Abstract
Many distributed inference problems in wireless sensor networks can be represented by probabilistic graphical models, where belief propagation, an iterative message passing algorithm provides a promising solution. In order to make the algorithm efficient and accurate, messages which carry the belief information from one node to the others should be formulated in an appropriate format. This paper presents two belief propagation algorithms where non-linear and non-Gaussian beliefs are approximated by Fourier density approximations, which significantly reduces power consumptions in the belief computation and transmission. We use self-localization in wireless sensor networks as an example to illustrate the performance of this method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Refernece
Gharavi, H., Kumar, S. (Eds.): Special issue on sensor networks and applications. In Proceedings of the IEEE, vol.91, no.8, Aug. 2003
Kumar, S., Zhao, F., Shepherd, D. (Eds.): Special issue on collaborative information processing. In IEEE Signal Processing Magazine, vol.19, no.2, Mar. 2002
Ihler, A., Fisher, J., Moses, R., Willsky, A.: Nonparametric belief propagation for self-calibration in sensor networks. In Proceedings of IPSN 2004
Kronmal, R., Tarter, M.: The estimation of probability densities and cumulatives by Fourier series methods. In Journal of the American Statistical Association, vol.63, no.323, pp.925–952, Sep. 1968
Brunn, D., Sawo, F., Hanebeck, U.D.: Efficient nonlinear Bayesian estimation based on Fourier densities. In Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), Germany 2006
Brunn, D., Sawo, F., Hanebeck, U.D.: Nonlinear multidimensional Bayesian estimation with Fourier densities. In Proceedings of the 2006 IEEE Conference on Decision and Control (CDC 2006), pp.1303–1308, San Diego, California, Dec. 2006
Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford, 1996
Clifford, P.: Markov random fields in statistics. In Grimmett, G.R., Welsh, D.J.A. (Eds.) Disorder in Physical Systems, pp.19C32. Oxford University Press, Oxford, 1990
Paskin, M., Guestrin, C.: A robust architecture for distributed inference in sensor networks. Intel Research, Technical Report IRB-TR-03-039, 2004.
Aji, S.M., McEliece, R.J.: The generalized distributive law. IEEE Transactions on Information Theory vol.46, pp.325–343, Mar. 2000
Murphy, K., Weiss, Y., Jordan, M.: Loopy-belief propagation for approximate inference: An empirical study. In Uncertainty in Artificial Intelligence vol.15, pp.467–475, Jul. 1999
Kschischang, F.R., Frey, B.J., Loeliger, H.A.: Factor graph and the sum-product algorithm. IEEE Transactions Information Theory, vol.47, no.2, pp.498–518, Feb. 2001.
Hanebeck, U.D.: Progressive Bayesian estimation for nonlinear discrete-time systems: the measurement step. In Proceedings of the 2003 IEEE Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2003), pp.173–178, Tokyo, Japan, Jul. 2003.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Na, C., Wang, H., Obradovic, D., Hanebeck, U.D. (2009). Fourier Density Approximation for Belief Propagation in Wireless Sensor Networks. In: Hahn, H., Ko, H., Lee, S. (eds) Multisensor Fusion and Integration for Intelligent Systems. Lecture Notes in Electrical Engineering, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89859-7_25
Download citation
DOI: https://doi.org/10.1007/978-3-540-89859-7_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89858-0
Online ISBN: 978-3-540-89859-7
eBook Packages: EngineeringEngineering (R0)