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An Investigation of Linear Estimation Models for Satellite Relative Motion Master of Science Thesis Defense

The problem of relative spacecraft motion estimation is considered with application to various reference and relative orbits. Mean circular and mean elliptic orbits are analyzed, with relative orbits ranging in size from 1 km to 10 km. Estimators are built for three propagation models: (i) Gim-Alfriend State Transition Matrix, (ii) the J2-Linearized Equations of Motion for Circular Orbits, and (iii) the Clohessy-Wiltshire Equations of Motion. Two estimation techniques are presented in an attempt to explore and determine which propagation model minimizes the error residual: the linear Kalman filter is presented under the assumption of vector based, GPS-type measurements; the extend Kalman filter is analyzed assuming angle-range, optical-type measurements. Sampling time is varied to look at the effect of sensor precision and accuracy. It is assumed that the orbit of one of the satellites, the chief, is known reasonably well. This work showed that the GA-STM is the most accurate propagation tool for any of the orbits analyzed. However, there are situations in which the CW propagation and the linear equations for circular motion provide a reasonable estimate for the relative position and velocity. The addition of a linear drift term to the CW equations improves their accuracy; however, their performance is still weak in comparison to the GA-STM. Analysis of larger relative orbits shows the introduction of errors in the radial velocity. Finally, it was shown that as the frequency of the measurement updates increases, the accuracy of the propagation model is less important.