Decentralized estimation in an inhomogeneous environment

We consider the decentralized estimation of a noise-corrupted deterministic parameter by a bandwidth constrained sensor network with a fusion center. 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 the local sensor compression schemes and final fusion function are independent of noise pdf. We show that its mean squared error is within a constant factor to that achieved by the classical centralized best linear unbiased estimator (BLUE).