The consensus extended Kalman filter is employed for the problem of multiple chief spacecraft cooperatively estimating the orbit of one deputy spacecraft in a connected communication network. The numerical results show that use of the consensus estimation strategy can improve the convergence performance of the filter and increase the system observability by excluding ambiguous orbits associated with angles-only and range-only measurements. The benefits of faster convergence and consensus speed by using communication networks with more connections are also illustrated. The improvements on system observability are further validated by the analytical observability criteria using Lie derivatives. The conditions for the ambiguous orbits to persist in the presence of consensus feedback are obtained for range-only measurements and verified by illustrative numerical examples. Finally, the numerical observability measures, observability Gramian and associated observability index and condition number are used to numerically illustrate the advantages of the proposed consensus estimation strategy.