Optimal Placement of Heterogeneous Sensors for Targets with Gaussian Priors

An optimal strategy for geometric sensor placement to enhance target tracking performance is developed. Recently, a considerable amount of work has been published on optimal conditions for single-update placement of homogeneous sensors (same type and same measurement quality) in which the targets are either assumed perfectly known or the target location uncertainty is averaged out via the expected value of the determinant of the Fisher information matrix (FIM). We derive conditions for optimal placement of heterogeneous sensors based on maximization of the information matrix to be updated by the heterogeneous sensors from an arbitrary Gaussian prior characterizing the uncertainty about the initial target location. The heterogeneous sensors can be of the same or different types (ranging sensors, bearing-only sensors, or both). The sensors can also make, over several time steps, multiple independent measurements of different qualities. Placement strategies are derived and their performance is illustrated via simulation examples.

[1]  Alfred O. Hero,et al.  Sensor Management: Past, Present, and Future , 2011, IEEE Sensors Journal.

[2]  C. Guestrin,et al.  Near-optimal sensor placements: maximizing information while minimizing communication cost , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[3]  Kenneth J. Hintz,et al.  Sensor measurement scheduling: an enhanced dynamic, preemptive algorithm , 1998 .

[4]  L.M. Kaplan,et al.  Global node selection for localization in a distributed sensor network , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[5]  Christopher M. Kreucher,et al.  Optimal Sensor Placement for a Constellation of Multistatic Narrowband Pixelated Sensors , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[6]  N. Levanon.  Lowest GDOP in 2-D scenarios , 2000 .

[7]  Bin Yang,et al.  Different Sensor Placement Strategies for TDOA Based Localization , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[8]  T. Kirubarajan,et al.  Optimal cooperative placement of GMTI UAVs for ground target tracking , 2004, 2004 IEEE Aerospace Conference Proceedings (IEEE Cat. No.04TH8720).

[9]  João Pedro Hespanha,et al.  Optimal sensor placement for time difference of arrival localization , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[10]  Keith Kastella.  Discrimination gain to optimize detection and classification , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[11]  Moe Z. Win,et al.  Position Error Bound for UWB Localization in Dense Cluttered Environments , 2006, 2006 IEEE International Conference on Communications.

[12]  Rémi Gribonval,et al.  Should Penalized Least Squares Regression be Interpreted as Maximum A Posteriori Estimation? , 2011, IEEE Transactions on Signal Processing.

[13]  Erik Blasch,et al.  Simultaneous feature-based identification and track fusion , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[14]  Nicholas Roy,et al.  Optimal Sensor Placement for Agent Localization , 2006, 2006 IEEE/ION Position, Location, And Navigation Symposium.

[15]  Erik Blasch,et al.  Optimal placement of heterogeneous sensors in target tracking , 2011, 14th International Conference on Information Fusion.

[16]  L. M. Kaplan.  Node selection for target tracking using bearing measurements from unattended ground sensors , 2003, 2003 IEEE Aerospace Conference Proceedings (Cat. No.03TH8652).

[17]  J. Chaffee,et al.  GDOP and the Cramer-Rao bound , 1994, Proceedings of 1994 IEEE Position, Location and Navigation Symposium - PLANS'94.

[18]  Claire J. Tomlin,et al.  Sensor Placement for Improved Robotic Navigation , 2010, Robotics: Science and Systems.

[19]  Brian D. O. Anderson,et al.  Optimality analysis of sensor-target localization geometries , 2010, Autom..

[20]  Thia Kirubarajan,et al.  Large-Scale Optimal Sensor Array Management for Multitarget Tracking , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[21]  Bin Yang,et al.  A Theoretical Analysis of 2D Sensor Arrays for TDOA Based Localization , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[22]  Bin Yang,et al.  Cramer-Rao bound and optimum sensor array for source localization from time differences of arrival , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[23]  Joaquín Aranda,et al.  Optimal Sensor Placement for Multiple Underwater Target Localization with Acoustic Range Measurements , 2011 .

[24]  R. Yarlagadda,et al.  GPS GDOP metric , 2000 .

[25]  Erik Blasch,et al.  Performance Measures of Covariance and Information Matrices in Resource Management for Target State Estimation , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[26]  Francesco Bullo,et al.  Optimal sensor placement and motion coordination for target tracking , 2006, Autom..

[27]  Keith D. Kastella,et al.  Foundations and Applications of Sensor Management , 2010 .

[28]  J. B. McKay,et al.  Geometry optimization for GPS navigation , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[29]  Hong Zhang.  Two-dimensional optimal sensor placement , 1995, IEEE Trans. Syst. Man Cybern..