GPS-based Relative Navigation in Earth Observation Missions Relying on Cooperative Satellites

this paper aims at identifying the best filtering approach to be used in relative orbit scenarios in which baselines can range from hundreds of meters to hundreds of kilometres. Specifically, those filtering approaches capable of providing relative positioning accuracy at the centimetre or millimetre level are investigated. To this end, hybrid approaches relying on the combination of kinematic and dynamic-based filtering schemes and exploiting the integer nature of Double-Difference (DD) CDGPS measurements are investigated and their performances are numerically investigated and compared. Dynamic filtering relies on a nonlinear model of the satellites’ relative orbital dynamics incorporating differential J2 effects. In order to increase the baseline determination accuracy in applications with highly variable baselines (up to hundreds of kilometres) nonlinear dynamic filtering schemes, such as the ones based on the Unscented Transform (UT), are investigated and their performances are compared with the ones of an augmented-state Extended Kalman Filter (i.e. a filter incorporating DD ambiguities in the state vector). The impact of different UT algorithms on the real-time applicability of the Unscented Kalman Filter is specifically evaluated. The analysis is conducted by using a numerical tool, developed in Matlab environment, which implements the GPS constellation, the satellites’ relative orbits, the GPS satellite signals, and the main error sources.