GPS code tracking in high altitude orbiting receivers

摘要

There is interest in the application of the GPS for navigation of satellites with altitudes greater than that of the GPS constellation itself. Candidate missions include geostationary (GEO) and High Earth Orbit (HEO) satellites, particularly those with large eccentricities. The challenges for HEO missions are the reduced power of the GPS signal at apogee and the large differences in line of sight dynamics between apogee and perigee. In this paper, design studies of the Delay Lock Loop (DLL) were performed to determine the closed loop bandwidth and the predetection integration time as a function of orbit position, allowing the tracking loops to adapt to expected signal strength and dynamic conditions. Approximations for the tracking threshold, based on discriminator error variance and steady state dynamic error were used to assess the number of satellites for which tracking was possible at specific receiver orbital positions. Tracking required that the error remain within the linear regime of the discriminator. Loops designed with these thresholds were then simulated using a Monte Carlo approach. These simulations used a nonlinear model for the early minus late discriminator function, a loop filter producing a second order closed loop transfer function, and simulated thermal noise. Line of sight dynamics were approximated as constant acceleration during tracking. Measurements of the time it takes the loop to diverge were computed for the simulated "path" of each satellite in view. Satellite visibility statistics were generated by averaging results over independent simulations computed for a range of GPS constellation epochs. Results of the Monte Carlo simulations are presented for the apogees of the Magnetospheric Multi-Scale (MMS) mission. Demodulation of the 50 bps data message (which requires a carrier lock) is not considered in these simulations. Several techniques for obtaining current ephemerides, without requiring this demodulation, are outlined. Analytical models based upon the integration of stochastic differential equations are presented, and the application of these models to the tracking and acquisition problem is examined.