1 Introduction
379(3)
13.1.1 Summary of Major Lessons Learned
380(1)
13.1.2 Organization of the
Chapter
381(1)
13.2 The Bernoulli Filter
382(6)
13.2.1 Bernoulli Filter: Modeling
383(1)
13.2.2 Bernoulli Filter: Time-Update
384(1)
13.2.3 Bernoulli Filter: Measurement Update
384(1)
13.2.4 Bernoulli Filter: State Estimation
385(1)
13.2.5 Bernoulli Filter: Error Estimation
386(1)
13.2.6 The Bernoulli Filter as an Exact PHD Filter
386(1)
13.2.7 Bernoulli Filter: Practical Implementation
387(1)
13.2.8 Bernoulli Filter: Implementations
388(1)
13.3 The Multisensor Bernoulli Filter
388(2)
13.4 The CBMeMBer Filter
390(9)
13.4.1 CBMeMBer Filter: Modeling
392(1)
13.4.2 CBMeMBer Filter: Predictor
392(1)
13.4.3 CBMeMBer Filter: Corrector
393(2)
13.4.4 CBMeMBer Filter: Merging and Pruning
395(1)
13.4.5 CBMeMBer Filter: State and Error Estimation
395(1)
13.4.6 CBMeMBer Filter: Track Management
396(1)
13.4.7 CBMeMBer Filter: Gaussian-Mixture and Particle Implementation
397(1)
13.4.8 CBMeMBer Filter: Performance
397(2)
13.5 Jump-Markov CBMeMBer Filter
399(6)
13.5.1 Jump-Markov CBMeMBer Filter: Modeling
399(1)
13.5.2 Jump-Markov CBMeMBer Filter: Predictor
400(1)
13.5.3 Jump-Markov CBMeMBer Filter: Corrector
401(2)
13.5.4 Jump-Markov CBMeMBer Filter: Performance
403(2)
Chapter 14 RFS Multitarget Smoothers
405(30)
14.1 Introduction
405(3)
14.1.1 Summary of Major Lessons Learned
406(2)
14.1.2 Organization of the
Chapter
408(1)
14.2 Single-Target Forward-Backward Smoother
408(6)
14.2.1 Derivation of Forward-Backward Smoother
409(1)
14.2.2 Vo-Vo Alternative Form of the Forward-Backward Smoother
410(2)
14.2.3 Vo-Vo Exact Closed-Form GM Forward-Backward Smoother
412(2)
14.3 General Multitarget Forward-Backward Smoother
414(2)
14.4 Bernoulli Forward-Backward Smoother
416(5)
14.4.1 Bernoulli Forward-Backward Smoother: Modeling
417(1)
14.4.2 Bernoulli Forward-Backward Smoother: Equations
417(3)
14.4.3 Bernoulli Forward-Backward Smoother: Exact GM Implementation
420(1)
14.4.4 Bernoulli Forward-BackWard Smoother: Results
421(1)
14.5 PHD Forward-Backward Smoother
421(12)
14.5.1 PHD Forward-Backward Smoother Equation
422(2)
14.5.2 Derivation of the PHD Forward-Backward Smoother
424(2)
14.5.3 Fast Particle-PHD Forward-Backward Smoother
426(3)
14.5.4 Alternative PHD Forward-Backward Smoother
429(1)
14.5.5 Gaussian-Mixture PHD Smoother
430(1)
14.5.6 Implementations of the PHD Forward-Backward Smoother
431(2)
14.6 ZTA-CPHD Smoother
433(2)
Chapter 15 Exact Closed-Form Multitarget Filter
435(66)
15.1 Introduction
435(10)
15.1.1 Exact Closed-Form Solution of the Single-Target Bayes Filter
437(3)
15.1.2 Exact Closed-Form Solution of the Multitarget Bayes Filter
440(2)
15.1.3 Overview of the Vo-Vo Filter Approach
442(2)
15.1.4 Summary of Major Lessons Learned
444(1)
15.1.5 Organization of the
Chapter
445(1)
15.2 Labeled RFSs
445(4)
15.2.1 Target Labels
446(1)
15.2.2 Labeled Multitarget State Sets
447(1)
15.2.3 Set Integrals for Labeled Multitarget States
448(1)
15.3 Examples of Labeled RFSs
449(16)
15.3.1 Labeled i.i.d.c. RFSs
449(4)
15.3.2 Labeled Poisson RFSs
453(1)
15.3.3 Labeled Multi-Bernoulli (LMB) RFSs
453(5)
15.3.4 Generalized Labeled Multi-Bernoulli (GLMB) RFSs
458(7)
15.4 Modeling for the Vo-Vo Filter
465(16)
15.4.1 Labeling Conventions
465(3)
15.4.2 Overview of the Vo-Vo Filter
468(4)
15.4.3 Basic Motion and Measurement Models
472(1)
15.4.4 Motion and Measurement Models with Target ID
473(1)
15.4.5 The Labeled Multitarget Likelihood Function
474(2)
15.4.6 The Labeled Multitarget Markov Density-Standard Version
476(4)
15.4.7 Labeled Multitarget Markov Density-Modified
480(1)
15.5 Closure of Multitarget Bayes Filter
481(15)
15.5.1 A "Road Map" for the Derivations
482(3)
15.5.2 Closure Under Measurement Update with Respect to Vo-Vo Priors
485(4)
15.5.3 Closure Under Time Update with Respect to Vo-Vo Priors
489(7)
15.6 Implementation of the Vo-Vo Filter: Sketch
496(3)
15.6.1 δ-GLMB Distributions
496(2)
15.6.2 δ-GLMB Version of the Vo-Vo Filter
498(1)
15.6.3 Characterization of Pruning
498(1)
15.7 Performance Results
499(4)
15.7.1 Gaussian Mixture Implementation of Vo-Vo Filter
499(1)
15.7.2 Particle Implementation of the Vo-Vo Filter
500(1)
III RFS Filters for Unknown Backgrounds 501(144)
Chapter 16 Introduction to Part III
503(16)
16.1 Introduction
505(1)
16.2 Overview of the Approach
506(2)
16.3 Models for Unknown Backgrounds
508(9)
16.3.1 A Model for Unknown Detection Profile
509(2)
16.3.2 A General Model for Unknown Clutter
511(3)
16.3.3 Unknown-Clutter Models: Poisson-Mixture
514(1)
16.3.4 Unknown-Clutter Models: General Bernoulli
515(1)
16.3.5 Unknown-Clutter Models: Simplified Bernoulli
516(1)
16.4 Organization of Part III
517(2)
Chapter 17 RFS Filters for Unknown PD
519(32)
17.1 Introduction
519(4)
17.1.1 Converting RFS Filters into pp-Agnostic Filters
520(1)
17.1.2 A Motion Model for Probability of Detection
521(1)
17.1.3 Summary of Major Lessons Learned
522(1)
17.1.4 Organization of the
Chapter
523(1)
17.2 The pp-CPHD Filter
523(5)
17.2.1 pD-CPHD Filter Models
523(1)
17.2.2 pp-CPHD Filter Time Update
524(1)
17.2.3 pp-CPHD Filter Measurement Update
525(2)
17.2.4 pD-CPHD Filter Multitarget State Estimation
527(1)
17.3 Beta-Gaussian Mixture (BGM) Approximation
528(6)
17.3.1 Overview of the BGM Approach
529(1)
17.3.2 Beta-Gaussian Mixtures (BGMs)
530(1)
17.3.3 Pruning BGM Components
531(1)
17.3.4 Merging BGM Components
532(2)
17.4 BGM Implementation of the pp-PHD Filter
534(6)
17.4.1 BGM pD-PHD Filter Modeling Assumptions
534(2)
17.4.2 BGM pD-PHD Filter Time Update
536(2)
17.4.3 BGM pD-PHD Filter Measurement Update
538(1)
17.4.4 BGM pD-PHD Filter Multitarget State Estimation
539(1)
17.5 BGM Implementation of the pD-CPHD Filter
540(6)
17.5.1 BGM pD-CPHD Filter Modeling Assumptions
540(1)
17.5.2 BGM pD-CPHD Filter Time Update
541(2)
17.5.3 BGM pD-CPHD Filter Measurement Update
543(3)
17.5.4 BGM pD-CPHD Filter Multitarget State Estimation
546(1)
17.6 The pD-CBMeMBer Filter
546(3)
17.7 Implementations of pD-Agnostic RFS Filters
549(2)
Chapter 18 RFS Filters for Unknown Clutter
551(94)
18.1 Introduction
551(4)
18.1.1 Summary of Major Lessons Learned
552(2)
18.1.2 Organization of the
Chapter
554(1)
18.2 A General Model for Unknown Bernoulli Clutter
555(5)
18.2.1 The General Joint Target-Clutter Model
556(2)
18.2.2 Phenomenology-Nonintermixing Motion Model
558(1)
18.2.3 Phenomenology-Intermixing Motion Model
558(2)
18.3 CPHD Filter for General Bernoulli Clutter
560(11)
18.3.1 General Bernoulli Clutter-Generator Model: CPHD Filter Time Update
563(1)
18.3.2 General Bernoulli Clutter Model: CPHD Filter Measurement Update
564(2)
18.3.3 General Bernoulli Clutter-Generator Model: PHD Filter Special Case
566(1)
18.3.4 General Bernoulli Clutter Model: Multitarget State Estimation
566(3)
18.3.5 General Bernoulli Clutter-Generator Model: Clutter Estimation
569(2)
18.4 The λ-CPHD Filter
571(14)
18.4.1 λ-CPHD Filter: Models
572(2)
18.4.2 λ-CPHD Filter: Time Update
574(1)
18.4.3 λ-CPHD Filter: Measurement Update
575(1)
18.4.4 λ-CPHD Filter: Multitarget State Estimation
576(1)
18.4.5 λ-CPHD Filter: Clutter Estimation
577(1)
18.4.6 Special Case: The k-PHD Filter
578(1)
18.4.7 λ-CPHD Filter Implementation: Gaussian Mixtures
579(6)
18.5 The k-CPHD Filter
585(32)
18.5.1 k-CPHD Filter: Models
586(1)
18.5.2 k-CPHD Filter: Time Update
587(2)
18.5.3 k-CPHD Filter: Measurement Update
589(1)
18.5.4 k-CPHD Filter: Multitarget State Estimation
590(1)
18.5.5 k-CPHD Filter: Clutter Estimation
591(2)
18.5.6 Special Case: The k-PHD Filter
593(1)
18.5.7 k-CPHD Filter: Beta-Gaussian Mixtures
594(9)
18.5.8 k-CPHD Filter Implementation: Normal-Wishart Mixtures
603(14)
18.6 Multisensor k-CPHD Filters
617(4)
18.6.1 Iterated-Corrector k-CPHD Filter
617(1)
18.6.2 Parallel-Combination k-CPHD Filter
617(4)
18.7 The K-CBMeMBer Filter
621(7)
18.7.1 k-CBMeMBer Filter: Modeling
622(2)
18.7.2 k-CBMeMBer Filter: Time Update
624(1)
18.7.3 k-CBMeMBer Filter: Measurement Update
625(2)
18.7.4 k-CBMeMBer Filter: Multitarget State Estimation
627(1)
18.7.5 k-CBMeMBer Filter: Clutter Estimation
627(1)
18.8 Implemented Clutter-Agnostic RFS Filters
628(3)
18.8.1 Implemented λ-CPHD Filter
628(1)
18.8.2 "Bootstrap" λ-CPHD Filter
629(1)
18.8.3 Implemented λ-CBMeMBer Filter
630(1)
18.8.4 Implemented NWM-PHD Filter
631(1)
18.9 Clutter-Agnostic Pseudofilters
631(5)
18.9.1 The λ-PHD Pseudofilter
632(3)
18.9.2 Pathological Behavior of the λ-PHD Pseudofilter
635(1)
18.10 CPHD/PHD Filters with Poisson-Mixture Clutter
636(5)
18.10.1 Poisson-Mixture Clutter-Agnostic CPHD Filter
638(2)
18.10.2 Poisson-Mixture Clutter-Agnostic PHD Filter
640(1)
18.11 Related Work
641(6)
8.11.1 Decoupled Target-Clutter PHD Filter
642(1)
18.11.2 The "Dual PHD" Filter
643(1)
18.11.3 The "iFilter "
644(1)
IV RFS Filters for Nonstandard Measurement Models 645(180)
Chapter 19 RFS Filters for Superpositional Sensors
647(24)
19.1 Introduction
647(7)
19.1.1 Examples of Superpositional Sensor Models
648(5)
19.1.2 Summary of Major Lessons Learned
653(1)
19.1.3 Organization of the
Chapter
653(1)
19.2 Exact Superpositional CPHD Filter
654(2)
19.3 Hauschildt's Approximation
656(5)
19.3.1 Hauschildt Σ-CPHD Filter: Overview
656(2)
19.3.2 Hauschildt Σ-CPHD Filter: Models
658(1)
19.3.3 Hauschildt Σ-CPHD Filter: Measurement Update
658(3)
19.3.4 Hauschildt Σ-CPHD Filter: Implementations
661(1)
19.4 Thouin-Nannuru-Coates (TNC) Approximation
661(10)
19.4.1 Generalized TNC Approximation: Overview
662(4)
19.4.2 TNC Σ-CPHD Filter: Models
666(1)
19.4.3 TNC Σ-CPHD Filter: Measurement Update
666(2)
19.4.4 TNC Σ-CPHD Filter: Implementations
668(3)
Chapter 20 US Filters for Pixelized Images
671(14)
20.1 Introduction
671(2)
20.1.1 Summary of Major Lessons Learned
672(1)
20.1.2 Organization of the
Chapter
672(1)
20.2 The IO Multitarget Measurement Model
673(3)
20.3 IO Motion Model
676(1)
20.4 IO-CPHD Filter
676(1)
20.5 IO-MeMBer Filter
677(2)
20.5.1 IO-MeMBer Filter: Measurement Update
677(1)
20.5.2 IO-MeMBer Filter: Track Merging
678(1)
20.5.3 IO-MeMBer Filter: Multitarget State Estimation
678(1)
20.5.4 IO-MeMBer Filter: Track Management
678(1)
20.6 Implementations of IO-MeMBer Filters
679(6)
20.6.1 Track-Before-Detect (TBD) in Image Data
679(1)
20.6.2 Tracking in Color Videos
680(3)
20.6.3 Tracking Road-Constrained Targets
683(2)
Chapter 21 RFS Filters for Cluster-Type Targets
685(72)
21.1 Introduction
685(6)
21.1.1 Summary of Major Lessons Learned
688(2)
21.1.2 Organization of the
Chapter
690(1)
21.2 Extended-Target Measurement Models
691(5)
21.2.1 The Statistics of Extended Targets
692(1)
21.2.2 Exact Rigid-Body (ERB) Model
692(2)
21.2.3 Approximate Rigid-Body (ARB) Model
694(1)
21.2.4 Approximate Poisson-Body (APB) Model
695(1)
21.3 Extended-Target Bernoulli Filters
696(2)
21.3.1 Extended-Target Bernoulli Filters: Performance
698(1)
21.4 Extended-Target PHD/CPHD Filters
698(18)
21.4.1 General Extended-Target PHD Filter
699(1)
21.4.2 PHD Filter for Extended Targets: ERB Model
700(1)
21.4.3 PHD Filter for Extended Targets: APB Model
700(16)
21.5 Extended-Target CPHD Filter: APB Model
716(4)
21.5.1 APB-CPHD Filter: Theory
717(1)
21.5.2 Gaussian Mixture APB-CPHD Filter: Performance
718(1)
21.5.3 Gamma Gaussian Inverse-Wishart APB-CPHD Filter: Performance
719(1)
21.5.4 APB-CPHD Filter of Lian et al.: Performance
719(1)
21.6 Cluster-Target Measurement Model
720(2)
21.6.1 Likelihood Function for Cluster Targets
720(1)
21.6.2 Estimation of Soft Clusters
721(1)
21.7 Cluster-Target PHD and CPHD Filters
722(2)
21.7.1 Cluster-Target CPHD Filter
722(2)
21.7.2 Cluster-Target PHD Filter
724(1)
21.8 Measurement Models for Level-1 Group Targets
724(10)
21.8.1 "Natural" State Representation of Single Level-1 Group Targets
725(1)
21.8.2 "Natural" State Representation of Multiple Level-1 Group Targets
726(2)
21.8.3 Simplified State Representation of Multiple Level-1 Group Targets
728(4)
21.8.4 Multiple Level-1 Group Targets with the Standard Measurement Model
732(2)
21.9 PHD/CPHD Filters for Level-1 Group Targets
734(9)
21.9.1 PHD Filter for Level-1 Group Targets: Standard Model
734(2)
21.9.2 CPHD Filter for Level-1 Group Targets: Standard Model
736(1)
21.9.3 PHD Filter for Single Level-1 Group Targets: Standard Measurement Model
736(6)
21.9.4 CPHD Filter for Single Level-1 Group Targets: Standard Model
742(1)
21.10 Measurement Models for General Group Targets
743(4)
21.10.1 Simplified State Representation of Level-l Group Targets
744(2)
21.10.2 Standard Measurement Model for Level-l Group Targets
746(1)
21.11 PHD/CPHD Filters for Level-l Group Targets
747(1)
21.12 A Model for Unresolved Targets
748(4)
21.13 Motion Model for Unresolved Targets
752(1)
21.14 The Unresolved-Target PHD Filter
752(2)
21.15 Approximate Unresolved-Target PHD Filter
754(1)
21.16 Approximate Unresolved-Target CPHD Filter
754(3)
Chapter 22 RFS Filters for Ambiguous Measurements
757(68)
22.1 Introduction
757(7)
22.1.1 Motivation: Quantized Measurements
758(1)
22.1.2 Generalized Measurements, Measurement Models, and Likelihoods
759(2)
22.1.3 Summary of Major Lessons Learned
761(3)
22.1.4 Organization of the
Chapter
764(1)
22.2 Random Set Models of Ambiguous Measurements
764(11)
22.2.1 Imprecise Measurements
765(1)
22.2.2 Vague Measurements
765(4)
22.2.3 Uncertain Measurements
769(4)
22.2.4 Contingent Measurements (Inference Rules)
773(1)
22.2.5 Generalized Fuzzy Measurements
774(1)
22.3 Generalized Likelihood Functions (GLFs)
775(8)
22.3.1 GLFs for Nonnoisy Nontraditional Measurements
776(2)
22.3.2 GLFs for Noisy Nontraditional Measurements
778(1)
22.3.3 Bayesian Processing of Generalized Measurements
778(1)
22.3.4 Bayes Optimality of the GLF Approach
779(4)
22.4 Unification of Expert-System Theories
783(9)
22.4.1 Bayesian Unification of Measurement Fusion
783(3)
22.4.2 Dempster's Rule Arises as a Particular Instance of Bayes' Rule
786(3)
22.4.3 Bayes-Optimal Measurement Conversion
789(3)
22.5 GLFs for Imperfectly Characterized Targets
792(6)
22.5.1 Example: Imperfectly Characterized Target Types
793(1)
22.5.2 Example: Received Signal Strength (RSS)
793(1)
22.5.3 Modeling Imperfectly Characterized Targets
794(1)
22.5.4 GLFs for Imperfectly Characterized Targets
795(3)
22.5.5 Bayes Filtering with Imperfectly Characterized Targets
798(1)
22.6 GLFs for Unknown Target Types
798(1)
22.6.1 Unmodeled Target Type
798(1)
22.6.2 Unmodeled Target Types-Imperfectly Characterized Measurement Function
799(1)
22.7 GLFs for Information with Unknown Correlations
799(1)
22.8 GLFs for Unreliable Information Sources
800(3)
22.9 Using GLFs in Multitarget Filters
803(2)
22.10 GLFs in RFS Multitarget Filters
805(9)
22.10.1 Using GLFs in PHD Filters
805(2)
22.10.2 Using GLFs in CPHD Filters
807(2)
22.10.3 Using GLFs in CBMeMBer Filters
809(1)
22.10.4 Using GLFs in Bernoulli Filters
810(1)
22.10.5 Implementations of RFS Filters for Nontraditional Measurements
810(4)
22.11 Using GLFs with Conventional Multitarget Filters
814(13)
22.11.1 Measurement-to-Track Association (MTA) with Nontraditional Measurements
814(1)
22.11.2 A Closed-Form Example: Fuzzy Measurements
815(3)
22.11.3 MTA with Joint Kinematic and Nonkinematic Measurements
818(7)
V Sensor, Platform, and Weapons Management 825(208)
Chapter 23 Introduction to Part V
827(34)
23.1 Basic Issues in Sensor Management
830(4)
23.1.1 Top-Down or Bottom-Up?
831(1)
23.1.2 Single-Step or Multistep?
831(1)
23.1.3 Information-Theoretic or Mission-Oriented?
832(2)
23.2 Information Theory and Intuition: An Example
834(6)
23.2.1 PENT for "Cookie Cutter" Sensor Fields of View (FoVs)
835(2)
23.2.2 PENT for General Sensor Fields of View
837(2)
23.2.3 Characteristics of PENT
839(1)
23.2.4 The Cardinality-Covariance Objective Function
839(1)
23.2.5 The Cauchy-Schwartz Objective Function
840(1)
23.3 Summary of RFS Sensor Control
840(18)
23.3.1 RFS Control Summary: General Approach (SingleStep)
841(6)
23.3.2 RFS Control Summary: Ideal Sensor Dynamics
847(2)
23.3.3 RFS Control Summary: Simplified Nonideal Sensor Dynamics
849(3)
23.3.4 RFS Control Summary: Control with PHD and CPHD Filters
852(1)
23.3.5 RFS Control Summary: "Pseudosensor" Approximation for Multisensor Control
853(2)
23.3.6 RFS Control Summary: General Approach (Multi-step)
855(3)
23.4 Organization of Part V
858(3)
Chapter 24 Single-Target Sensor Management
861(28)
24.1 Introduction
861(2)
24.1.1 Summary of Major Lessons Learned
861(1)
24.1.2 Organization of the
Chapter
862(1)
24.2 Example: Missile-Tracking Cameras
863(6)
24.2.1 Single-Camera Missile Tracking
863(4)
24.2.2 Two-Camera Missile Tracking
867(2)
24.3 Single-Sensor, Single-Target Control: Modeling
869(3)
24.4 Single-Sensor, Single-Target Control: Single-Step
872(1)
24.5 Single-Sensor, Single-Target Control: Objective Functions
872(3)
24.5.1 Kullback-Leibler Information Gain
873(1)
24.5.2 Csiszar Information Gain
874(1)
24.5.3 Cauchy-Schwartz Information Gain
874(1)
24.6 Single-Sensor, Single-Target Control: Hedging
875(2)
24.6.1 Expected-Value Hedging
875(1)
24.6.2 Minimum-Value Hedging
875(1)
24.6.3 Multisample Approximate Hedging
875(1)
24.6.4 Single-Sample Approximate Hedging
876(1)
24.6.5 Mixed Expected-Value and PM Hedging
877(1)
24.7 Single-Sensor, Single-Target Control: Optimization
877(1)
24.8 Special Case 1: Ideal Sensor Dynamics
878(2)
24.9 Simple Example: Linear-Gaussian Case
880(2)
24.10 Special Case 2: Simplified Nonideal Dynamics
882(7)
24.10.1 Simplified Nonideal Single-Sensor Dynamics: Modeling
883(2)
24.10.2 Simplified Nonideal Single-Sensor Dynamics: Filtering Equations
885(1)
24.10.3 Simplified Nonideal Single-Sensor Dydamics:- Optimization
886(3)
Chapter 25 Multitarget Sensor Management
889(60)
25.1 Introduction
889(3)
25.1.1 Summary of Major Lessons Learned
890(1)
25.1.2 Organization of the
Chapter
891(1)
25.2 Multitarget Control: Target and Sensor State Spaces
892(3)
25.2.1 Target State Spaces
892(1)
25.2.2 Sensor State Spaces
893(1)
25.2.3 Joint Multisensor-Multitarget State Space
893(1)
25.2.4 Integrals and Set Integrals on State Spaces
894(1)
25.2.5 p.g.fl.'s on Target/Sensor State Spaces
895(1)
25.3 Multitarget Control: Control Spaces
895(1)
25.4 Multitarget Control: Measurement Spaces
896(4)
25.4.1 Sensor Measurements
896(1)
25.4.2 Actuator-Sensor Measurements
897(1)
25.4.3 Joint Multisensor-Multitarget Measurements
897(1)
25.4.4 Integrals and Set Integrals on Measurement Spaces
898(1)
25.4.5 p.g.fl.'s on Measurement Spaces
899(1)
25.5 Multitarget Control: Motion Models
900(3)
25.5.1 Single-Target and Multitarget Motion Models
901(1)
25.5.2 Single-Sensor Motion and Multisensor Motion with Sensor Controls
901(1)
25.5.3 Joint Multisensor-Multitarget Motion
902(1)
25.6 Multitarget Control: Measurement Models
903(5)
25.6.1 Measurements: Assumptions
904(1)
25.6.2 Measurements: Sensor Noise
905(1)
25.6.3 Measurements: Fields of View (FoVs) and Clutter
905(1)
25.6.4 Measurements: Actuator Sensors and Transmission Failure
906(1)
25.6.5 Measurements: Multitarget Likelihood Functions
907(1)
25.6.6 Measurements: Joint Multitarget Likelihood Functions
908(1)
25.7 Multitarget Control: Summary of Notation
908(3)
25.7.1 Notation for Spaces of Interest
908(2)
25.7.2 Notation for Motion Models
910(1)
25.7.3 Notation for Measurement Models
910(1)
25.8 Multitarget Control: Single Step
911(2)
25.9 Multitarget Control: Objective Functions
913(6)
25.9.1 Information-Theoretic Objective Functions
914(2)
25.9.2 The PENT Objective Function
916(1)
25.9.3 The Cardinality-Variance Objective Function
916(1)
25.9.4 PENT as an Approximate Information-Theoretic Objective Function
917(2)
25.10 Multisensor-Multitarget Control: Hedging
919(11)
25.10.1 Hedging Using Predicted Measurement Set (PMS)?
920(2)
25.10.2 Predicted Ideal Measurement Set (PIMS): A General Approach
922(4)
25.10.3 Predicted Ideal Measurement Set (PIMS): Special Cases
926(3)
25.10.4 Predicted Ideal Measurement Set (DIMS): Derivation of General Approach
929(1)
25.11 Multisensor-Multitarget Control: Optimization
930(1)
25.12 Sensor Management with Ideal Sensor Dynamics
931(3)
25.13 Simplified Nonideal Multisensor Dynamics
934(6)
25.13.1 Simplified Nonideal Multisensor Dynamics: Assumptions
934(2)
25.13.2 Simplified Nonideal Multisensor Dynamics: Filtering Equations
936(2)
25.13.3 Simplified Nonideal Single-Sensor Dynamics: Hedgingand Optimization
938(2)
25.14 Target Prioritization
940(9)
25.14.1 The Concept of Tactical Significance
941(1)
25.14.2 Tactical Importance Functions (TIFs) and HigherLevel Fusion
941(3)
25.14.3 Characteristics of TIFs
944(1)
25.14.4 The Multitarget Statistics of TIFs
945(2)
25.14.5 Posterior Expected Number of Targets of Interest (PENTI)
947(1)
25.14.6 Biasing the Cardinality Variance to Targets of Interest (ToIs)
948(1)
Chapter 26 Approximate Sensor Management
949(84)
26.1 Introduction
949(1)
26.1.1 Summary of Major Lessons Learned
949(1)
26.1.2 Organization of the
Chapter
950(1)
26.2 Sensor Management with Bernoulli Filters
950(10)
26.2.1 Sensor Management with Bernoulli Filters: Filtering Equations
954(1)
26.2.2 Sensor Management with Bernoulli Filters: Objective Functions
955(2)
26.2.3 Bernoulli Filter Control: Hedging
957(2)
26.2.4 Bernoulli Filter Control: Multisensor
959(1)
26.3 Sensor Management with PHD Filters
960(29)
26.3.1 Single-Sensor, Single-Step PHD Filter Control
960(14)
26.3.2 PHD Filter Sensor Management: Multisensor SingleStep
974(15)
26.4 Sensor Management with CPHD Filters
989(19)
26.4.1 Single-Sensor, Single-Step CPHD Filter Control
990(11)
26.4.2 Multisensor, Single-Step CPHD Filter Control
1001(7)
26.5 Sensor Management with CBMeMBer Filters
1008(13)
26.5.1 Single-Sensor, Single-Step CBMeMBer Filter Contro
1008(7)
26.5.2 Multisensor, Single-Step CBMeMBer Control
1015(6)
26.6 RFS Sensor Management Implementations
1021(61)
26.6.1 RFS Control Implementations: Multitarget Bayes Filter
1021(3)
26.6.2 RFS Control Implementations: Bernoulli Filters
1024(1)
26.6.3 RFS Control Implementations: PHD Filters
1025(5)
26.6.4 RFS Control Implementations: CBMeMBer Filters
1030(3)
Appendix A Glossary of Notation and Terminology 1033(8)
A.1 Transparent Notational System
1033(1)
A.2 General Mathematics
1034(1)
A.3 Set Theory
1035(1)
A.4 Fuzzy Logic and Dempster-Shafer Theory
1036(1)
A.5 Probability and Statistics
1036(2)
A.6 Random Sets
1038(1)
A.7 Multitarget Calculus
1038(1)
A.8 Finite-Set Statistics
1039(1)
A.9 Generalized Measurements
1040(1)
Appendix B Bayesian Analysis of Dynamic Systems 1041(4)
B.1 Formal Bayes Modeling in General
1041(2)
B.2 The Bayes Filter in General
1043(2)
Appendix C Rigorous Functional Derivatives 1045(4)
C.1 Nonconstructive Definition of the Functional Derivative
1045(2)
C.2 The Constructive Radon-Niko4m Derivative
1047(1)
C.3 Constructive Definition of the Functional Derivative
1048(1)
Appendix D Partitions of Finite Sets 1049(4)
D.1 Counting Partitions
1049(1)
D.2 Recursive Construction of Partitions
1050(3)
Appendix E Beta Distributions 1053(2)
Appendix F Markov Time Update of Beta Distributions 1055(4)
Appendix G Normal-Wishart Distributions 1059(12)
G.1 Proof of (G.8)
1063(1)
G.2 Proof of (G.22)
1064(3)
G.3 Proof of (G.23)
1067(3)
G.4 Proof of (G.29)
1070(1)
Appendix H Complex-Number Gaussian Distributions 1071(2)
Appendix I Statistics of Level-1 Group Targets 1073(4)
Appendix J FISST Calculus and Moyal's Calculus 1077(10)
J.1 A "Point Process "Functional Calculus
1079(1)
J.2 Volterra Functional Derivatives
1080(2)
J.3 Moyal's Functional Calculus of p.g.fl.'s
1082(5)
J.3.1 Moyal's p.g.fl.
1082(2)
J.3.2 Moyal's Functional Calculus
1084(3)
Appendix K Mathematical Derivations 1087(2)
References 1089(20)
About the Author 1109(1)
Index 1110
Ronald Mahler is a senior staff research scientist at Lockheed Martin Advanced Technology Laboratories in Eagan, MN. He earned his Ph.D. in mathematics from Brandeis University, Waltham, MA.
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