Clock Ensembling to Mitigate GNSS Atomic Clock Frequency Jumps

Abstract

Recent results suggest that the long-term frequency instability of high-quality rubidium (Rb) atomic frequency standards (RAFS), like those flying on GPS, Galileo, and BeiDou satellites, is driven by jumps in the lamplight intensity of the RAFS [1]. Briefly, in the device a Rb rf-discharge lamp generates light that is used to create the atomic-clock signal and to produce the correction signal that stabilizes the frequency of the RAFS’ crystal oscillator [2]. Unfortunately, due to the light-shift effect [3], any lamplight jumps will be mapped onto the atomic clock’s frequency, and this has been observed on GPS satellites [1,4]. Moreover, Valerio et al. [5] have shown that these frequency jumps lead to long-term frequency instability that mimics “normal” (Wiener process) random-walk behavior as assessed through the Allan deviation (ADEV). Since long-term frequency instability drives the clock’s contribution to the GNSS signal-in-space user-range-error (SIS-URE), mitigating RAFS frequency jumps would have immediate benefit to GNSS. Here, we consider clock ensembling as a means to mitigate this type of random process. For a continuous-time Wiener process (e.g., clock frequency noise with a power spectrum that scales like 1/f2, with f the Fourier frequency), ensembling with N clocks reduces the ensemble’s random-walk ADEV by . Discrete frequency jumps, however, are handled differently with ensembling. Specifically, in the simplest ensembling case (i.e., equal-weight phase averaging) a frequency jump for a single ensemble member appears in the ensemble timescale as a frequency jump reduced in size by 1/N. Thus, when jumps cause random-walk behavior in the ADEV of individual ensemble members, and when these jumps are uncorrelated between clocks, we might expect the ensemble ADEV to be reduced by 1/N as opposed to the expected . This would not only provides means for distinguishing the cause of random-walk behavior (i.e., jump driven random-walk ADEV vs. Wiener-process driven random-walk ADEV), it would suggest that ensembling could prove effective as a means for significantly reducing the clock’s contribution to the GNSS SIS-URE. In what follows, we will first discuss the origin of light-shift induced jumps in GNSS RAFS, and their role in limiting the GNSS SIS-URE. We will then discuss our Monte Carlo simulation of RAFS suffering lamplight-induced frequency jumps. We conclude by showing that a simple ensembling of GNSS RAFS (i.e., equal-weight averaging of the RAFS’ phase) leads to a reduction in random-walk ADEV that (for time intervals not too much longer than the mean time between jumps) an ensemble timescale ADEV that is improved by more than what a scaling would suggest.