How to Utilize Sensor Network Data to Efficiently Perform Model Calibration and Spatial Field Reconstruction

Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)


This chapter provides a tutorial overview of some modern applications of the statistical modeling that can be developed based upon spatial wireless sensor network data. We then develop a range of new results relating to two important problems that arise in spatial field reconstructions from wireless sensor networks. The first new result allows one to accurately and efficiently obtain a spatial field reconstruction which is optimal in the sense that it is the Spatial Best Linear Unbiased Estimator for the field reconstruction. This estimator is obtained under three different system model configurations that represent different types of heterogeneous and homogeneous wireless sensor networks. The second novelty presented in this chapter relates to development of a framework that allows one to incorporate multiple sensed modalities from related spatial processes into the spatial field reconstruction. This is of practical significance for instance, if there are d spatial physical processes that are all being monitored by a wireless sensor network and it is believed that there is a relationship between the variability in the target spatial process to be reconstructed and the other spatial processes being monitored. In such settings it should be beneficial to incorporate these other spatial modalities into the estimation and spatial reconstruction of the target process. In this chapter we develop a spatial covariance regression framework to provide such estimation functionality. In addition, we develop a highly efficient estimation procedure for the model parameters via an Expectation Maximization algorithm. Results of the estimation and spatial field reconstructions are provided for two different real-world applications related to modeling the spatial relationships between coastal wind speeds and ocean height bathymetry measurements based on sensor network observations.


Wireless Sensor Network Expectation Maximization Algorithm Fusion Center Gaussian Random Field Spatial Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Adler, R., Taylor, J.: Random Fields and Geometry, vol. 115. Springer, New York (2007)Google Scholar
  2. 2.
    Agrawal, P., Patwari, N.: Correlated link shadow fading in multi-hop wireless networks. IEEE Trans. Wirel. Commun. 8(8), 4024–4036 (2009)CrossRefGoogle Scholar
  3. 3.
    Akyildiz, I., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless sensor networks: a survey. Comput. Netw. 38(4), 393–422 (2002)CrossRefGoogle Scholar
  4. 4.
    Akyildiz, I., Vuran, M., Akan, O.: On exploiting spatial and temporal correlation in wireless sensor networks. In: Proceedings of WiOpt’04: Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks pp. 71–80 (2004)Google Scholar
  5. 5.
    Anastasi, G., Conti, M., Di Francesco, M., Passarella, A.: Energy conservation in wireless sensor networks: a survey. Ad Hoc Netw. 7(3), 537–568 (2009)CrossRefGoogle Scholar
  6. 6.
    Berger, J.: Statistical Decision Theory and Bayesian Analysis. Springer, New York (1985)Google Scholar
  7. 7.
    Berz, G.: Windstorm and storm surges in Europe: loss trends and possible counter-actions from the viewpoint of an international reinsurer. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 363(1831), 1431–1440 (2005)CrossRefGoogle Scholar
  8. 8.
    Boyd, J.: Chebyshev and Fourier Spectral Methods. Dover Publications, New York (2001)Google Scholar
  9. 9.
    Chintalapudi, K., Fu, T., Paek, J., Kothari, N., Rangwala, S., Caffrey, J., Govindan, R., Johnson, E., Masri, S.: Monitoring civil structures with a wireless sensor network. IEEE Internet Comput. 10(2), 26–34 (2006)CrossRefGoogle Scholar
  10. 10.
    Clenshaw, C., Curtis, A.: A method for numerical integration on an automatic computer. Numer. Math. 2(1), 197–205 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Cohen, K., Leshem, A.: Energy-efficient detection in wireless sensor networks using likelihood ratio and channel state information. IEEE J. Sel. Areas Commun. 29(8), 1671–1683 (2011)CrossRefGoogle Scholar
  12. 12.
    Fazel, F., Fazel, M., Stojanovic, M.: Random access sensor networks: field reconstruction from incomplete data. In: IEEE Information Theory and Applications Workshop (ITA), pp. 300–305 (2012)Google Scholar
  13. 13.
    Flather, R., Smith, J., Richards, J., Bell, C., Blackman, D.: Direct estimates of extreme storm surge elevations from a 40-year numerical model simulation and from observations. Global Atmos. Ocean Syst. 6(2), 165–176 (1998)Google Scholar
  14. 14.
    Fonseca, C., Ferreira, H.: Stability and contagion measures for spatial extreme value analyses. arXiv:1206.1228 (2012)
  15. 15.
    French, J.P., Sain, S.R.: Spatio-Temporal Exceedance Locations and Confidence Regions. Annals of Applied Statistics. Prepress (2013)Google Scholar
  16. 16.
    Gu, D., Hu, H.: Spatial Gaussian process regression with mobile sensor networks. IEEE Trans. Neural Netw. Learn. Syst. 23(8), 1279–1290 (2012)CrossRefGoogle Scholar
  17. 17.
    Hoff, P.D., Niu, X.: A Covariance Regression Model. arXiv:1102.5721 (2011)
  18. 18.
    Højsgaard, S., Edwards, D., Lauritzen, S.: Gaussian graphical models. In: Graphical Models with R, pp. 77–116. Springer, New York (2012)Google Scholar
  19. 19.
    Katenka, N., Levina, E., Michailidis, G.: Local vote decision fusion for target detection in wireless sensor networks. IEEE Trans. Signal Process. 56(1), 329–338 (2008)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Kottas, A., Wang, Z., Rodriguez, A.: Spatial modeling for risk assessment of extreme values from environmental time series: a Bayesian nonparametric approach. Environmetrics 23(8), 649–662 (2012). doi: 10.1002/env.2177
  21. 21.
    Krause, A., Singh, A., Guestrin, C.: Near-optimal sensor placements in gaussian processes: theory, efficient algorithms and empirical studies. J. Mach. Learn. Res. 9, 235–284 (2008)zbMATHGoogle Scholar
  22. 22.
    Lorincz, K., Malan, D.J., Fulford-Jones, T.R., Nawoj, A., Clavel, A., Shnayder, V., Mainland, G., Welsh, M., Moulton, S.: Sensor networks for emergency response: challenges and opportunities. IEEE Pervasive Comput. 3(4), 16–23 (2004)CrossRefGoogle Scholar
  23. 23.
    Masazade, E., Niu, R., Varshney, P., Keskinoz, M.: Energy aware iterative source localization for wireless sensor networks. IEEE Trans. Signal Process. 58(9), 4824–4835 (2010)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Matamoros, J., Fabbri, F., Antón-Haro, C., Dardari, D.: On the estimation of randomly sampled 2D spatial fields under bandwidth constraints. IEEE Trans. Wirel. Commun. 10(12), 4184–4192 (2011)CrossRefGoogle Scholar
  25. 25.
    Matern, B.: Spatial variation. meddelanden fraan statens skogsforskningsinstitut, 49(5), 1–144. Also appeared as Lecture Notes in Statistics, vol. 36 (1986)Google Scholar
  26. 26.
    Msechu, E., Giannakis, G.: Sensor-centric data reduction for estimation with WSNs via censoring and quantization. IEEE Trans. Signal Process. 60(1), 400–414 (2012)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Nevat, I., Peters, G., Collings, I.: Location-aware cooperative spectrum sensing via Gaussian processes. In: IEEE Australian Communications Theory Workshop (AusCTW), pp. 19–24 (2012)Google Scholar
  28. 28.
    Nevat, I., Peters, G.W., Collings, I.B.: Location-aware cooperative spectrum sensing via gaussian processes. In: Communications Theory Workshop (AusCTW), 2012 Australian, pp. 19–24. IEEE (2012)Google Scholar
  29. 29.
    Nevat, I., Peters, G.W., Collings, I.B.: Estimation of correlated and quantized spatial random fields in wireless sensor networks. In: 2013 IEEE International Conference on Communications (ICC), pp. 1931–1935. IEEE (2013)Google Scholar
  30. 30.
    Nevat, I., Peters, G.W., Collings, I.B.: Random field reconstruction with quantization in wireless sensor networks. IEEE Trans. Signal Process. 61, 6020–6033 (2013)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Niu, R., Varshney, P.K.: Target location estimation in sensor networks with quantized data. IEEE Trans. Signal Process. 54(12), 4519–4528 (2006)CrossRefGoogle Scholar
  32. 32.
    Ozdemir, O., Niu, R., Varshney, P.K.: Channel aware target localization with quantized data in wireless sensor networks. IEEE Trans. Signal Process. 57(3), 1190–1202 (2009)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Park, S., Choi, S.: Gaussian processes for source separation. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 1909–1912 (2008)Google Scholar
  34. 34.
    Peters, G., Nevat, I., Lin, S., Matsui, T.: Modelling threshold exceedence levels for spatial stochastic processes observed by sensor networks. In: 2014 IEEE Ninth International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), pp. 1–7. IEEE (2014)Google Scholar
  35. 35.
    Rajasegarar, S., Havens, T.C., Karunasekera, S., Leckie, C., Bezdek, J.C., Jamriska, M., Gunatilaka, A., Skvortsov, A., Palaniswami, M.: High-resolution monitoring of atmospheric pollutants using a system of low-cost sensors. IEEE Trans. Geosci. Remote Sens. 52, 3823–3832 (2014)CrossRefGoogle Scholar
  36. 36.
    Rajasegarar, S., Zhang, P., Zhou, Y., Karunasekera, S., Leckie, C., Palaniswami, M.: High resolution spatio-temporal monitoring of air pollutants using wireless sensor networks. In: 2014 IEEE Ninth International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), pp. 1–6. IEEE (2014)Google Scholar
  37. 37.
    Rasmussen, C., Williams, C.: Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). The MIT Press (2005)Google Scholar
  38. 38.
    Schabenberger, O., Pierce, F.J.: Contemporary Statistical Models for the Plant and Soil Sciences. CRC Press, Boca Raton (2002)Google Scholar
  39. 39.
    Sohraby, K., Minoli, D., Znati, T.: Wireless Sensor Networks: Technology, Protocols, and Applications. Wiley, Hoboken (2007)Google Scholar
  40. 40.
    Stein, M.L.: Interpolation of Spatial Data: Some Theory for Kriging. Springer, New York (1999)Google Scholar
  41. 41.
    Vanmarcke, E.: Random Fields: Analysis and Synthesis. World Scientific Publishing Company Inc., Singapore (2010)Google Scholar
  42. 42.
    Vuran, M.C., Akan, O.B., Akyildiz, I.F.: Spatio-temporal correlation: theory and applications for wireless sensor networks. Comput. Netw. J., Elsevier 45, 245–259 (2004)CrossRefzbMATHGoogle Scholar
  43. 43.
    Werner-Allen, G., Lorincz, K., Ruiz, M., Marcillo, O., Johnson, J., Lees, J., Welsh, M.: Deploying a wireless sensor network on an active volcano. IEEE Internet Comput. 10(2), 18–25 (2006)CrossRefGoogle Scholar
  44. 44.
    Wu, T., Cheng, Q.: Distributed estimation over fading channels using one-bit quantization. IEEE Trans. Wirel. Commun. 8(12), 5779–5784 (2009)CrossRefGoogle Scholar
  45. 45.
    Xu, Y., Choi, J.: Adaptive sampling for learning Gaussian processes using mobile sensor networks. Int. J. Sens. 11(3), 3051–3066 (2011)CrossRefGoogle Scholar
  46. 46.
    Zheng, Y., Niu, R., Varshney, P.: Closed-form performance for location estimation based on quantized data in sensor networks. In: 13th Conference on Information Fusion (FUSION), pp. 1–7. IEEE (2010)Google Scholar
  47. 47.
    Zhou, Y., Li, J., Wang, D.: Posterior cramér-rao lower bounds for target tracking in sensor networks with quantized range-only measurements. IEEE Signal Process. Lett. 17(2), 157–160 (2010)CrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of Statistical ScienceUniversity College LondonLondonUK
  2. 2.Institute for Infocomm ResearchA*STARSingaporeSingapore
  3. 3.The Institute of Statistical MathematicsTokyoJapan

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