Modelbased Calibration for Sensor Networks Miodrag Potkonjak Computer

Model-based Calibration for Sensor Networks Miodrag Potkonjak Computer Science Dept, University of California, Los Angeles NSF Center for Embedded Networked Sensing, UCLA NSF U. S. National Science Foundation #CCR-0120778 Center for Embedded Networked Sensing

Why Calibration? Process of mapping raw sensor readings to the corrected values (golden standards, consistency among sensors) ® Inevitable due to the natural process of device aging and imperfections ® Particularly important in wireless embedded sensor networks ® Manual calibration is either infeasible or expensive ® Model of error: systematic bias vs. random noise Objective: Identify and correct the systematic bias in the sensor reading so it is as close as possible to the correct values Center for Embedded Networked Sensing

Model-based Approach ® Off-line vs. On-line ® How the correct values are generated ® Off-line: Non-parametric statistical methods ® Availability of expensive accurate sensors ® Piece-wise polynomial data fitting and validation ® Off-line: Nonlinear function minimization ® Densely deployed network ® Minimization of discrepancies ® Statistical analysis: Percentile method ® Intervals of confidence Center for Embedded Networked Sensing

State-of-the-art ® Hightower, J. , Vakili, C. , and Borriello, G. ® “Design and Calibration of the Spot. ON Ad-Hoc Location Sensing System” ® ® Whitehouse, K. , and Culler, D. ® “Calibration as parameter Estimation in Sensor Networks” ® ® ACM WSNA, 2002. Elson, J. , Girod, L. , and Estrin, D. ® “Fine-Grained Network Time Synchronization using Reference Broadcasts” ® ® unpublished, 2001. OSDI, 2002. Bychkovskiy, V. , Megerian, S. , Estrin, D. , and Potkonjak, M. ® “Colibration: A Collaborative Approach to In-Place Sensor calibration” ® IPSN, 2003. Center for Embedded Networked Sensing

Parameter Estimation-based vs. Model-based Approach Center for Embedded Networked Sensing

Point-Light Model K light sources: • • • Courtesy to: Miniature silicon solar cell Photoconductor Extech model 407026 commercial digital light meter Center for Embedded Networked Sensing

Off-line Calibration Piece-wise Calibration Function ® Calibrated accurate high-cost light meters as standards {C} ® Non-calibrated inaccurate sensor readings {R} ® Piece-wise mapping function Center for Embedded Networked Sensing

Off-line Calibration Dijkstra Piece-wise Calibration Function ® A set of pairs of real numbers {{ri, ci} | ri R={r 1, r 2, …, rn}, ci C={c 1, c 2, …, cn}}, where R is the data produced by low-cost sensors; and corresponding C is the data produced by high-accuracy instrument ® Primal problem: ® Given discrepancy level, find the function that consists of the least number of parameters ® Dual problem: ® Given number of parameters, find the function that induce the smallest discrepancy 2 1 ® Degree limit = 2; TOLERANCE Center for Embedded Networked Sensing

Statistical Analysis of Results Percentile Method: Confidence Interval ® ® Resubstitution using different subsets Data points [0, 375] ® Data points (375, 1600] Center for Embedded Networked Sensing

On-line Calibration Technical Details: Nonlinear Function Minimization time steps ® N sensors, m light sources, k time steps Center for Embedded Networked Sensing

On-line Calibration Experimental Results ® 1 light source ® light source location ® 2 light sources ® ® 3 light sources light source intensity Center for Embedded Networked Sensing

Future Directions ® On-line localized and distributed ® Build model and broadcast model ® Obstacles and faults ® Perturbation-based analysis ® Other phenomena models (e. g. statistical and HMM) Center for Embedded Networked Sensing

Conclusion ® Model-based calibration ® Off-line and On-line ® Nonlinear function minimization and resubstitution ® Generic and easy to generalize Center for Embedded Networked Sensing