Probabilistic Search for Tracking Targets - Theory and Modern Applications

Informationen zum Autor Eugene Kagan, Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, IsraelIrad Ben-Gal, Department of Industrial Engineering, Tel-Aviv University, Israel Klappentext Presents a probabilistic and information-theoretic framework for a search for static or moving targets in discrete time and space.Probabilistic Search for Tracking Targets uses an information-theoretic scheme to present a unified approach for known search methods to allow the development of new algorithms of search. The book addresses search methods under different constraints and assumptions, such as search uncertainty under incomplete information, probabilistic search scheme, observation errors, group testing, search games, distribution of search efforts, single and multiple targets and search agents, as well as online or offline search schemes. The proposed approach is associated with path planning techniques, optimal search algorithms, Markov decision models, decision trees, stochastic local search, artificial intelligence and heuristic information-seeking methods. Furthermore, this book presents novel methods of search for static and moving targets along with practical algorithms of partitioning and search and screening.Probabilistic Search for Tracking Targets includes complete material for undergraduate and graduate courses in modern applications of probabilistic search, decision-making and group testing, and provides several directions for further research in the search theory.The authors:* Provide a generalized information-theoretic approach to the problem of real-time search for both static and moving targets over a discrete space.* Present a theoretical framework, which covers known information-theoretic algorithms of search, and forms a basis for development and analysis of different algorithms of search over probabilistic space.* Use numerous examples of group testing, search and path planning algorithms to illustrate direct implementation in the form of running routines.* Consider a relation of the suggested approach with known search theories and methods such as search and screening theory, search games, Markov decision process models of search, data mining methods, coding theory and decision trees.* Discuss relevant search applications, such as quality-control search for nonconforming units in a batch or a military search for a hidden target.* Provide an accompanying website featuring the algorithms discussed throughout the book, along with practical implementations procedures. Zusammenfassung This text looks at search algorithms that are applicable in various practical settings. With the implementation of suitable data structures and metrics within the suggested search algorithms, the book presents a unified framework to demonstrate immediate merits and applications. Inhaltsverzeichnis List of figures xiPreface xvNotation and terms xvii1 Introduction 11.1 Motivation and applications 41.2 General description of the search problem 51.3 Solution approaches in the literature 71.4 Methods of local search 111.5 Objectives and structure of the book 14References 152 Problem of search for static and moving targets 192.1 Methods of search and screening 202.1.1 General definitions and notation 202.1.2 Target location density for a Markovian search 242.1.3 The search-planning problem 302.2 Group-testing search 552.2.1 General definitions and notation 562.2.2 Combinatorial group-testing search for static targets 632.2.3 Search with unknown number of targets and erroneous observations 712.2.4 Basic information theory search with known location probabilities 842.3 Path planning and search over graphs 1082.3.1 General BF* and A* algorithms 1092.3.2 Real-time search and learning real-time A* algorithm 1222.3.3 Moving target search and the fringe-retrieving A* algorithm 1312.4 Summary 140References 1403 M...

List of contents

List of figures xi
 
Preface xv
 
Notation and terms xvii
 
1 Introduction 1
 
1.1 Motivation and applications 4
 
1.2 General description of the search problem 5
 
1.3 Solution approaches in the literature 7
 
1.4 Methods of local search 11
 
1.5 Objectives and structure of the book 14
 
References 15
 
2 Problem of search for static and moving targets 19
 
2.1 Methods of search and screening 20
 
2.1.1 General definitions and notation 20
 
2.1.2 Target location density for a Markovian search 24
 
2.1.3 The search-planning problem 30
 
2.2 Group-testing search 55
 
2.2.1 General definitions and notation 56
 
2.2.2 Combinatorial group-testing search for static targets 63
 
2.2.3 Search with unknown number of targets and erroneous observations 71
 
2.2.4 Basic information theory search with known location probabilities 84
 
2.3 Path planning and search over graphs 108
 
2.3.1 General BF* and A* algorithms 109
 
2.3.2 Real-time search and learning real-time A* algorithm 122
 
2.3.3 Moving target search and the fringe-retrieving A* algorithm 131
 
2.4 Summary 140
 
References 140
 
3 Models of search and decision making 145
 
3.1 Model of search based on MDP 146
 
3.1.1 General definitions 146
 
3.1.2 Search with probabilistic and informational decision rules 152
 
3.2 Partially observable MDP model and dynamic programming approach 161
 
3.2.1 MDP with uncertain observations 162
 
3.2.2 Simple Pollock model of search 166
 
3.2.3 Ross model with single-point observations 174
 
3.3 Models of moving target search with constrained paths 179
 
3.3.1 Eagle model with finite and infinite horizons 180
 
3.3.2 Branch-and-bound procedure of constrained search with single searcher 184
 
3.3.3 Constrained path search with multiple searchers 189
 
3.4 Game theory models of search 192
 
3.4.1 Game theory model of search and screening 192
 
3.4.2 Probabilistic pursuit-evasion games 201
 
3.4.3 Pursuit-evasion games on graphs 206
 
3.5 Summary 214
 
References 215
 
4 Methods of information theory search 218
 
4.1 Entropy and informational distances between partitions 219
 
4.2 Static target search: Informational LRTA* algorithm 227
 
4.2.1 Informational LRTA* algorithm and its properties 228
 
4.2.2 Group-testing search using the ILRTA* algorithm 234
 
4.2.3 Search by the ILRTA* algorithm with multiple searchers 244
 
4.3 Moving target search: Informational moving target search algorithm 254
 
4.3.1 The informational MTS algorithm and its properties 254
 
4.3.2 Simple search using the IMTS algorithm 260
 
4.3.3 Dependence of the IMTS algorithm's actions on the target's movement 269
 
4.4 Remarks on programming of the ILRTA* and IMTS algorithms 270
 
4.4.1 Data structures 270
 
4.4.2 Operations and algorithms 282
 
4.5 Summary 290
 
References 290
 
5 Applications and perspectives 293
 
5.1 Creating classification trees by using the recursive ILRTA* algorithm 293
 
5.1.1 Recursive ILRTA* algorithm 294
 
5.1.2 Recursive ILRTA* with weighted distances and simulation results 297
 
5.2 Informational search and screening algorithm with single and multiple searchers 299
 
5.2.1 Definitions and assumptions 299
 
5.2.2 Outline of the algorithm and related functions 300
 
5.2.3 Numerical simulations of search with single and multiple searcher

Product details

• Authors: BEN GAL IRAD KAGAN EUGENE, I Ben-Gal, Ira Ben-Gal, Irad Ben-Gal, Irad (Tel-Aviv University Ben-Gal, Irad Kagan Ben-Gal, Ben-Gal Irad, Eugene Kagan, Eugene (Tel-Aviv University Kagan, Kagan Eugene
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 03.05.2013
• EAN: 9780470973936
• ISBN: 978-0-470-97393-6
• No. of pages: 352
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Social sciences, law, business > Business > Business administration; Statistik, Mathematik, Data Mining, Statistics, Signalverarbeitung, Mathematics, Signal Processing, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Data Mining Statistics, Mathematik in den Ingenieurwissenschaften, Applied Mathematics in Engineering