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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., {"references":["D. Estrin, G. Pottie and M. Srivastava, Intrumenting the world with\nwireless sensor networks, Proc. IEEE ICASSP, pp. 2033-2036, May 2001.","D. Bertsekas, A new class of incremental gradient methods for least\nsquares problems, SIAM J. Optim., vol.7, no. 4, pp. 913-926, Nov.1997.","C. Lopes and A. H. Sayed, Distributed adaptive incremental strategies:\nFormulation and performance analysis, Proc. ICASSP-06, Toulouse,\nFrance, vol. 3, pp. 584-587, May 2006.","C. Lopes and A. H. Sayed, \"Distributed processing over adaptive networks,\nProc. Adaptive Sensor Array Processing Workshop, MIT Lincoln\nLaboratory, MA, June 2006.","C. G. Lopes and A. H. Sayed, \"Incremental adaptive strategies over\ndistributed networks, IEEE Transactions on Signal Processing, vol. 55,\nno. 8, pp. 4064-4077, August 2007.","A. H. Sayed and C. Lopes, Distributed recursive least-squares strategies\nover adaptive networks, Proc. 40th Asilomar Conference on Signals,\nSystems and Computers, Pacific Grove, CA, pp. 233-237, October-\nNovember, 2006.","C. G. Lopes and A. H. Sayed, Diffusion least-mean-squares over adaptive\nnetworks, Proc. ICASSP-07, Honolulu, Hawaii, vol. 3, pp. 917-920, April\n2007.","F. Cattivelli, C. G. Lopes, and A. H. Sayed, A diffusion RLS scheme\nfor distributed estimation over adaptive networks, Proc. IEEE Workshop\non Signal Processing Advances in Wireless Communications (SPAWC),\nHelsinki, Finland, pp. 1-5, June 2007.","C. G. Lopes, and A. H. Sayed, Steady-state performance of adaptive\ndiffusion least-mean squares, Proc. IEEE Workshop on Statistical Signal\nProcessing (SSP), pp. 136-140, Madison, WI, August 2007.\n[10] C. G. Lopes and A. H. Sayed, Diffusion least-mean squares over adaptive\nnetworks: Formulation and performance analysis, to appear in IEEE\nTransactions on Signal Processing, 2008.\n[11] F. Cattivelli, C. G. Lopes, and A. H. Sayed, Diffusion recursive leastsquares\nfor distributed estimation over adaptive networks, to appear in\nIEEE Transactions on Signal Processing, 2008."]}