This study presents a precise relative navigation algorithm using both laser and Global Positioning System (GPS) measurements in real time. The measurement model of the navigation algorithm between two spacecraft is comprised of relative distances measured by laser instruments and single differences of GPS pseudo-range measurements in spherical coordinates. Based on the measurement model, the Extended Kalman Filter (EKF) is applied to smooth the pseudo-range measurements and to obtain the relative navigation solution. While the navigation algorithm using only laser measurements might become inaccurate because of the limited accuracy of spacecraft attitude estimation when the distance between spacecraft is rather large, the proposed approach is able to provide an accurate solution even in such cases by employing the smoothed GPS pseudo-range measurements. Numerical simulations demonstrate that the errors of the proposed algorithm are reduced by more than about 12% compared to those of an algorithm using only laser measurements, as the accuracy of angular measurements is greater than 0.001° at relative distances greater than 30 km.

This work presents fuel-optimal altitude maintenance of Low-Earth-Orbit (LEO) spacecrafts experiencing non-negligible air drag and J2 perturbation. A pseudospectral (direct) method is first applied to roughly estimate an optimal fuel consumption strategy, which is employed as an initial guess to precisely determine itself. Based on the physical specifications of KOrea Multi-Purpose SATellite-2 (KOMPSAT-2), a Korean artificial satellite, numerical simulations show that a satellite ascends with full thrust at the early stage of the maneuver period and then descends with null thrust. While the thrust profile is presumably bang-off, it is difficult to precisely determine the switching time by using a pseudospectral method only. This is expected, since the optimal switching epoch does not coincide with one of the collocation points prescribed by the pseudospectral method, in general. As an attempt to precisely determine the switching time and the associated optimal thrust history, a shooting (indirect) method is then employed with the initial guess being obtained through the pseudospectral method. This hybrid process allows the determination of the optimal fuel consumption for LEO spacecrafts and their thrust profiles efficiently and precisely.