Magnetic-Only Orbit and Attitude Estimation Using the Square-Root Unscented Kalman Filter: Application to the PROBA-2 Spacecraft

In this paper a new technique to estimate simultaneously the orbit and the attitude of a spacecraft based solely on the magnetic field is described. This magnetic-only orbital and attitude estimation scheme uses a Square-Root Unscented Kalman Filter algorithm and is applied to a sun-synchronous low-Earth orbit spacecraft. The resulting software, to be validated in orbit as a flight technology-demonstration experiment on board the European PROBA-2 spacecraft, is validated in this paper using a high-fidelity real-world software simulator. This paper describes the estimation filter algorithm, the dynamic models and the measurement models required to implement the algorithm. The high-fidelity simulator is quickly reviewed and the critical functions (e.g. Earth magnetic field model and magnetometer) are analyzed and described in detail. All model uncertainties are addressed and defined for realistic scenarios relevant to sun-synchronous low-Earth orbits. Next, the computation of the tuning parameters of the estimation filter is detailed for the proposed scenarios and the numerical simulations results are analyzed. Two realistic scenarios are defined for the validation: (A) bias-type errors are assumed calibrated and compensated and (B) a nominal scenario for the PROBA-2 mission in which the biases are only approximately calibrated. The results obtained for the Scenario A demonstrate that the technique can achieve RSS position error of less than 2 km, a RSS attitude error of less than 1.4 degree and a time of convergence of less than 2 orbits. Finally, further improvements, expected to be implemented prior to the PROBA-2 launch, are proposed.