This paper investigates the consensus problem for a team of agents with inconsistent information, which is a core component for many proposed distributed planning schemes. Kalman filtering approaches to the consensus problem have been proposed, and they were shown to converge for strongly connected networks. However, it is demonstrated in this paper that these previous techniques can result in biased estimates that deviate from the centralized solution, if it had been computed. A modification to the basic algorithm is presented to ensure the Kalman filter converges to an unbiased estimate. The proof of convergence for this modified distributed Kalman consensus algorithm to the unbiased estimate is then provided for both static and dynamic communication networks. These results are demonstrated in simulation using several simple examples.