Abstract
The distributed nature of observations collected by inexpensive wireless sensors necessitates transmission of the individual sensor data under stringent bandwidth and power constraints. These constraints motivate: i) a means of reducing the dimensionality of local sensor observations; ii) quantization of sensor observations prior to digital transmission; and iii) estimators based on the quantized digital messages. These three problems are addressed in the present paper. We start deriving linear estimators of stationary random signals based on reduced-dimensionality observations. For uncorrelated sensor data, we develop mean-square error (MSE) optimal estimators in closed-form; while for correlated sensor data, we derive sub-optimal iterative estimators which guarantee convergence at least to a stationary point. We then determine lower and upper bounds for the Distortion-Rate (D-R) function and a novel alternating scheme that numerically determines an achievable upper bound of the D-R function for general distributed estimation using multiple sensors. We finally derive distributed estimators based on binary observations along with their fundamental error-variance limits for pragmatic signal models including: i) known univariate but generally non-Gaussian noise probability density functions (pdfs); ii) known noise pdfs with a finite number of unknown parameters; and iii) practical generalizations to multivariate and possibly correlated pdfs. Estimators utilizing either independent or colored binary observations are developed, analyzed and tested with numerical examples.
Prepared through collaborative participation in the Communications and Networks Consortium sponsored by the U. S. Army Research Laboratory under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U. S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Abdallah and H. Papadopoulos, Sequential signal encoding and estimation for distributed sensor networks, in Proc. of the International Conference on Acoustics, Speech, and Signal Processing, 4: 2577–2580, Salt Lake City, Utah, May 2001.
B. Beferull-Lozano, R.L. Konsbruck, and M. Vetterli, Rate-Distortion problem for physics based distributed sensing, in Proc. of the International Conference on Acoustics, Speech, and Signal Processing, 3: 913–916, Montreal, Canada, May 2004.
T. Berger, Rate Distortion Theory: A Mathematical Basis for Data Compression. Prentice Hall, 1971.
T. Berger, Multiterminal Source Coding, in Lectures Presented at CISM Summer School on the Info. Theory Approach to Comm., July 1977.
D. Blatt and A. Hero, Distributed maximum likelihood estimation for sensor networks, in Proc. of the International Conference on Acoustics, Speech, and Signal Processing, 3: 929–932, Montreal, Canada, May 2004.
S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, 2004.
J. Chen, X. Zhang, T. Berger,and S.B. Wicker, An Upper Bound on the Sum-Rate Distortion Function and Its Corresponding Rate Allocation Schemes for the CEO Problem, IEEE Journal on Selected Areas in Communications, pp. 406–411, August 2004.
T. Cover and J. Thomas, Elements of Information Theory. John Wiley and Sons, 2nd edition ed., 1991.
E. Ertin, R. Moses, and L. Potter, Network parameter estimation with detection failures, in Proc. of the Intnl. Conference on Acoustics, Speech, and Signal Processing, 2: 273–276, Montreal, Canada, May 2004.
M. Gastpar, P.L. Draggoti, and M. Vetterli, The distributed Karhunen-Loève transform, IEEE Transactions on Information Theory, submitted Nov. 2004 (available at http://www.eecs.berkeley.edu/∼gastpar/).
J. Gubner, Distributed Estimation and Quantization, IEEE Transactions on Information Theory, 39: 1456–1459, 1993.
P. Ishwar, R. Puri, K. Ramchadran, and S. Pradhan, On Rate-Constrained Distributed Estimation in Unreliable Sensor Networks, IEEE Journal on Selected Areas in Communications, pp. 765–775, April 2005.
S.M. Kay, Fundamentals of Statistical Signal Processing — Estimation Theory. Prentice Hall, 1993.
S. Kumar, F. Zao, and D. Shepherd, eds., Special issue on collaborative information processing, Vol. 19 of IEEE Signal Proc. Magazine, March 2002.
W. Lam and A. Reibman, Quantizer design for decentralized systems with communication constraints, IEEE Transactions on Communications, 41: 1602–1605, Aug. 1993.
Z.-Q. Luo, An isotropic universal decentralized estimation scheme for a bandwidth constrained ad hoc sensor network, IEEE Journal on Selected Areas in Communications, 23: 735–744, April 2005.
Z.-Q. Luo, Universal Decentralized Estimation in a Bandwidth Constrained Sensor Network, IEEE Transactions on Information Theory, 51: 2210–2219, June 2005.
Z.-Q. Luo, G.B. Giannakis, and S. Zhang, Optimal linear decentralized estimation in a bandwidth constrained sensor network, in Proc. of the Intl. Symp. on Info. Theory, pp. 1441–1445, Adelaide, Australia, Sept. 4–9 2005.
Z.-Q. Luo and J.-J. Xiao, Decentralized estimation in an inhomogeneous sensing environment, IEEE Transactions on Information Theory, 51: 3564–3575, October 2005.
A. Mainwaring, D. Culler, J. Polastre, R. Szewczyk, and J. Anderson, Wireless sensor networks for habitat monitoring, in Proc. of the 1st ACM International Workshop on Wireless Sensor Networks and Applications, 3: 88–97, Atlanta, Georgia, 2002.
R.D. Nowak, Distributed EM algorithms for density estimation and clustering in sensor networks, IEEE Transactions on Signal Processing, 51: 2245–2253, August 2002.
Y. Oohama, The Rate-Distortion Function for the Quadratic Gaussian CEO Problem, IEEE Transactions On Information Theory, pp. 1057–1070, May 1998.
A. Pandya, A. Kansal, G. Pottie, and M. Srivastava, Fidelity and Resource Sensitive Data Gathering, in Proc. of the 42nd Allerton Conference, Allerton, IL, September 2004.
H. Papadopoulos, G. Wornell, and A. Oppenheim, Sequential signal encoding from noisy measurements using quantizers with dynamic bias control, IEEE Transactions on Information Theory, 47: 978–1002, 2001.
S.S. Pradhan, J. Kusuma, and K. Ramchandran, Distributed compression in a dense microsensor network, IEEE Signal Processing Magazine, 19: 51–60, March 2002.
M.G. Rabbat and R.D. Nowak, Decentralized source localization and tracking, in Proc. of the 2004 IEEE Intnl. Conference on Acoustics, Speech, and Signal Processing, 3: 921–924, Montreal, Canada, May 2004.
A. Ribeiro and G.B. Giannakis, Bandwidth-Constrained Distributed Estimation for Wireless Sensor Networks, Part I: Gaussian Case, IEEE Transactions on Signal Processing, 54: 1131–1143, March 2006.
A. Ribeiro and G.B. Giannakis, Bandwidth-Constrained Distributed Estimation for Wireless Sensor Networks, Part II: Unknown pdf, IEEE Transactions on Signal Processing, 2006, to appear.
D.J. Sakrison, Source encoding in the presence of random disturbance, IEEE Transactions on Information Theory, pp. 165–167, January 1968.
I.D. Schizas, G.B. Giannakis, and N. Jindal, Distortion-Rate Analysis for Distributed Estimation with Wireless Sensor Networks, IEEE Transactions On Information Theory, submitted December 2005 (available at http://spincom.ece.umn.edu/).
I.D. Schizas, G.B. Giannakis, and Z.-Q. Luo, Distributed estimation using reduced dimensionality sensor observations, IEEE Transactions on Signal Processing, submitted November 2005 (available at http://spincom.ece.umn.edu/).
Y. Sung, L. Tong, and A. Swami, Asymptotic locally optimal detector for largescale sensor networks under the Poisson regime, in Proc. of the International Conference on Acoustics, Speech, and Signal Processing, 2: 1077–1080, Montreal, Canada, May 2004.
P.K. Varshney, Distributed Detection and Data Fusion. Springer-Verlag, 1997.
H. Viswanathan and T. Berger, The Quadratic Gaussian CEO Problem, IEEE Transactions on Information Theory, pp. 1549–1559, September 1997.
J. Wolf and J. Ziv, Transmission of noisy information to a noisy receiver with minimum distortion, IEEE Transactions on Information Theory, pp. 406–411, July 1970.
A. Wyner and J. Ziv, The Rate-Distortion Function for Source Coding with Side Information at the Decoder, IEEE Trans, on Info. Theory, pp. 1–10, January 1976.
K. Zhang, X.R. Li, P. Zhang, and H. Li, Optimal linear estimation fusion-Part VI: Sensor data compression, in Proc. of the Intl. Conf. on Info. Fusion, pp. 221–228, Queensland, Australia 2003.
Y. Zhu, E. Song, J. Zhou, and Z. You, Optimal dimensionality reduction of sensor data in multisensor estimation fusion, IEEE Transactions on Signal Processing, 53: 1631–1639, May 2005.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Schizas, I.D., Ribeiro, A., Giannakis, G.B. (2007). Dimensionality Reduction, Compression and Quantization for Distributed Estimation with Wireless Sensor Networks. In: Agrawal, P., Fleming, P.J., Zhang, L., Andrews, D.M., Yin, G. (eds) Wireless Communications. The IMA Volumes in Mathematics and its Applications, vol 143. Springer, New York, NY. https://doi.org/10.1007/978-0-387-48945-2_12
Download citation
DOI: https://doi.org/10.1007/978-0-387-48945-2_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-37269-3
Online ISBN: 978-0-387-48945-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)