Autonomous satellite navigation by stellar refraction

Abstract

This paper describes the error analysis of an autonomous navigator using refraction measurements of starlight passing through the upper atmosphere. The analysis is based on a discrete linear Kalman filter. The filter generated steady-state values of navigator performance for a variety of test cases. Results of these simulations show that in low-Earth orbit position-error standard deviations of less than 0.100 km may be obtained using only 40 star sightings per orbit. N autonomous navigation system is a satellite subsystem designed to estimate the spacecraft's current position and velocity without assistance from ground tracking. Such systems can detect deviations'from a desired trajectory and thus enable satellites to initiate their own orbital corrections. The real-time acquisition of satellite position may also assist the performance of other mission functions. With these capabilities incorporated within £ satellite its users can benefit from lower maintenance costs and assured mission continuity should terrestrial tracking or communication be interrupted for extended periods.1'2 ; ' Many autonomous navigation schemes, drawing from a wide range of methodologies , have been proposed and a few implemented. One important glass of navigators uses angular measurements between the sun or fixed stars and the limb of the Earth to update satellite;,position. Although, in concept, systems of this type are simple, their accuracy and utility have been limited by the difficulty of sensing the Earth's horizon precisely. The horizon, viewed from orbit, appears as diffuse atmospheric bands gradually blending into the darkness of space; the edge of the Earth's surface is completely obscured. Consequently, limb-sensing navigators are presented with an inherently ill-defined target with which to chart the satellite's course.3 It is proposed that an'autonomous navigation system use measurements of refracted starlight to sense the depth of the interposing atmosphere. The problem of directly detecting the Earth's horizon is circumvented by using stellar observations and knowledge of the optical properties of the*atmospher e to infer the location of the Earth's surface. The method is simple and, because it utilizes multiple-star observations, provides inputs for autonomous attitude determination. The passage of starlight through the Earth's atmosphere bends the rays inward (see Fig. 1).Viewed from orbit, % setting star's image persists along the Earth's limb well after its true position has passed below the horizon. This refractiofi is greatest near the Earth's surface and grows progressively weaker at higher altitudes. The starlight refraction angle, /?, may be expressed