Navigation Algorithms and Observability Analysis for Formation Flying Missions

Navigation algorithms and the corresponding observability analysis for formation flying missions are developed. In particular, the advantages and concerns associated with the use of combinations of inertial and relative measurements are examined. The methodology of the observability analysis relates the physical geometry of the observers, as well as the spacecraft formation, to a measure of linear time-invariant system observability. The investigation also examines the robustness of the extended Kalman filter while simultaneously processing inertial and relative range measurements. It has been shown that processing relative range measurements in conjunction with inertial range measurements can directly increase the accuracy of the inertial state estimate. However, it has also been shown that when there is relatively large uncertainty in the state estimate, the addition of relative measurements can cause an otherwise convergent filter to diverge. This paper considers several methods for preventing this divergence, as well as an in-depth examination of second-order terms to explain the basis of the problem. In particular, to illustrate their potential significance, analytical bounds are derived for the second-order terms.