Advertisement

GeoInformatica

, 14:101 | Cite as

Spatial interpolation in wireless sensor networks: localized algorithms for variogram modeling and Kriging

  • Muhammad Umer
  • Lars Kulik
  • Egemen Tanin
Article

Abstract

Wireless sensor networks (WSNs) are rapidly emerging as the prominent technology for monitoring physical phenomena. However, large scale WSNs are known to suffer from coverage holes, i.e., large regions of deployment area where no sensing coverage can be provided. Such holes are the result of hardware failures, extensive costs for redeployment or the hostility of deployment areas. Coverage holes can adversely affect the accurate representation of natural phenomena that are monitored by a WSN. In this work, we propose to exploit the spatial correlation of physical phenomena to make monitoring systems more resilient to coverage holes. We show that a phenomenon can be interpolated inside a coverage hole with a high level of accuracy from the available nodal data given a model of its spatial correlation. However, due to energy limitations of sensor nodes it is imperative to perform this interpolation in an energy efficient manner that minimizes communication among nodes. In this paper, we present highly energy efficient methods for spatial interpolation in WSNs. First, we build a correlation model of the phenomenon being monitored in a distributed manner. Then, a purely localized and distributed spatial interpolation scheme based on Kriging interpolates the phenomenon inside coverage holes. We test the cost and accuracy of our scheme with extensive simulations and show that it is significantly more energy efficient than global interpolations and remarkably more accurate than simple averaging.

Keywords

Wireless sensor networks Coverage holes Spatial interpolation Kriging 

References

  1. 1.
    Ahmed N, Kanhere SS, Jha S (2005) The holes problem in wireless sensor networks: a survey. Mob Comput Commun Rev 9(2):4–18CrossRefGoogle Scholar
  2. 2.
    Biswas R, Thrun S, Guibas LJ (2004) A probabilistic approach to inference with limited information in sensor networks. In: Proceedings of IPSN, Berkeley, 26–27 April 2004, pp 269–276Google Scholar
  3. 3.
    Bonfils BJ, Bonnet P (2003) Adaptive and decentralized operator placement for in-network query processing. In: Proceedings of IPSN, Palo Alto, 22–23 April 2003, pp 47–62Google Scholar
  4. 4.
    Chu D, Deshpande A, Hellerstein J, Hong W (2006) Approximate data collection in sensor networks using probabilistic models. In: Proceedings of ICDE, Atlanta, 3–7 April 2006, p 48Google Scholar
  5. 5.
    Coman A, Nascimento MA (2007) A distributed algorithm for joins in sensor networks. In: Proceedings of SSDBM, Banff, 9–11 July 2007, p 27Google Scholar
  6. 6.
    Cressie NA (1993) Statistics for spatial data. Wiley, New York (1993)Google Scholar
  7. 7.
    Crossbow Technologies (2007) Crossbow Technologies homepage. http://www.xbow.com
  8. 8.
    Curran PJ, Atkinson PM (1998) Geostatistics and remote sensing. Prog Phys Geogr 22(1):61–78Google Scholar
  9. 9.
    Deshpande A, Guestrin C, Madden SR, Hellerstein JM, Hong, W (2004) Model-driven data acquisition in sensor networks. In: Proceedings of VLDB, Toronto, August 2004, pp 588–599Google Scholar
  10. 10.
    Gambino F, Kopp VC, Costa JFCL, Kopp JC, Fallon G, Davies N (2004) Incorporating uncertainty in coal seam depth determination via seismic reflection and Geostatistics. In: Proceedings of 7th international geostatistics congress, Banff, 26 September–1 October 2004, pp 537–542Google Scholar
  11. 11.
    Gnawali O, Yarvis M, Heidemann J, Govindan R (2004) Interaction of retransmission, blacklisting, and routing metrics for reliability in sensor network routing. In: Proceedings of IEEE SECON, Santa Clara, 4–7 October 2004, pp 34–43Google Scholar
  12. 12.
    Guestrin C, Bodik P, Thibaux R, Paskin M, Madden S (2004) Distributed regression: an efficient framework for modeling sensor network data. In: Proceedings of IPSN, Berkeley, 26–27 April 2004, pp 1–10Google Scholar
  13. 13.
    Guestrin C, Krause A, Singh AP (2005) Near-optimal sensor placements in Gaussian processes. In: Proceedings of ICML, Bonn, 7–11 August 2005, pp 265–272Google Scholar
  14. 14.
    Gupta H, Chowdhary V (2007) Communication-efficient implementation of join in sensor networks. Ad Hoc Netw 5(6):929–942CrossRefGoogle Scholar
  15. 15.
    Huang CF, Tseng YC (2005) The coverage problem in a wireless sensor network. Mob Netw Appl 10(4):519–528CrossRefGoogle Scholar
  16. 16.
    Hull B, Bychkovsky V, Zhang Y, Chen K, Goraczko M, Miu A, Shih E, Balakrishnan H, Madden S (2006) Cartel: a distributed mobile sensor computing system. In: Proceedings of SenSys, Boulder, November 2006, pp 125–138Google Scholar
  17. 17.
    Isaaks E, Srivatava RM (1989) An introduction to applied geostatistics. Oxford, New YorkGoogle Scholar
  18. 18.
    Jin G, Nittel S (2008) Towards spatial window queries over continuous phenomena in sensor networks. IEEE Trans Parallel Distrib Syst 19(4):559–571CrossRefGoogle Scholar
  19. 19.
    Krause A, Guestrin C, Gupta A, Kleinberg J (2006) Near-optimal sensor placements: maximizing information while minimizing communication cost. In: Proceedings of IPSN, Nashville, 19–21 April 2006, pp 2–10Google Scholar
  20. 20.
    Kröller A, Fekete SP, Pfisterer D, Fischer S (2006) Deterministic boundary recognition and topology extraction for large sensor networks. In: Proceedings of SODA, pp 1000–1009. ACM, New York (2006)CrossRefGoogle Scholar
  21. 21.
    Madden SR, Franklin MJ, Hellerstein JM, Hong W (2005) TinyDB: an acquisitional query processing system for sensor networks. ACM Trans Database Syst 30(1):122–173CrossRefGoogle Scholar
  22. 22.
    Morrison JL (1974) Observed statistical trends in various interpolation algorithms useful for first stage interpolation. Can Cartogr 11(2):142–159Google Scholar
  23. 23.
    NASA Volcano Sensorweb (2007) Volcano sensorweb homepage. http://sensorwebs.jpl.nasa.gov/
  24. 24.
    Nath S, Gibbons PB, Seshan S, Anderson ZR (2004) Synopsis diffusion for robust aggregation in sensor networks. In: Proceedings of SenSys, Baltimore, 3–5 November 2004, pp 250–262Google Scholar
  25. 25.
    Network Simulator (2006) Network simulator homepage. http://www.isi.edu/nsnam/ns/doc
  26. 26.
    Pattem S, Krishnamachari B, Govindan R (2004) The impact of spatial correlation on routing with compression in wireless sensor networks. In: Proceedings of IPSN, Berkeley, 26–27 April 2004, pp 28–35Google Scholar
  27. 27.
    Pottie GJ, Kaiser WJ (2000) Wireless integrated network sensors. Commun ACM 43(5):51–58CrossRefGoogle Scholar
  28. 28.
    Secure CITI (2006) Exploratory research on sensor-based infrastructure for early Tsunami detection. http://www.cs.pitt.edu/s-citi/tsunami/
  29. 29.
    Sharaf MA, Beaver J, Labrinidis A, Chrysanthis PK (2004) Balancing energy efficiency and quality of aggregate data in sensor networks. VLDB J 13(4):384–403CrossRefGoogle Scholar
  30. 30.
    Sharifzadeh M, Shahabi C (2006) Utilizing Voronoi cells of location data streams for accurate computation of aggregate functions in sensor networks. GeoInformatica 10(1):9–36CrossRefGoogle Scholar
  31. 31.
    Shrivastava N, Buragohain C, Agrawal D, Suri S (2004) Medians and beyond: new aggregation techniques for sensor networks. In: Proceedings of SenSys, Baltimore, 3–5 November 2004, pp 239–249Google Scholar
  32. 32.
    Silberstein A, Braynard R, Yang J (2006) Constraint chaining: on energy-efficient continuous monitoring in sensor networks. In: Proceedings of SIGMOD, Chicago, 26–29 June 2006, pp 157–168Google Scholar
  33. 33.
    Somasundara AA, Jea DD, Estrin D, Srivastava MB (2006) Controllably mobile infrastructure for low energy embedded networks. IEEE Trans Mob Comput 5(8):958–973CrossRefGoogle Scholar
  34. 34.
    Strangeways I (2003) Measuring the natural environment. Cambridge University Press, New YorkGoogle Scholar
  35. 35.
    Tolle G, Polastre J, Szewczyk R, Culler D, Turner N, Tu K, Burgess S, Dawson T, Buonadonna P, Gay D, Hong W, Hong W (2005) A macroscope in the Redwoods. In: Proceedings of SenSys, San Diego, 2–4 November 2005, pp 51–63Google Scholar
  36. 36.
    Umer M, Kulik L, Tanin E (2008) Kriging for localized spatial interpolation in sensor networks. In: Proceedings of SSDBM, Hong Kong, 9–11 July 2008, pp 525–532Google Scholar
  37. 37.
    USGS Digital Elevation Models (2007) USGS digital elevation models homepage. http://data.geocomm.com/dem/
  38. 38.
    Wang Y, Gao J, Mitchell JS (2006) Boundary recognition in sensor networks by topological methods. In: Proceedings of MobiCom, Los Angeles, 23–29 September 2006, pp 122–133Google Scholar
  39. 39.
    Yang X, Lim HB, Özsu TM, Tan KL (2007) In-network execution of monitoring queries in sensor networks. In: Proceedings of SIGMOD, Beijing, 12–14 June 2007, pp 521–532Google Scholar
  40. 40.
    Yiu ML, Mamoulis N, Bakiras S (2009) Retrieval of spatial join pattern instances from sensor networks. GeoInformatica 13(1):57–84Google Scholar
  41. 41.
    Zhang H, Moura JMF, Krogh B (2005) Estimation in sensor networks: a graph approach. In: Proceedings of IPSN. IEEE, Piscataway, p. 27Google Scholar
  42. 42.
    Zimmerman D, Pavlik C, Ruggles A, Armstrong M (199) An experimental comparison of ordinary and universal Kriging and inverse distance weighting. Math Geol 31:375–390CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.National ICT Australia, Department of Computer Science & Software EngineeringUniversity of MelbourneMelbourneAustralia

Personalised recommendations