Decentralized estimation in an inhomogeneous sensing environment

We consider decentralized estimation of a noise-corrupted deterministic parameter by a bandwidth-constrained sensor network with a fusion center. The sensor noises are assumed to be additive, zero mean, spatially uncorrelated, but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment. The classical best linear unbiased estimator (BLUE) linearly combines the real-valued sensor observations to minimize the mean square error (MSE). Unfortunately, such a scheme cannot be implemented in a practical bandwidth-constrained sensor network due to its requirement to transmit real-valued messages. In this paper, we construct a decentralized estimation scheme (DES) where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal-to-noise ratio (SNR). The resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter. The proposed DES is universal in the sense that each sensor compression scheme requires only the knowledge of local SNR, rather than the noise probability distribution functions (pdf), while the final fusion step is also independent of the local noise pdfs. We show that the MSE of the proposed DES is within a constant factor of 25/8 of that achieved by the classical centralized BLUE estimator.