Data Fusion and Optimal Placement of Fixed and Mobile Sensors

1. DATA FUSION AND OPTIMAL PLACEMENT OF FIXED AND MOBILE SENSORS Arnie Neidhardt, Hanan Luss, and K.R. Krishnan Telcordia Technologies, New Jersey Presenter:K.R. Krishnan Director Network Models and Algorithms krk@research.telcordia.com 732-699-2646 Sensors Applications Symposium Atlanta, February 13, 2007

2. Outline of Talk • Background • Small devices, like cell phones, can be equipped to act as mobile sensors, offering an ‘opportunistic’ mobile sensor-pool to supplement fixed-sensors. • Two issues considered • An algorithm for data fusion between fixed and mobile sensors for uncertainty-reduction • The formulation of models for optimum sensor-placement for • Positioning fixed sensors • Adaptive activation of auxiliary sensors (pre-positioned or dispatched) for finer-grained monitoring to supplement fixed-sensor data SAS2008

3. Cellular Sensing: Examples • ‘Dirty Bomb’ Detection and Localization with phone equipped with radiation detector and GPS • April 2006 demonstration by Oak Ridge National Lab and Vanderbilt University • Sensors to track pollution • College of Engineering, UC Berkeley http://www.engadget.com/2005/08/12/cellphone-based-pollution-sensor-being-developed-at-berkeley/ • Cell phones on cyclists to monitor air pollution, Cambridge University http://technology.newscientist.com/article/dn13130 SAS2008

4. Threat Detection: Second-Tier Mobile Sensing Fuse readings from fixed sensors on cell towers If threat is detected with low probability, poll cell-phone sensors N N N N P P P N P Notification Fuse readings to corroborate & pinpoint threat Alert response coordination SAS2008

5. Two-Level Data Fusion: Fixed and Mobile Sensors Network Model ‘Nodes’show discrete locations of sensors and objects ‘Links’connect nodes within sensing range of each other • Data Fusion #1: Reach a decision on the presence or absence of a threat at each location by “fusing” readings from multiple primary sensors • Probability of error is distance-dependent Data Fusion #2: If primary sensing is inadequate, turn on additional secondary sensors to reach more definitive conclusion SAS2008

6. Questions for Data Fusion and Sensor Placement • Data Fusion • Are fixed-sensor readings sufficient for reliable decision on presence or absence of threat? • If auxiliary mobile-sensor readings are also needed, what is the final decision given both sets of readings, and what probability of error is associated with it? • Sensor Location • Where do you locate sensors to cover a geographic area? • When auxiliary readings are needed: Which auxiliary sensors do we activate or poll? OR To which locations do we dispatch mobile sensors (e.g., robots)? SAS2008

7. Data Fusion Model • Initial Decision Point (after fixed-sensor data collected) • Declare threat present or absent without polling mobile sensors • OR • Defer decision and poll mobile sensors • Final Decision Point (after both fixed-sensor and mobile-sensor data collected) • Declare threat present or absent SAS2008

8. Data Fusion and Decision for a Single Cell Define likelihood ratios: • for fixed-sensor data • for combined fixed-and-mobile sensor data Π(threat) = prior probability of presence of threat SAS2008

9. A D B Decision Rule D = Relative cost of acting on false alarm and ignoring real threat A and B depend on number and properties of available mobile sensors In later example: D= 0.5×10-4 π (Threat) =10-4 • INITIAL DECISION POINT • If Lf< A → No Threat, If Lf> B → Threat; • Mobile sensor data NOT needed for decision • If A  LfB, mobile sensors polled • FINAL DECISION POINT • If Lc < D → No Threat, If Lc D → Threat SAS2008

10. Example: 5 Fixed Sensors, 10 Mobile Sensors Kf = number of fixed sensors reporting threat Km= number of mobile sensors reporting threat SAS2008

11. Models for Optimum Sensor-Placement • What is a “Fair” Solution? One could consider the “minimax” objective” in the facility-location model: • Locate P facilities (e.g., fire stations) so that the maximal distance (or reaching time) from a node (neighborhood) to its closest facility is minimized. Can be solved using mixed-integer programming solvers, Lagrangian relaxation, etc. Significant computational effort for large problems (NP-hard) SAS2008

12. 7 9 10 7 9 15 9 10 8 15 10, 9, 9, 0 10, 8, 7, 0 9 8 Is Minimax a Good Objective? • It does the best possible for the most unfortunate neighborhood. • It leaves significant design flexibility that may not be properly exploited. • A true equitable solution would provide the lexicographic minimax solution. Better solution • Very difficult problem: Requires repeated (up to n2) solutions of mixed integer • programs (Ogryczak, European Journal of OR, 1997). SAS2008

13. Equitable Fixed-Sensor Placement (static model) N = set of locations to be monitored Objective function The lexicographic minimax solution • The algorithm for emergency facility locations cannotbe directly extended (owing to possibility of coverage of each location by multiple sensors) • Need new methods Constraints SAS2008

14. Equitable Sensor Placement: Dynamic Model for “Quiet” Scenario • No threats detected, but active-sensor configuration varied at regular intervals for security reasons • All locations have sensors, but only P are activated at any point in time (e.g. to conserve battery power) • Sensors take measurements every t (e.g., 15) minutes • Every T (e.g., 3) days, p% of activated sensors must be replaced (e.g., the longest activated, random, etc.) • New constraints are added to the model; not a major complication as long as model solved in a myopic way. SAS2008

15. Equitable Sensor Placement: Adaptive Activation of Auxiliary Sensors • Threat-indications received, finer observations needed to pinpoint precise location • Sensors detect possible targets in some areas. • Q mobile sensors (e.g., robots or UAVs) sent in for more observations. • Similar models (with a mix of fixed and mobile sensors) zooming in on a more limited area. SAS2008

16. Future Research • Algorithms for Equitable Sensor-Placement • Sensor Model enhancements • Vector of readings (position, temperature,…) from each sensor • Multiple types of sensors for same type of object (detecting heat emission, or electromagnetic radiation, or…) • Multiple types of sensors for multiple types of object • Decision Model enhancements • Include and account for time-correlation in sensor readings in successive detection-intervals in reaching decisions • Peer-to-Peer model for sensor network • No fixed central data-collector or decision-maker • Sensors report to close neighbors, adaptively form a hierarchy of clusters, each ‘electing’ its leader for formulating and reporting cluster-decision SAS2008