A Geometric Transversals Approach to Analyzing the Probability of Track Detection for Maneuvering Targets

There is considerable precedence in the sensor tracking and estimation literature for modeling maneuvering targets by Markov motion models in order to estimate the target state from multiple, distributed sensor measurements. Although the transition probability density functions of these Markov models are routinely outputted by tracking and estimation algorithms, little work has been done to use them in sensor coordination and control algorithms. This paper presents a geometric transversals approach for representing the probability of track detection by multiple, distributed sensors, as a function of the Markov model transition probabilities. By this approach, the Markov parameters of maneuvering targets that may be detected by the sensors are represented by three-dimensional cones that are finitely generated by the sensors fields-of-view in a spatiotemporal Euclidian space. Then, the problem of deploying a sensor network for the purpose of maximizing the expected number of target detections can be formulated as a nonlinear program that can be solved numerically for the optimal sensor placement. Numerical results show that the optimal sensor placements obtained by this geometric transversals approach significantly outperform greedy, grid, or randomized sensor deployments.

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

[2]  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).

[3]  Krishnendu Chakrabarty,et al.  Sensor placement for effective coverage and surveillance in distributed sensor networks , 2003, 2003 IEEE Wireless Communications and Networking, 2003. WCNC 2003..

[4]  Thomas A. Wettergren Statistical Analysis of Detection Performance for Large Distributed Sensor Systems , 2003 .

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

[6]  Xin Chen,et al.  Multitarget Multisensor Tracking , 2014 .

[7]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[8]  Rafael Fierro,et al.  A Multi-Vehicle Framework for the Development of Robotic Games: The Marco Polo Case , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

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

[10]  Héctor H. González-Baños,et al.  A randomized art-gallery algorithm for sensor placement , 2001, SCG '01.

[11]  Katta G. Murty,et al.  Nonlinear Programming Theory and Algorithms , 2007, Technometrics.

[12]  Yu-Chee Tseng,et al.  The Coverage Problem in a Wireless Sensor Network , 2003, WSNA '03.

[13]  Yaakov Bar-Shalom,et al.  Multitarget-Multisensor Tracking: Applications and Advances , 1992 .

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

[15]  Di Tian,et al.  A coverage-preserving node scheduling scheme for large wireless sensor networks , 2002, WSNA '02.

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

[17]  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).

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

[19]  Rafael Fierro,et al.  A Geometric Optimization Approach to Detecting and Intercepting Dynamic Targets , 2007, 2007 American Control Conference.

[20]  Yakov Bar-Shalom,et al.  Multitarget-Multisensor Tracking: Principles and Techniques , 1995 .

[21]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

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

[23]  Gaurav S. Sukhatme,et al.  An Incremental Self-Deployment Algorithm for Mobile Sensor Networks , 2002, Auton. Robots.

[24]  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..

[25]  Rekha Jain,et al.  Wireless Sensor Network -A Survey , 2013 .

[26]  Yu-Chee Tseng,et al.  The Coverage Problem in a Wireless Sensor Network , 2005, Mob. Networks Appl..

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

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

[29]  R. Vanderbei LOQO:an interior point code for quadratic programming , 1999 .

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

[31]  S. Sitharama Iyengar,et al.  Grid Coverage for Surveillance and Target Location in Distributed Sensor Networks , 2002, IEEE Trans. Computers.

[32]  J. A. George,et al.  Packing different-sized circles into a rectangular container , 1995 .

[33]  Anil V. Rao,et al.  Optimal Control of an Underwater Sensor Network for Cooperative Target Tracking , 2009, IEEE Journal of Oceanic Engineering.

[34]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[35]  Thomas A. Wettergren,et al.  Robust Deployment of Dynamic Sensor Networks for Cooperative Track Detection , 2009, IEEE Sensors Journal.