1. ACE in the Hole - Adaptive Contour Estimation using Collaborating Mobile Sensors Sumana Srinivasan, Krithi Ramamritham and Purushottam Kulkarni Department of CSE, Indian Institute of Technology Bombay, Mumbai. Contour Estimation Estimation of the boundary formed by connecting a set of points of equal value in a field e.g., temperature, pressure, pollutant concentration Applications: Estimating extent of oil spills - a prerequisite for containment and corrective action (as in figure), tracking pollutant flows, study of plankton assemblages Problem Definition Given a scalar field with varying field value, the task is to estimate a contour of a given value with maximum precision and minimum latency Problem Definition Given a scalar field with varying field value, the task is to estimate a contour of a given value with maximum precision and minimum latency Mobile SensorsStatic Sensors In-situ Sensing Remote Sensing Exploit mobility to increase samples. + Fewer sensors can yield high accuracy and coverage  Higher sensor cost and energy + Can adapt to dynamic contours without redeployment Combine local samples to form a global estimate.  High density and large number of sensors for high accuracy and coverage + Low sensor cost and energy  Cannot adapt to dynamic contours, high cost of redeployment Uses image processing for estimation.  Low accuracy due to obstructions and inclement weather affect accuracy  Large coverage possible  High deployment cost Contour Estimation Techniques 11x8 grid with granularity 8 cm with single slit neon source. ATMEGA 128, 11MHz processor, 2.4GHz CDMA, 3 white line sensors, 2 shaft encoders, 2 ultra low power DC motors, rotating arm with 2 servo motors Feasibility and Energy Characterization on Robotic Test bed 2700J 1587J 1417J 1335J 3890J 3342J 1249J ACE DD ACE DD Non-clustered Clustered Small 2030J ACE DD ACE DD Non-clustered Clustered Medium Total EnergyAlgorithmDeploymentContours Comparison of Sensors Movement Strategies Summary of Results Adaptive Contour Estimation (ACE) Minimizes latency 7-22% over DD and 4-38% over SA Maximizes convergence percentage 8-45% over DD and 30-62% over SA Maximizes precision by 15-40% for bounded steps Consumes 7-24% less energy over DD Latency and prediction error are highly correlated Summary of Results Adaptive Contour Estimation (ACE) Minimizes latency 7-22% over DD and 4-38% over SA Maximizes convergence percentage 8-45% over DD and 30-62% over SA Maximizes precision by 15-40% for bounded steps Consumes 7-24% less energy over DD Latency and prediction error are highly correlated Sensors directly approach the contour DD Latency = 818 Sensors only spread around the centroid SA Latency = 623 Sensors 7 and 8 overlap ACE (without redirection) Latency = 451 Sensors 1,5,7,9 redirected without overlap ACE (with redirection) Latency = 383 AssumptionsParameter Continuous Error free,, self-localized Single-hop Mobility+Communication+Computation+ Sensing Step-wise discrete Contour Sensor Communication Energy Movement Challenges 1. How do sensors approach and surround the contour efficiently? 2. How do sensors co-ordinate for distributed contour estimation? 3. How do sensors adapt to different deployments, sizes and shapes of contours? Challenges 1. How do sensors approach and surround the contour efficiently? 2. How do sensors co-ordinate for distributed contour estimation? 3. How do sensors adapt to different deployments, sizes and shapes of contours? System Model and Evaluation Metrics Precision = N est  #points on the estimated contour N act  #points on the actual contour Latency = argmax i (P i ) P i  Path length of i th tracing sensor Indicator of energy consumed STEP 1: Converge Phase STEP 2: Coverage Phase Use wall moving algorithm to trace STEP 2: Coverage Phase Use wall moving algorithm to trace 1. Direct Descent DD Choose direction that minimizes the distance function Latency high when sensors are collocated and contour is big. Need to spread!! 2. Spread Always SA Choose direction that minimizes spread function Latency high when sensors are deployed far and contour is small. Need to spread judiciously!! ACE provides best-of-both-worlds solution Enables sensors to intelligently choose between direct descent and spread Adapts to type of deployment, size of contour and distance from contour Distributed co-ordination for efficient contour coverage Performs high precision, low latency and low energy estimation Other Issues Handle limited transmission range Support discontinuous contours ACE provides best-of-both-worlds solution Enables sensors to intelligently choose between direct descent and spread Adapts to type of deployment, size of contour and distance from contour Distributed co-ordination for efficient contour coverage Performs high precision, low latency and low energy estimation Other Issues Handle limited transmission range Support discontinuous contours 3. Adaptive Contour Estimation ACE Choose direction that minimizes the adaptive spread function ACE Algorithm Movement Strategies Evaluation Setup and Simulation Parameters ValueDescriptionParameter 500, 140 2000 1000 Every 5 steps √2 √ l > 50% of field area > 10% - 50% of field area < 10% of field area Length of grid Maximum steps allowed per sensor Number of simulation runs Estimation frequency Sensing radius Transmission range Large Medium Small l n max n sim n est r sense R trans Contours Latency Comparison (Unbounded Energy) 78 22 4 483  5 1119  12 326  11 100 31 11 441  5 1006  17 319  7 100 99 96 375  8 845  23 276  25 Clustered Large Medium Small 100 78 29 229  4 780  16 319  7 100 71 63 142  2 681  15 268  7 100 139  2 498  11 248  8 Large Medium Small CP Latency SADD Non-clustered ACE DeploymentContours Non-clustered deployment (Medium contour) Clustered deployment (Medium contour) Very high probability that ACE has lesser latency than DD - Factor of 6 for non-clustered and 8 for clustered deployments Very high probability that ACE has lesser latency than DD - Factor of 6 for non-clustered and 8 for clustered deployments Sensitivity to Design Parameters ACE adapts best to distance from the contour, size of contour and extent of spread of sensors ACE adapts best to distance from the contour, size of contour and extent of spread of sensors Small Contour Medium Contour Distribution of Latency Differences Precision Comparison (Bounded Energy) Max. steps > 100: Non-clustered: ACE > DD by 20-25% and ACE > SA by 25-30% Clustered: ACE > DD and SA by 30-45% Max. steps ≤ 100: ACE  DD for all deployments Max. steps > 100: Non-clustered: ACE > DD by 20-25% and ACE > SA by 25-30% Clustered: ACE > DD and SA by 30-45% Max. steps ≤ 100: ACE  DD for all deployments Non-clustered deployment (Medium contour)Clustered deployment (Medium contour) Non-clustered: Large and Small contours: ACE  DD Medium contour: ACE < DD by 22% and ACE < SA by 38% Clustered: All contours, ACE < DD by 7-12% and ACE < SA by 4-20% Convergence Percentage is uniformly higher than DD and SA Non-clustered: Large and Small contours: ACE  DD Medium contour: ACE < DD by 22% and ACE < SA by 38% Clustered: All contours, ACE < DD by 7-12% and ACE < SA by 4-20% Convergence Percentage is uniformly higher than DD and SA Pollutant Field WQMAP - a tool for simulating pollutant dispersion, Three pollutant load sites, 120 time steps for simulation Light Field Measurements taken at every grid point on 15x15 grid with three light sources using Crossbow Mote Distance from Contour,  Use Nonlinear regression to fit (x i, y i,z i ) and compute coefficients using Nelder Mead simplex optimization Estimate (xˆ, yˆ) such that f((xˆ, yˆ) =  If (x,y) is the current position of the sensor, then Size of contour, .  = Area of envelope bounding estimated points on contour Area of field Spread of sensors, S S = Area of convex hull of current positions Area of field Target Angle  ' Estimating centroid Centroid of envelope bounding estimated points on contour if sensors converge or estimated convergence points if sensors not converged. Conclusions Convergence Percentage, CP = Number of runs at least one sensor converged on the contour Total number of runs Acknowledgement: We thank Parmesh Ramanathan, Sachitanand Malewar, Amey Apte and GRAM++ team at IITB for their support.