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This paper presents a novel scheme for estimating an unknown deterministic vector in a multi-hop progressive decentralized fashion in a wireless sensor network. Under this scheme, each sensor performs the best linear unbiased estimation of the unknown vector using the data measured by the sensor and the estimations received from its up stream sensors, and the estimation at each sensor is first quantized and then forwarded to its down stream sensor. The final estimation of the unknown vector resides at a fusion center. The number of quantization bits assigned to each sensor is computed offline via an optimization algorithm that minimizes the network transmission energy subject to a pre-determined upper bound on the mean square error of the final estimation at the fusion center. This optimization algorithm utilizes any given routing tree from all sensors to the fusion center. Comparing to the conventional non …