Performance Bounds for the Rate-Constrained Universal Decentralized Estimators

We consider decentralized estimation of a noise-corrupted deterministic parameter using a bandwidth-constrained sensor network with a fusion center (FC). Each sensor´s noise is additive, zero mean, and independent across sensors. A decentralized estimator is said to be universal if the local sensor quantization rules and the final fusion rule at the FC are independent of sensor noise pdf. Assuming that information rate from each sensor to the FC is constrained to one bit per sample, we derive a Crameacuter-Rao lower bound (CRLB) on the mean-squared error (MSE) performance of a class of rate-constrained universal decentralized estimators. Our results show that if sensor observation noise has finite range in [-U,U], then the minimum MSE performance of any one-bit rate-constrained universal decentralized estimator is at least U²/(4K), where K is the total number sensors. This bound implies that the recently proposed universal decentralized estimators are optimal up to a constant factor of 4