A sigma-point batch filter for spacecraft orbit estimation using the geomagnetic field measurements

This paper presents spacecraft orbit estimation using only the geomagnetic field measurement via a batch processor based on the unscented transformation. Orbit estimation is performed for different inclinations and observation spans. Truth model based tests show that the magnetometer-based orbit determination has a dependency on the orbital inclination; i.e., on the gradient of the geomagnetic field. This is the main reason of the dominant cross-track error in a polar orbit and the along-track for an equatorial orbit. This phenomenon is mainly caused by the dipole property of the geomagnetic field. Additionally, the proposed unscented batch filter is compared with the Bayesian batch filter to investigate the filter's performance. The comparison results show that the unscented batch filter has strength in convergence speed over the Bayesian filter. The proposed algorithm is evaluated using the real magnetometer data of the CHAMP. The achieved position accuracies are similar in the both filters; i.e., approximately 1-2 km depending on the magnetometer noise level. However, the unscented batch filter can estimate the orbit more rapidly than the Bayesian filter when nonlinearity is strengthened. It shows the unscented batch filter has strength beyond that of the Bayesian one in highly nonlinear situations.