Concept for a System for Trajectory Estimation and Orbital Drift Detection for Low Thrust Geostationary Satellites

Abstract

This thesis develops an algorithm for detecting orbital drift for low-thrust satellites using electric propulsion systems for orbit raising maneuvers. The use of electricity-based systems as the primary source of propulsion for unmanned spacecraft is an area of great interest due to the potential gains in payload that using high specific impulse (Isp) propulsion could provide. Because of the limit in thrust, research has been done into trajectories that minimize the travel time for orbit raising from a parking orbit to the destination orbit. These maneuvers may take several days to complete depending on the destination orbit, allowing more time for perturbations to cause the satellite to go off course compared to satellites using chemical thrusters. In order to make these trajectories robust, a system to detect and correct orbital drift during the maneuver must be used. This thesis develops the former for a planar orbit maneuver and provides a conceptual framework for the latter. Detecting orbital drift consists of two parts: orbit determination and future trajectory estimation and correction. The dynamics of the system are derived to provide a dynamical model for orbit determination. An Extended Kalman Filter based upon this model of the satellite’s orbit with the planned thrust profile is developed to per-form orbit determination. The precision of the EKF is then tuned by modifying the process noise and measurement noise models until the uncertainty is reduced to the amount of noise in GPS measurements. Using precision GPS, it is possible to deter-mine the orbit with certainty on the order of 10m in position and .1m/s in velocity. Trajectory estimation is carried out by propagating the equations of motion from the current state estimate to the end of the thrust profile. Propagation is done in parallel to running the EKF to simulate a satellite constantly updating the estimate of its final location as it receives new GPS measurements. The evolution of the final state estimate is then examined to determine if it converges to the desired value within estimated uncertainty, which would indicate the satellite is on the correct trajectory. To complement this process, the GPS measurements are also examined to determine if they begin to diverge from the planned trajectory, which would indicate orbital drift. This method is tested by simulating thruster misalignment of 1 degree. A new trajectory is generated with the altered thrust profile and given to the system as GPS measurements, which uses the original thrust profile for propagation. Compared with the expected uncertainty from GPS error, the drift in the trajectory is clearly detectable within the first 20% of the mission time. The next step would be to develop a system for trajectory correction that applies a control law to drive the difference between the projected final state, given by the Many simplifying assumptions were made in this thesis so that the framework for the system could be developed. These assumptions include neglecting drag and gravity errors, modeling process and measurement noise as uncorrelated Gaussian white noises. The effects of relaxing these assumptions are discussed, along with the need for more detailed models of GPS measurements and availability. Extending the dynamical model to three dimensions so more sophisticated maneuvers could be examined would be desirable. Stochastic force determination to account for unmodeled forces is also proposed as an extension of the algorithm developed here.