Instant Active Positioning with One LEO Satellite

Autonomous position determination in the Globalstar satellite communication system is discussed. ( ) The two-way communication between a user terminal on the earth’s surface and a single low earth orbit LEO satellite makes it possible to derive range and range-rate and determine the user terminal position instantly. Expected accuracy is presented, and a simple direct solution is given. INTRODUCTION Globalstar 1 is a satellite communication system designed to provide voice and low-rate data Ž . communication to user terminals UTs on the earth. The satellite constellation includes 48 low Ž . earth orbit LEO satellites at a height of 1400 km, arranged in eight orbits with an inclination of 52 deg. The Globalstar satellite acts as a bent-pipe Ž . relay between a regional gateway GW and the UT. The orbit of the satellite is known accurately. Primarily for operational reasons, before a UT phone call is connected, the system needs to know the UT position with a horizontal accuracy of better than 10 km. Connection of the call cannot be delayed for more than about 3 s, and a call should go through even if the UT sees only one Globalstar satellite. Hence there is a need for instant coarse positioning using the system’s own satellite and signals 2 . While two-satellite, two-dimensional Ž . 2-D , active positioning is found in other operational systems 3, 4 , single-satellite instant positioning is unique. This paper therefore concentrates on this aspect of Globalstar positioning. Single-satellite positioning is based on measurements of range and range rate. The range between the satellite and the UT is derived from a round-trip delay measurement, from which the known GW-tosatellite leg is removed. Globalstar uses a code Ž . division multiple access CDMA concept, which utilizes a wideband spread-spectrum signal, as in GPS. Hence the delay measurement resolution is relatively high. Range rate is derived from Doppler measurements. In a passive satellite Doppler naviNAVIGATION: Journal of The Institute of Navigation Vol. 46, No. 2, Summer 1999 Printed in the U.S.A. gation system, such as TRANSIT 5 , the true Doppler cannot be separated from the UT oscillator frequency offset; hence only Doppler differences Ž . rather than absolute Doppler can be measured. Ž . When the UT is active receives and transmits and uses the same master oscillator in its receiver and transmitter, two Doppler measurements one at Ž . the satellite in practice at the GW and one at Ž . the UT and communicated to the GW provide enough information to separate the true Doppler Ž . from the UT frequency offset see Appendix A . This paper derives the expected accuracy of 2-D positioning based on one range and one range-rate measurement to a single satellite. In the third dimension, the UT is assumed to be on the earth’s surface. The horizontal error resulting from an elevation error is also derived. Finally, a simple direct solution is presented that can be used by itself or to provide a first estimate for an iterative positioning algorithm. POSITIONING BASED ON RANGE AND RANGE RATE The positioned UT is located at one of the two Ž . intersections between three surfaces see Figure 1 : Ž . the range sphere, the range-rate Doppler cone, and the earth’s surface. The range sphere is centered at the satellite antenna, which is also where the apex of the cone is located. The cone axis of Ž . symmetry is the velocity vector. Delay range and Ž . Doppler range-rate errors cause an error in the determined UT position. The cross-track positioning error is magnified dramatically when the intersection is near the satellite subtrack on the earth’s surface. An error in the UT assumed height above