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.
Introduction to the Book - Overview of Finite-Set Statistics. Recent Advances in Finite-Set Statistics. Organization of the Book.; I. Elements of Finite-Set Statistics; Random Finite Sets -Introduction. Single-Sensor, Single-Target Statistics. Random Finite Sets (RFSs). Multiobject Statistics in a Nutshell. ; Multiobject Calculus -Introduction. Basic Concepts. Set Integrals. Multiobject Differential Calculus. Key Formulas of Multiobject Calculus.; Multiobject Statistics -Introduction. Basic Multiobject Statistical Descriptors. Important Multiobject Processes. Basic Derived RFSs.; Multiobject Modeling and Filtering -Introduction. The Multisensor-Multitarget Bayes Filter. Multitarget Bayes Optimality. RFS Multitarget Motion Models. RFS Multitarget Measurement Models. Multitarget Markov Densities. Multisensor-Multitarget Likelihood Functions. The Multitarget Bayes Filter in p.g.fl. Form. The Factored Multitarget Bayes Filter. Approximate Multitarget Filters.; Multiobject Metrology -Introduction. Multiobject Miss Distance. Multiobject Information Functionals.; II. RFS Filters: Standard Measurement Model; Introduction to Part II - Summary of Major Lessons Learned. Standard Multitarget Measurement Model. An Approximate Standard Likelihood Function. Standard Multitarget Motion Model. Standard Motion Model with Target Spawning. Organization of Part II. ; Classical PHD and CPHD Filters -Introduction. A General PHD Filter. Arbitrary-Clutter PHD Filter. Classical PHD Filter. Classical Cardinalized PHD (CPHD) Filter. Zero False Alarms (ZFA) CPHD Filter. PHD Filter for State-Dependent Poisson Clutter. ; Implementing Classical PHD/CPHD Filters -Introduction. Spooky Action at a Distanceù. Merging and Splitting for PHD Filters. Merging and Splitting for CPHD Filters. Gaussian Mixture (GM) Implementation. Sequential Monte Carlo (SMC) Implementation.; Multisensor PHD and CPHD Filters -Introduction. The Multisensor-Multitarget Bayes Filter. The General Multisensor PHD Filter. The Multisensor Classical PHD Filter. Iterated-Corrector Multisensor PHD/CPHD Filters. Parallel Combination Multisensor PHD and CPHD Filters. An Erroneous Averaged Multisensor PHD Filter. Performance Comparisons. ; Jump-Markov PHD/CPHD Filters -Introduction. Jump-Markov Filters: A Review. Multitarget Jump-Markov Systems. Jump-Markov PHD Filter. Jump-Markov CPHD Filter. Variable State Space Jump-Markov CPHD Filters. Implementing Jump-Markov PHD/CPHD Filters. Implemented Jump-Markov PHD/CPHD Filters.; Joint Tracking and Sensor-Bias Estimation -Introduction. Modeling Sensor Biases. Optimal Joint Tracking and Registration. The BURT-PHD Filter. Single-Filter BURT-PHD Filters. Implemented BURT-PHD Filters.; Multi-Bernoulli Filters -Introduction. The Bernoulli Filter. The Multisensor Bernoulli Filter. The CBMeMBer Filter. Jump-Markov CBMeMBer Filter. ; RFS Multitarget Smoothers -Introduction. Single-Target Forward-Backward Smoother. General Multitarget Forward-Backward Smoother. Bernoulli Forward-Backward Smoother. PHD Forward-Backward Smoother. ZTA-CPHD Smoother.; Exact Closed-Form Multitarget Filter -Introduction. Labeled RFSs. Examples of Labeled RFSs. Modeling for the Vo-Vo Filter. Closure of Multitarget Bayes Filter. Implementation of the Vo-Vo Filter: Sketch Performance Results. ; III. RFS Filters for Unknown Backgrounds; Introduction to Part III -Introduction. Overview of the Approach. Models for Unknown Backgrounds. Organization of Part III; RFS Filters for Unknown pD -Introduction. The pD-CPHD Filter. Beta-Gaussian Mixture (BGM). Approximation. BGM Implementation of the pD-PHD Filter. BGM Implementation of the pD-CPHD Filter. The pD-CBMeMBer Filter. Implementations of pD-Agnostic RFS Filters.; RFS Filters for Unknown Clutter -Introduction. A General Model for Unknown Bernoulli Clutter. CPHD Filter for General Bernoulli Clutter. The Œª-CPHD Filter. The Œ?-CPHD Filter. Multisensor Œ?-CPHD Filters. The Œ?-CBMeMBer Filter. Implemented Clutter-Agnostic RFS Filters. Clutter-Agnostic Pseudofilters. CPHD/PHD Filters with Poisson-Mixture Clutter. Related Work.; IV. RFS Filters for Nonstandard Measurement Models; RFS Filters for Superpositional Sensors -Introduction. Exact Superpositional CPHD Filter. Hauschildt 's Approximation. Thouin-Nannuru-Coates (TNC) Approximation.; RFS Filters for Pixelized Images -Introduction. The IO Multitarget Measurement Model. IO Motion Model. IO-CPHD Filter. IO-MeMBer Filter. Implementations of IO-MeMBer Filters.; RFS Filters for Cluster-Type Targets -Introduction. Extended-Target Measurement Models. Extended-Target Bernoulli Filters. Extended-Target PHD/CPHD Filters. Extended-Target CPHD Filter: APB Model. Cluster-Target Measurement Model. Cluster-Target PHD and CPHD Filters. Measurement Models for Level-1 Group Targets. PHD/CPHD Filters for Level-1 Group Targets. Measurement Models for General Group Targets. PHD/CPHD Filters for Level-‚Ñì Group Targets. A Model for Unresolved Targets. Motion Model for Unresolved Targets. The Unresolved-Target PHD Filter. Approximate Unresolved-Target PHD Filter. Approximate Unresolved-Target CPHD Filter. ; RFS Filters for Ambiguous Measurements -Introduction. Random Set Models of Ambiguous Measurements. Generalized Likelihood Functions (GLFs). Unification of Expert-System Theories. GLFs for Imperfectly Characterized Targets. GLFs for Unknown Target Types. GLFs for Information with Unknown Correlations. GLFs for Unreliable Information Sources. Using GLFs in Multitarget Filters. GLFs in RFS Multitarget Filters. Using GLFs with Conventional Multitarget Filters. ; V. Sensor, Platform, and Weapons Management; Introduction to Part V - Basic Issues in Sensor Management. Information Theory and Intuition: An Example. Summary of RFS Sensor Control. Organization of Part V.; Single-Target Sensor Management -Introduction. Example: Missile-Tracking Cameras. Single-Sensor, Single-Target Control: Modeling. Single-Sensor, Single-Target Control: Single-Step. Single-Sensor, Single-Target Control: Objective Functions. Single-Sensor, Single-Target Control: Hedging. Single-Sensor, Single-Target Control: Optimization. Special Case 1: Ideal Sensor Dynamics. Simple Example: Linear-Gaussian Case. Special Case 2: Simplified Nonideal Dynamics. ; Multitarget Sensor Management -Introduction. Multitarget Control: Target and Sensor State Spaces. Multitarget Control: Control Spaces. Multitarget Control: Measurement Spaces. Multitarget Control: Motion Models. Multitarget Control: Measurement Models. Multitarget Control: Summary of Notation. Multitarget Control: Single Step. Multitarget Control: Objective Functions. Multisensor-Multitarget Control: Hedging. Multisensor-Multitarget Control: Optimization. Sensor Management with Ideal Sensor Dynamics. Simplified Nonideal Multisensor Dynamics. Target Prioritization. ; Approximate Sensor Management -Introduction. Sensor Management with Bernoulli Filters. Sensor Management with PHD Filters. Sensor Management with CPHD Filters. Sensor Management with CBMeMBer Filters. RFS Sensor Management Implementations. ; Appendix A Glossary of Notation and Terminology. References. About the Author. Index. ;
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Ronald P.S. Mahler
Ronald P.S. 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. He is recipient of the 2005 IEEE AESS Harry Rowe Mimno Award, the 2007 IEEE AESS M. Barry Carlton Award, and the 2007 JDL-DFG Joseph Mignogna Data Fusion Award.