Orbit determination error analysis and station-keeping for libration point trajectories
Abstract
In the elliptic restricted three-body problem (ER3BP), the two primary masses are assumed to be in known elliptic orbits about their common center of mass. The third (infinitesimal) mass may be positioned near one of the five known Lagrange points located in the coordinate system rotating with the primaries. The bounded motion of the infinitesimal mass relative to a Lagrange point can then be computed. In particular, for the Sun$-$Earth+Moon three-body system (where the Earth+Moon barycenter is treated as one primary mass), orbits in the vicinity of the Lagrange point L$\sb1$ between the Sun and the Earth are ideal for the study of solar-terrestrial interactions. A quasi-periodic "Lissajous" trajectory and a much larger, nearly periodic "halo-type" orbit are used in this effort as nominal paths near L$\sb1$ in the Sun$-$Earth+Moon ER3BP. Trajectory determination for a spacecraft that moves under the influence of the two-body system of forces will be affected by many error sources, including tracking errors and modeling uncertainty. Orbit determination error analysis seeks to quantify the impact of these errors. Covariance analysis is a method of error analysis used in this effort to predict state vector error levels. After a predetermined tracking period, using a selected range and range-rate tracking schedule, specific covariance matrix entries are used to compute standard deviations for each of the six states. The results of error analysis using the Kalman and batch weighted least squares filters are compared, and consider covariance analysis is used to incorporate additional error sources, such as solar radiation pressure uncertainty. The means and the probability distributions of these state errors are tested using statistical hypothesis tests and goodness of fit tests, respectively. The state error levels are then used in Monte Carlo simulations of three station-keeping methods--two delta-velocity controllers and an on/off controller developed from a state feedback algorithm. The total control cost from a single station-keeping simulation is a random variable, and a group of 30 such simulations is used as a random sample. Station-keeping costs for a spacecraft near Lissajous and halo-type nominal paths are then compared using statistical hypothesis tests.
Degree
Ph.D.
Advisors
Howell, Purdue University.
Subject Area
Aerospace materials|Mechanics|Mathematics
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