Space-based relative orbit estimation using information sharing and the consensus Kalman filter

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 improvements on system observability by using consensus estimation are shown by the analytical observability criteria using Lie derivatives for the case of angles-only measurements. The conditions for the ambiguous orbits to persist in the presence of consensus feedback are obtained for range-only measurements. Through numerical results, it is shown 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 effects of periodic link failures are studied through multiple numerical examples. Finally, the numerical observability measures, observability Gramian, and associated observability index and condition number are used to verify the advantages of the proposed consensus estimation strategy.