Session P2b: Present and Future Space Clocks for Space Applications

Investigation of NANOGrav 15-year Pulsar Dataset as Natural Oscillators for Space Missions
Vednarayan S. Iyer, Thejesh N. Bandi, Department of Physics and Astronomy, University of Alabama
Location: Seaview A/B
Date/Time: Wednesday, Jan. 29, 11:48 a.m.

Navigation for deep-space missions is presently done by using ESA’s European Space Tracking (ESTRACK) network and NASA’s Deep Space Network (DSN). The spacecraft’s radial position is estimated with an accuracy down to 1 m, however the perpendicular position with reference to the Earth has inaccuracies up to 4 km per astronomical unit [1]. This necessitates specialized ground infrastructure, leading to meticulous operations and elevated expenses. Therefore, for deep space missions, an onboard autonomous PNT determination is valuable.
Pulsars are spinning neutron stars emitting periodic signals – from seconds to milliseconds. The idea of using pulsars for navigation has been around since 1967, when the first pulsar was discovered. In this work, we focus on investigating the radio signals from pulsars for space timekeeping and navigation using the latest 15-years data from NANOGrav [2]. Our approach has three main objectives: 1) analyzing the stability of pulsars for finding the most stable pulsars and comparing them with the current space clocks, 2) estimating the position accuracy based on the pulsar stability, and 3) forming an ensemble of pulsars to study the improvements of timing and positioning accuracies. We start by calculating the timing residuals for 68 pulsars in the dataset using PINT Python library [3]. We use these residuals to calculate the stability of pulsars using the ?_z(?) method [4], and then we compute the range accuracy, ?_R. Further, we use a classical weighing algorithm to build an ensemble of 5 pulsars, which have similar observation duration and data size. In our algorithm, we synchronize the data of these pulsars by using a combination of cubic interpolation and moving average, for estimating a Pulsar Ensemble Time (PET). Recent proposals with renewed interest have focused on the navigation methods utilizing the observation of celestial pulsed X-ray sources, as they require significantly smaller detector size than for radio pulsars [5,6]. We note that the detector parameters and related corrections need to be taken into consideration for an actual implementation in space.
Our preliminary analysis shows the pulsars exhibit stabilities as good as the state-of-the-art space clocks such as DSAC and RAFS over longer averaging times of months and beyond. Stability of these space clocks is at the level of 1e-15 over 50 days, but maintaining the performances (without synchronization) over decades is challenging, for instance considering missions like Voyager, Cassini or the upcoming Europa mission. On the other hand, pulsars are naturally stable over decades and therefore are well suited for long term missions. In our analysis, PSR J1024-0729 showed an astonishingly low ?_z of 1.878e-17 at 10 years of averaging. We estimate position accuracies of less than 100 m for most of the pulsars up to a decade. The resulting PET stability is better than any individual pulsar by an order of magnitude. We further calculated the range accuracy using PET, which resulted in two important conclusions. The range accuracy of PET is at least a factor of two better than the constituent pulsars and the accuracy remained always below 20 m throughout a decade. This means one can effectively use an ensemble of pulsars to mitigate the noises present in individual pulsars, for building a reliable space-based PNT system. Such a solution is valuable for NASA's Artemis program, where one could use PET for developing the Coordinated Lunar Time (LTC), as well as for deep space navigation. The advantage of this method leverages naturally available stable pulsar oscillators.
This work shows promise towards the use of pulsars – the naturally stable oscillators – for precise navigation and timekeeping in space. We conclude that an onboard ensemble with a combination of atomic clocks and pulsar signals would provide a long-term, reliable and robust PNT system that can serve space missions (by using X-Ray signals) and novel ground missions (by using radio signals) for several decades.
[1] Yidi, W., Zheng, W., Zhang, S., Minyu, G., Liansheng, L., Jiang, K., Xiaoqian, C., Zhang, X., Zheng, S., & Fangjun, L. (2023). Review of x-ray pulsar spacecraft autonomous navigation. Chinese Journal of Aeronautics, 36(10), 44–63.
[2] Agazie, G., Alam, M. F.,., . . . Nanograv Collaboration. (2023). The NANOGrav 15 yr Data Set: Observations and Timing of 68 Millisecond Pulsars., 951(1), Article L9, L9.
[3] Luo, J., Ransom, S., Demorest, P., Ray, F. (2021). Pint: A modern software package for pulsar timing. The Astrophysical Journal, 911, 45.
[4] Matsakis, D., Taylor, J., & Eubanks, M. (1997). A statistic for describing pulsar and clock stabilities. Astronomy and Astrophysics,326, 924–928.
[5] Lohan, K., & Putnam, Z. (2022). Characterization of candidate solutions for x-ray pulsar navigation. IEEE Transactions on Aerospace and Electronic Systems
[6] Chester, T., & Butman, S. (1981). Navigation using x-ray pulsars. The telecommunication and data acquisition report, 22–25