Method for the efficient determination of GPS satellite orbital position

摘要

A GPS navigation receiver which calculates the GPS satellites' positions by numerical integration. The GPS receiver of the present invention integrates over eccentric anomaly E as an independent variable rather than time, in order to use an integration method that is exact for sinusoidal motion, since the components of motion and time are sinusoidally related to the eccentric anomaly E. Using eccentric anomaly as an independent variable, the GPS receiver performs Leapfrog integration on a first sample and a second sample to determine a subsequent sample. The subsequent sample is uniformly spaced with respect to eccentric anomaly in comparison to the first sample and the second sample. The Leapfrog integration of the present invention is computationally efficient and exact over longer step sizes.