Distributed Estimation Using an Improved Incremental Distributed LMS Algorithm

In this paper we consider the problem of distributed adaptive estimation in wireless sensor networks for two different observation noise conditions. In the first case, we assume that there are some sensors with high observation noise variance (noisy sensors) in the network. In the second case, different variance for observation noise is assumed among the sensors which is more close to real scenario. In both cases, an initial estimate of each sensor-s observation noise is obtained. For the first case, we show that when there are such sensors in the network, the performance of conventional distributed adaptive estimation algorithms such as incremental distributed least mean square (IDLMS) algorithm drastically decreases. In addition, detecting and ignoring these sensors leads to a better performance in a sense of estimation. In the next step, we propose a simple algorithm to detect theses noisy sensors and modify the IDLMS algorithm to deal with noisy sensors. For the second case, we propose a new algorithm in which the step-size parameter is adjusted for each sensor according to its observation noise variance. As the simulation results show, the proposed methods outperforms the IDLMS algorithm in the same condition.

• Amir Rastegarnia
• Mohammad Ali Tinati
• Azam Khalili

• Distributes estimation
• sensor networks
• adaptive filter
• IDLMS.

[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] Lopes, C. G. and Sayed, A. H., Distributed adaptive incremental
strategies: formulation and perform, Proc. ICASSP 06, 3: 584-587, 2006.
[4] Lopes, C. G. and Sayed, A. H., Incremental adaptive strategies over
distributed networks, IEEE trans. on signal processing, vol. 55, pp. 4064-
4077, 2007.
[5] Rabbat M. G. and Nowak, R. D., Quantized incremental algorithms for
distributed optimization, IEEE Journal on Sel. Areas in Comm., vol. 23,
pp. 798-808, 2005.
[6] Lopes, C. G. and Sayed, A. H., Diffusion least- mean squares over
adaptive networks, Proc. ICASSP 07, vol. 3, pp. 917-920, 2007.
[7] Sayed, A. H. and Lopes, C. G., Distributed recursive least-squares
strategies over adaptive networks, Proc. Asilomar Conference on Signals,
Systems and Computers, pp. 233-237, 2006.
[8] A. H. Sayed, Fundamentals of Adaptive Filtering, Wiley, NJ, 2003.