Minimum energy decentralized estimation in a wireless sensor network with correlated sensor noises

Consider the problem of estimating an unknown parameter by a sensor network with a fusion center (FC). Sensor observations are corrupted by additive noises with an arbitrary spatial correlation. Due to bandwidth and energy limitation, each sensor is only able to transmit a finite number of bits to the FC, while the latter must combine the received bits to estimate the unknown parameter. We require the decentralized estimator to have a mean-squared error (MSB) that is within a constant factor to that of the best linear unbiased estimator (BLUE). We minimize the total sensor transmitted energy by selecting sensor quantization levels using the knowledge of noise covariance matrix while meeting the target MSE requirement. Computer simulations show that our designs can achieve energy savings up to 70% when compared to the uniform quantization strategy whereby each sensor generates the same number of bits, irrespective of the quality of its observation and the condition of its channel to the FC.