Interpolation schemes for orbit determination with the global positioning system

This paper demonstrates that the Global Positioning System (GPS) and simple interpolation schemes can be utilized to satisfy typical orbit determination demands of applications satellites. The complete GPS consists of 24 satellites and permits a position fix of a user satellite at any arbitrary instant. The interpolation formulae used in this report fit generalized Keplerian orbits through a number of position fixes. For a given accuracy level the telemetry requirements as measured by the time intervals between position fixes and the computational load of an interpolation as measured by the number of points through which a generalized Keplerian orbit is fitted vary inversely. A set of possible compromises between these two factors is presented. The Phase I GPS consists of 6 satellites and permits a position fix of a user satellite just 36% of the time. It is shown that with this system more sophisticated interpolation schemes which model atmospheric drag and higher degree terms of the earth's gravity field must be employed to obtain accurate orbits.