1. Fuzzy Angle Fuzzy Distance + Angle AG = 90 DG = 1 Annual Conference of ITA ACITA 2009 Exact and Fuzzy Sensor Assignment Hosam Rowaih 1 Matthew P. Johnson 2 Diego Pizzocar 3 Amotz Bar-Noy 2 Lance Kaplan 4 Thomas La Porta 1 Alun Preece 3 1 Pennsylvania State University 2 City University of New York 3 Cardiff University (funded by ITA via IBM UK) 4 US Army Research Lab Acknowledgements Research was sponsored by the U.S. Army Research Laboratory and the U.K. Ministry of Defence and was accomplished under Agreement Number W911NF-06-3-0001. The views and conclusions contained in this document are those of the author(s) and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Army Research Laboratory, the U.S. Government, the U.K. Ministry of Defence or the U.K. Government. The U.S. and U.K. Governments are authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon. Introduction Sensor network performing multiple simultaneous tasks, each requiring multiple sensors competition for limited sensing resources Directional sensors can only be assigned to one task at a time Problem: which sensors should be assigned to which tasks? Two NP-hard apps with nonlinear utility: n Event Detection n Target Localization Localization Task: choose two sensors that minimize location uncertainty: Network: maximize the sum of task utilities u j defined as: Fuzzy location: based on distance and a fuzzy angle divides the circle into sectors based on an angle granularity (AG) System Model Sensor types: imagery and acoustic Detection use: both imagery and acoustic Localization use: only acoustic Dynamic system tasks arrive and depart over time Tasks: different profits different locations Utility = function of assigned sensors Localization and high profit detection tasks can preempt low profit detection Fuzzy location benefits: Lower computational cost: fewer assignment choices to consider Privacy: sensors not disclosing their exact location Tradeoff between solution quality and computational cost / privacy 1000 sensors in 400m x 400m field 70% acoustic, 30% imagery Sensing range = 40m Detection probability: Acoustic SNR = 60 dB, Imagery SNR = 66 dB False detection probability PFA = 0.001 Minimum required uncertainty for localization = 16 Corresponds to error area of 4m x 4m Poisson task arrival with rate = 10 tasks/hour 70% detection, 30% localization Lifetimes and profits vary uniformly: Detection: lifetime between 1 hour and 5 hours, profits in [0, 0.1] Localization: lifetime between 5 minutes and 30 minutes, profits in [0.1, 1] Compare results to upper bound on optimal Solve the problem by ignoring competition Event Detection Target Localization Sensors not assigned to localization tasks propose with exact locations Leader compare possible pairs: Determine θ: separating angle Use distances and θ to calculate uncertainty Choose best pair If number of proposing sensors is large: Set a threshold distance Dt Sensor further from this distance ignore advertisement Evaluation Finer granularity leads to better solution Fuzzy can achieve profits that are within 1% of exact Localization is affected more by competition Detection with Exact Location Task leaders advertise tasks and location requirements to nearby sensors Sensors propose to tasks Task: assign n sensors that maximize cumulative detection probability (CDP) Network: maximize the sum of task utilities (CDPs) weighted by profits: Tasks competing with arriving task (within distance 2Rs) compete in rounds: Sensors (re)calculate how much they can help tasks (marginally) and propose: Tasks accept the best proposals Detection with Fuzzy Location Detection probability depends on distance For fuzzy location, distance is discretized S2S2S2S2 S3S3S3S3 S1S1S1S1 x DG = 1