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A sensor network's motes observe the environment, make estimates based on their observations, and send/relay these estimates to a Cluster-Head (CH). There are two sources of error in these multi-hop networks: observations are corrupted by noise and transmissions suffer communication errors. A novel scheme based on dithered quantization and channel compensation is used to ensure that each mote's local estimate received by the CH is unbiased. The CH fuses these unbiased local estimates into a global one using a Best Linear Unbiased Estimator (BLUE). We determine both the minimum energy required for the network to produce a BLUE estimate with a prescribed error variance and show how this energy should be allocated across the rings of a multi-hop network and the motes in each ring.