Probabilistic Track Coverage in Cooperative Sensor Networks

The quality of service of a network performing cooperative track detection is represented by the probability of obtaining multiple elementary detections over time along a target track. Recently, two different lines of research, namely, distributed-search theory and geometric transversals, have been used in the literature for deriving the probability of track detection as a function of random and deterministic sensors' positions, respectively. In this paper, we prove that these two approaches are equivalent under the same problem formulation. Also, we present a new performance function that is derived by extending the geometric-transversal approach to the case of random sensors' positions using Poisson flats. As a result, a unified approach for addressing track detection in both deterministic and probabilistic sensor networks is obtained. The new performance function is validated through numerical simulations and is shown to bring about considerable computational savings for both deterministic and probabilistic sensor networks.

[1]  Joseph Mecke.  Randomr-flats meeting a ball , 1988 .

[2]  Philip M. Morse,et al.  Methods of Operations Research , 1952 .

[3]  S.X. Yang,et al.  A neural network approach to complete coverage path planning , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[5]  Thomas A. Wettergren,et al.  Assessing Design Tradeoffs in Deploying Undersea Distributed Sensor Networks , 2007, OCEANS 2007.

[6]  T.A. Wettergren.  Performance of search via track-before-detect for distributed sensor networks , 2008, IEEE Transactions on Aerospace and Electronic Systems.

[7]  Pramod K. Varshney,et al.  Energy-efficient deployment of Intelligent Mobile sensor networks , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[8]  L. Santaló.  Integral geometry and geometric probability , 1976 .

[9]  L. Stone.  Theory of Optimal Search , 1975 .

[10]  R.L. Streit,et al.  Tracking with distributed sets of proximity sensors using geometric invariants , 2004, IEEE Transactions on Aerospace and Electronic Systems.

[11]  A. Banerjee.  Convex Analysis and Optimization , 2006 .

[12]  Krishna R. Pattipati,et al.  A Multisensor-Multitarget Data Association Algorithm for Heterogeneous Sensors , 1992, 1992 American Control Conference.

[13]  Thomas A. Wettergren,et al.  Sensor Repositioning to Improve Undersea Sensor Field Coverage , 2007, OCEANS 2007.

[14]  Cumulative detection probabilities for a randomly moving source in a sparse field of sensors , 1989, Twenty-Third Asilomar Conference on Signals, Systems and Computers, 1989..

[15]  R. Pollack,et al.  Geometric Transversal Theory , 1993 .

[16]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[17]  J. Mecke.  Extremal Properties of Some Geometric Processes , 1987 .

[18]  Steven Skiena,et al.  Implementing discrete mathematics - combinatorics and graph theory with Mathematica , 1990 .

[19]  P. Deb.  Finite Mixture Models , 2008 .

[20]  David A. Castañón.  Optimal search strategies in dynamic hypothesis testing , 1995, IEEE Trans. Syst. Man Cybern..

[21]  B. O. Koopman.  Search and Screening: General Principles and Historical Applications , 1980 .

[22]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[23]  Silvia Ferrari,et al.  A Geometric Transversal Approach to Analyzing Track Coverage in Sensor Networks , 2008, IEEE Transactions on Computers.

[24]  B. Turchiano,et al.  Supervisory control of mobile sensor networks: math formulation, simulation, and implementation , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  S. Ferrari.  Track coverage in sensor networks , 2006, 2006 American Control Conference.

[26]  G. Matheron.  Random Sets and Integral Geometry , 1976 .

[27]  Aubrey B. Poore,et al.  Multidimensional assignment formulation of data association problems arising from multitarget and multisensor tracking , 1994, Comput. Optim. Appl..

[28]  DAVID G. KENDALL,et al.  Introduction to Mathematical Statistics , 1947, Nature.

[29]  Ming Xiang,et al.  On the performance of distributed Neyman-Pearson detection systems , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[30]  J.-P. Le Cadre,et al.  Searching tracks , 2000 .

[31]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[32]  Kamal Premaratne,et al.  Transmission Rate Allocation in Multisensor Target Tracking Over a Shared Network , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[33]  Aubrey B. Poore,et al.  A Numerical Study of Some Data Association Problems Arising in Multitarget Tracking , 1994 .

[34]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[35]  Sampath Kannan,et al.  Sampling based sensor-network deployment , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[36]  E. Helly.  Über Mengen konvexer Körper mit gemeinschaftlichen Punkte. , 1923 .