Tracking Dynamic Phenomena: Sensor Networks to the Rescue

1. Tracking Dynamic Phenomena: Sensor Networks to the Rescue Krithi Ramamritham Dept of Computer Sc. & Engg. Indian Institute of Technology Bombay www.cse.iitb.ac.in/~krithi

2. More and more of the informationwe consume is coming from sensors in the field…….

3. Traffic Management # Vehicles expected on Pacifica Highway above threshold?

4. Early Warning System For Landslide Prediction using Sensor Networks

5. Major Landslides • Major Landslide Prone Areas • Himalayas • Western ghats

6. Wireless agri sensors for crop disease forecasts wind speed wind direction air temperature relative humidity solar radiation evaporation rate Upload updates periodically

7. Sensornet Apps…. smart cooling in data centers redwood forest microclimate monitoring http://www.hpl.hp.com/research/dca/smart_cooling/ and More… condition-based maintenance bridge structural integrity

8. Types of Sensors • Weather • Vibration • 2 or 3 axis accelerometers • Tracking • Microphone (for ranging and acoustic signatures) • Magnetometer • GPS • RFID Reader EEPROM • 512K off chip, 32K on chip • Many megabytes in the future • Writes at disk speeds, reads at RAM speeds • Interface : random access, read/write pages

9. Power Consumption and Lifetime • Power typically supplied by a small battery • 1000-2000 mAH • Lifetime, power consumption varies by application • Mica2 processor: • 5mA active, 1 mA idle, 5 uA sleeping • CC1000 Radio • 5 mA listen, 10 mA xmit/receive, ~20mS / packet • Sensors • 1 uA -> 100’s mA, 1 uS -> 1 S / sample

10. Queries over Sensors • Query sensornet through a (remote) base station • Sensor nodes have severe resource constraints • Limited battery power, memory, processor, radio range… • Communication is the major source of battery drain • transmitting a single bit of data is equivalent to 100s of instructions http://www.intel.com/research/exploratory/motes.htm base station (root, coordinator…)

11. Local storage policy: store data on nodes base + simple + data collection is cheap - queries are flooded, costly queries

12. In-network Computation in Trees • Goal is for root to compute a function of data at leaves • Trivial solution: push all data up tree and compute at base station • Strains nodes near root: batteries drain, disconnecting network • Very wasteful: no attempt at saving communication • Can do much better by “In-network” query processing • Simple example: computing max • Each node hears from all children, computes max and sends to parent (each node sends only one item)

13. Distributed Processing BS-1 BS-2 CH-1 CH-3 CH-(m-1) In-network aggregationProbabilistic estimation 1 2 n n 1 2 n 1 2 CH-2 CH-m CH-4 1 2 n 1 2 n 1 2 n

14. Statistical Techniques • Approximations, summaries, and sampling based on statistics and statistical models • Applications: • Limited bandwidth and large number of nodes -> data reduction • Lossiness -> predictive modeling • Uncertainty -> tracking correlations and changes over time • Physical models -> improved query answering

15. Monitoring Dynamic Physical Phenomena A disaster management team is interested in tracking an oil spill with the help of sensors. Sensors track the perimeter of” spill. Will the spill hit the shore before 5pm?

16. Remote/Range Sensing of Boundaries • Solution Space Characteristics • Static sensors • Range sensing • Approximate location • Dynamic Boundary

17. Assumptions • Random distribution of n static sensors • Sensors know their own locations • Boundaries are smooth : belong to C2 class • Second derivative continuous • No abrupt changes of boundary along x axis • Errors in sensor observations independent and mean zero • Boundaries are curve instead of contour

18. Problem Definition Compute confidence band at all timessuch that actual boundary lies within the interval with a confidence Width of the intervals should not exceed a certain value δ Objective Update with minimal communication overheads to increase sensornet lifetime Confidence band should have low loss of coverage

19. Overview • Motivation • Problem: Estimation of boundary • Solution Approach • Spatial Estimation through in-network aggregation • Estimate at minimal locations along the boundary • Tracking dynamics using Temporal Correlation • Experimental Results • Future Work

20. Estimate Boundary and Confidence Interval at any x h x h δ • Gather observations from sensors within h-neighborhood • Use Spatial Aggegation to estimate CIs for entire boundary

21. Boundary at any x • continuous, bounded and symmetric • Non-negative • k has support [-1, 1] k (-1) = k (1) = 0 Kernel Properties • Normalized – integrates to one • Defines shape of weights • xi values: predictor vars • yi values: response vars • Relationship modeled as non-parametricregression

22. Kernel Smoothing • d(x) is estimated as avg. of kernel weighted y’s measured by sensors in a neighborhood of x • Choices of weight sequences Nadaraya-Watson [Nadaraya 1964], Gasser-Mϋller • what should be the neighborhood of x? • weight is non-zero only if |x-xi| < h K(u) = .75 × (1 − u2) I(|u| ≤ 1).

23. Optimal (h) selection • Accuracy of estimation depends on h • Avg. Square Error = Bias + Variance • At optimal h, bias and variance balance Penalty function and ASE h

24. Estimation of Confidence Intervals • How to find the pointwise confidence intervals of d(x)? • = conditional variance of Y | X=x • Require Distributed Estimation

25. Partial Aggregates of sumof kernel x observation sum of kernel sum of kernel x observation2

26. Data Dissemination Scheme • Nodes organized into clusters • CHs form a tree • Nodes send Observations to Cluster Heads (CHs) • CHs perform local aggregations • BS computes final Confidence Intervals B S N1, D1, Q1 N2, D2, Q2 CH CH S2 S1

27. Estimation using Real Sensors Experiment using robot with range sensors Error Variance changes with x Confidence Intervals cover the boundary if # Obs > 100

28. Confidence Intervals • Increase in confidence implies wider interval • Increase in noise variance implies wider interval

29. DBTR: Dynamic Boundary Tracking é ù ( , ) d x t i = ( , ) s x t ê ú & i ( , ) d x t ë û i Can periodic update scheme work? • Process model to track the dynamics • Linear dynamics can be modeled using Kalman Filter • state = distance, velocity Assumption: constant mean velocity and Gaussian Noise

30. Tracking the Dynamics • new state = F xold state + noise • new position = old position + velocity x ts+ noise • new velocity = old velocity + noise • observation = H xstate + noise

31. When to update Confidence Intervals? • Spatial estimation involves communication overheads but gives more accurate information • Temporal estimation gives the changes in boundary at specific location • Minimize the frequency of updates • Update the boundary only if it has changed by cδ

32. Block Diagram for TE & SE Prediction Update no changed by cδ Regression yes • Use Spatial Estimation as a feedback • Feedback improves the accuracy of Temporal Estimation

33. Simulation Results • Randomly distributed nodes in 100x100 field • TOSSIM as well as MATLAB • Real sensor traces • # of boundary points k = 10 to 50 • σ2 = .5 to 2.0 • Metrics • Accuracy of Estimation - LOC • Communication Overheads

34. Loss of Coverage • DBTR better than individual techniques • Spatial Est. better than temporal for lower δ • Temporal Est. improves for larger δ

35. Loss of Coverage vs. change in y Better Coverage with more frequent updates Increasing δ helps in improving coverage

36. Communication Overhead(Dynamics of Boundary) δ = 1.2

37. Communication Overhead(Points changing at different velocity) • DBTR adaptively updates based on velocity of boundary. • More Communication overheads for higher velocity

38. Comparison with a Periodic Scheme DBTR has less communication overheads Has comparable loss of coverage

39. Heuristic for Minimal # Estimation Pts • Estimating at more locations reduces Interpolation Error • Prediction Error Function shows the same trend as LOC with variation of k • Increase estimation points until Prediction Error Function stabilizes

40. Communication Overhead – (Spatial) • Distributed scheme does not change much with network size scalable solution • Value of h reduces with network density • Distributed performs ~20-50% better than centralized for k = 10

41. Verification of Heuristic for deriving k Prediction Error Function stabilizes at k=12 LOC < 4 % at k=12

42. Effect of Variance of Sensing Angle on LOC

43. Comparisons

44. Conclusions & Future Work • A practical low overhead strategy for tracking dynamic boundary • DBTR does not require prior knowledge about the dynamics • Confidence band with LOC < 2% from estimates at a few selected locations • Handle situations where the boundary changes very fast • Strategy for estimating boundary in presence of a deadline • Comparison with Parametric and other Approaches • Boundary tracking with sensors having local sensing capability.

45. Acknowledgment • Subhasri Duttagupta • Prof. Purushottam Kulkarni • Prof. Kannan M. Moudgalya • Prof. Parmesh Ramanathan

46. Loss of Coverage vs. Conf. Level Better Coverage with higher ON nodes δ Should be higher than the error variance

47. References [1] K. Moore, Y. Chen, and Z. Song, “Diffusion-based path planning in mobile actuator-sensor networks (mas-net): Some preliminary results,” in Intelligent Computing: Theory and Application II. SPIE Defense and Security Symposium, 2004. [2] M. F. Fingas and C. E. Brown, “Review of Oil Spill Remote Sensing,” in Eighth Int. Oil Spill Conference, SPILLCON , 2000. [3] R. Nowak, U. Mitra, and R. Willett, “Estimating inhomogeneous fields using wireless sensor networks,” IEEE Journal on Selected Areas in Communications, vol. 22, no. 6, pp. 999-1006, 2004. [4] K. Wang and P. Ramanathan, “Collaborative sensing using sensors of uncoordinated mobility,” in Intl. Conference on Distributed Computing in Sensor Systems, June 2005. W. H¨ardle, Applied Nonparametric Regression. Cambridge University Press, 1990. G. Werner-Allen et al., “Deploying Wireless sensor Network on an Active Volcano”, IEEE Internet Computing, March/April 2006.

48. References • E. A. Nadaraya, “On estimating regression,” Theory Prob. Appl. 10, 186-90, 1964. • T. Gasser and H. G. M¨uller, “Estimating regression functions and their derivatives by the kernel method,” Scandanavian Journal of Statistics, 11, 171-85 , 1984. • W. Heinzelman, A. Chandrakasan, and H. Balakrishnan, “An application-specific communication protocol for wireless microsensor networks,” IEEE Transactions on Wireless Communications, vol. 1, no. 4, pp. 660-670 , Oct 2002.

49. Thank You!

50. Smooth Boundary • CIs using non-parametic regression • Uses Spatial Correlation • PAs sent from CHs to parents using multi-hop