A Diffusion Least-Mean Square Algorithm for Distributed Estimation over Sensor Networks

Authors: Amir Rastegarnia, Mohammad Ali Tinati, Azam Khalili

Abstract:

In this paper we consider the issue of distributed adaptive estimation over sensor networks. To deal with more realistic scenario, different variance for observation noise is assumed for sensors in the network. To solve the problem of different variance of observation noise, the proposed method is divided into two phases: I) Estimating each sensor-s observation noise variance and II) using the estimated variances to obtain the desired parameter. Our proposed algorithm is based on a diffusion least mean square (LMS) implementation with linear combiner model. In the proposed algorithm, the step-size parameter the coefficients of linear combiner are adjusted according to estimated observation noise variances. As the simulation results show, the proposed algorithm considerably improves the diffusion LMS algorithm given in literature.

Keywords: Adaptive filter, distributed estimation, sensor network, diffusion.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1060289

References:

[1] D. Estrin, G. Pottie and M. Srivastava, Intrumenting the world with wireless sensor networks, Proc. IEEE ICASSP, pp. 2033-2036, May 2001.
[2] D. Bertsekas, A new class of incremental gradient methods for least squares problems, SIAM J. Optim., vol.7, no. 4, pp. 913-926, Nov.1997.
[3] C. Lopes and A. H. Sayed, Distributed adaptive incremental strategies: Formulation and performance analysis, Proc. ICASSP-06, Toulouse, France, vol. 3, pp. 584-587, May 2006.
[4] C. Lopes and A. H. Sayed, "Distributed processing over adaptive networks, Proc. Adaptive Sensor Array Processing Workshop, MIT Lincoln Laboratory, MA, June 2006.
[5] C. G. Lopes and A. H. Sayed, "Incremental adaptive strategies over distributed networks, IEEE Transactions on Signal Processing, vol. 55, no. 8, pp. 4064-4077, August 2007.
[6] A. H. Sayed and C. Lopes, Distributed recursive least-squares strategies over adaptive networks, Proc. 40th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, pp. 233-237, October- November, 2006.
[7] C. G. Lopes and A. H. Sayed, Diffusion least-mean-squares over adaptive networks, Proc. ICASSP-07, Honolulu, Hawaii, vol. 3, pp. 917-920, April 2007.
[8] F. Cattivelli, C. G. Lopes, and A. H. Sayed, A diffusion RLS scheme for distributed estimation over adaptive networks, Proc. IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Helsinki, Finland, pp. 1-5, June 2007.
[9] C. G. Lopes, and A. H. Sayed, Steady-state performance of adaptive diffusion least-mean squares, Proc. IEEE Workshop on Statistical Signal Processing (SSP), pp. 136-140, Madison, WI, August 2007.
[10] C. G. Lopes and A. H. Sayed, Diffusion least-mean squares over adaptive networks: Formulation and performance analysis, to appear in IEEE Transactions on Signal Processing, 2008.
[11] F. Cattivelli, C. G. Lopes, and A. H. Sayed, Diffusion recursive leastsquares for distributed estimation over adaptive networks, to appear in IEEE Transactions on Signal Processing, 2008.