Relative semimajor axis estimation using augmented GPS navigation for HEO formation

This paper deals with the investigation of the impact of relative navigation error on relative semimajor axis (SMA) estimation for formation flying of spacecraft in high earth orbit (HEO). The use of carrier-phase/code-phase differential Global Positioning System(GPS) measurements in relative navigation filters is analyzed, with a particular augmentation of crosslink range measurement when no visible GPS satellites occurs in HEO. Two types of relative navigation filter design are proposed for relative SMA estimation analysis: one uses relative position and velocity information and chief radius/true anomaly knowledge while the other one uses reduced states. Although relative semimajor axis error is dependent on all of the coplanar position and velocity uncertainties in highly eccentric orbits, analytical methods and numerical simulations show that the typical HEO Kalman filter seldom satisfies correlation and balance requirements. Moreover, relative SMA uncertainty for HEO formation was more sensitive to radial position and intrack velocity error than that of the near-circular reference orbit according to numerical analysis. Orbit eccentricity has a large impact on the relative SMA estimation error. Kalman filters using reduced states have little effect on relative SMA uncertainty. A HEO formation with real orbit perturbations was analyzed and adaptive two-sensor tracking algorithm was proposed for integrated GPS/crosslink measurement. The combination of these simulations and analysis provides new insights concerning the relative navigation performance in determining relative SMA knowledge for HEO formation missions.