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We consider the distributed state estimation of a linear dynamic system, observed by various sensors, as a problem in information fusion. We introduce a novel model of trust, using weights on the graph links and nodes that represent the sensor network. These weights can represent several interpretations of trustworthiness in sensor networks. We describe two algorithms that integrate distributed Kalman filtering with these trust weights. We consider two interpretations of these trust weights as information accuracy and reliability. We show that by appropriate use of these weights the distributed estimation algorithm avoids using information from untrusted sensors. Simulation experiments further demonstrate the behavior of these algorithms.