A peer-to-peer estimator computes local estimates at each node by combining the information from neighboring nodes without the need of central coordination. Although more flexible and scalable, peer-to-peer minimum variance estimators are difficult to design because of message losses and lack of network coordination. In this paper, we propose a new peer-to-peer estimator that allows to recover a time-varying scalar signal from measurements corrupted by an unknown non-zero mean independent noise or disturbances. Message losses occurring over the network and absence of central coordination are considered. Novel theoretical solutions are developed by taking advantage of a model of the signal dynamics. The proposed approach simultaneously guarantees a bounded mean value and minimum variance of the estimation error. Simulation results illustrate the performance of the proposed method.