The paper considers the sensor network whose sensors observe a common quantity and are affected by arbitrary additive bounded noises with a known upper bound. During the experiment, any sensor can communicate only a finite and given number of bits of information to the decision center. The contributions of the particular sensors, the rules of data encoding, decoding, and fusion, as well as the estimation scheme should be designed to achieve the best overall performance in estimation of the observed quantity by the decision center. The optimal algorithm is obtained that minimizes the maximal feasible error. It is shown that it considerably over-performs a 'natural' algorithm proposed in recent papers in the area and examined only in the idealized case of noiseless sensors. This analysis highlights the need for special decentralized data encoding rules that are robust against the sensor noises in the context of networked cooperative observation. Such a rule is the core of the proposed optimal algorithm.