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Decentralized estimation of a noise-corrupted source parameter by a bandwidth-constrained sensor network feeding, through a noisy channel, a fusion center is considered. The sensors, due to bandwidth constraints, provide binary representatives of a noise-corrupted source parameter. Recently, proposed decentralized, distributed estimation, and power scheduling methods do no consider errors occurring during the transmission of binary observations from the sensors to fusion center. In this paper, we extend the decentralized estimation model to the case where imperfect transmission channels are considered. The proposed estimator, which operates on additive channel noise corrupted versions of quantized noisy sensor observations, is approached from maximum likelihood (ML) perspective. The resulting ML estimate is a root, in the region of interest (ROI), of a derivative polynomial function. We analyze the natural logarithm of the polynomial within the ROI showing that the function is log-concave, thereby indicating that numerical methods, such as Newton's algorithm, can be utilized to obtain the optimal solution. Due to complexity and implementation issues associated with the numerical methods, we derive and analyze simpler suboptimal solutions, i.e., the two-stage and mean estimators. The two-stage estimator first estimates the binary observations from noisy fusion center observations utilizing a threshold operation, followed by an estimate of the source parameter. The optimal threshold is the maximum a posteriori (MAP) detector for binary detection and minimizes the probability of binary observation estimation error. Optimal threshold expressions for commonly utilized light-(Gaussian) and heavy-tailed (Cauchy) channel noise models are derived. The mean estimator simply averages the noisy fusion center observations. The output variances of means of the proposed suboptimal estimators are derived. In addition, a computational complexity analysis is presented comparing the - proposed ML optimal and suboptimal two-stage and mean estimators. Numerical examples evaluating and comparing the performance of proposed ML, two-stage and mean estimators are also presented.
Date of Publication: April 2008