Monte Carlo Simulation of Precise Timekeeping in Elliptical Orbits

Nathan P. Wells

Abstract:	We describe a Monte Carlo simulation of precise timekeeping for oscillators in highly elliptical orbits. Relativistic effects, including gravitational red shift, time dilation, and Sagnac effect are included. A numerical model generates clock noise using a discrete Fast Fourier Transform (FFT) technique that allows a range of clocks to be modeled by summing terms with a spectral density of f??for arbitrary values of ???We include models of high quality crystal oscillators, rubidium atomic frequency standards (RAFS), and Cs clocks. Linear frequency drift and periodic thermal effects are also included. The time error of the clock is obtained via integration of the frequency noise. Additionally, time transfer noise and bias are included. A two state Kalman filter is implemented to assess the current state of the clock’s time and frequency offsets. Due to the non-constant relativistic frequency shifts, a periodic oscillation in the time and frequency error is observed. We discuss the impact of the periodic relativistic disturbance on the time keeping system The simulation is capable of running 10,000 simulations of 20 days of operation (equivalent to 548 years) on a six core workstation in 15 minutes using shared memory parallel computing. This efficiency allows multiple scenarios to be investigated rapidly and include statistical distributions with probabilities at the 3 sigma level. We demonstrate that under a concept of operations where measurements are made over a seven hour window followed by five hour non-measurement period, an update-on-demand time and frequency management algorithm is able to demonstrate sub 50 ?s time keeping at a 3 sigma level for a crystal oscillator. This level of timekeeping is perfectly adequate for many satellite communications issues. We also quantify the workload of a ground station by computing the probability distribution of time between updates.
Published in:	Proceedings of the 47th Annual Precise Time and Time Interval Systems and Applications Meeting January 25 - 28, 2016 Hyatt Regency Monterey Monterey, California
Pages:	212 - 217
Cite this article:	Wells, Nathan P., "Monte Carlo Simulation of Precise Timekeeping in Elliptical Orbits," Proceedings of the 47th Annual Precise Time and Time Interval Systems and Applications Meeting, Monterey, California, January 2016, pp. 212-217. https://doi.org/10.33012/2016.13166
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