Improved Earth Sensor Performance Using a Sequentially Correlated Noise Model

Spacecraft attitude estimation by means of an extended Kalman filter requires a reasonably true model of the inherent noise of each sensor. For some sensors, the largest uncorrected noise comes not from the sensor itself, but from errors in the model for the predicted observations. This is certainly the case for Earth horizon sensors. The Earth horizon as seen from low Earth orbit is nearly a circle whose radius depends primarily on altitude. A straightforward latitude-dependent correction is added to this to account for the oblateness of the Earth. There also are both seasonal and stochastic variations in the horizon height. The seasonal variations can be predicted to some limited degree based on models derived from historical data. The stochastic component characteristically shows variations that are correlated both in time and space but which are unpredictable over long time spans. This work investigates whether Earth horizon sensor performance can be improved by solving for its systematic error as an augmentation of an attitude Kalman filter. It is found that using only Earth and Sun sensors, the augmented state is not fully observable. Even when magnetometer data is included, only the pitch axis component of the error can be improved; the roll component is unobservable.