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By measuring the nuclear magnetic spin precession frequencies of polarized $^{129}$Xe and $^{3}$He, a new upper limit on the $^{129}$Xe atomic electric dipole moment (EDM) $ d_\mathrm{A} (^{129}\mathrm{Xe})$ was reported in Phys. Rev. Lett. 123, 143003 (2019). Here, we propose a new evaluation method based on global phase fitting (GPF) for analyzing the continuous phase development of the $^{3}$He-$^{129}$Xe comagnetometer signal. The Cramer-Rao Lower Bound on the $^{129}$Xe EDM for the GPF method is theoretically derived and shows the potential benefit of our new approach. The robustness of the GPF method is verified with Monte-Carlo studies. By optimizing the analysis parameters and adding data that could not be analyzed with the former method, we obtain a result of $d_\mathrm{A} (^{129}\mathrm{Xe}) = 1.1 \pm 3.6~\mathrm{(stat)} \pm 2.0~\mathrm{(syst)} \times 10^{-28}~ e~\mathrm{cm}$ in an unblinded analysis. For the systematic uncertainty analyses, we adopted all methods from the aforementioned PRL publication except the comagnetometer phase drift, which can be omitted using the GPF method. The updated null result can be interpreted as a new upper limit of $| d_\mathrm{A} (^{129}\mathrm{Xe}) | < 8.3 \times 10^{-28}~e~\mathrm{cm}$ at the 95\% C.L., Comment: Acknowledgement changed; Format changed and several wordings are modified to avoid potential confusions

We report results of a new technique to measure the electric dipole moment of $^{129}$Xe with $^3$He comagnetometry. Both species are polarized using spin-exchange optical pumping, transferred to a measurement cell, and transported into a magnetically shielded room, where SQUID magnetometers detect free precession in applied electric and magnetic fields. The result from a one week measurement campaign in 2017 and a 2.5 week campaign in 2018, combined with detailed study of systematic effects, is $d_A(^{129}\mathrm{Xe}) = (1.4 \pm 6.6_\mathrm{stat} \pm 2.0_\mathrm{syst})\times10^{-28}~e\,\mathrm{cm}$. This corresponds to an upper limit of $|d_A(^{129}\mathrm{Xe})| < 1.4 \times 10^{-27} ~e\,\mathrm{cm}~(95\%~\mathrm{CL})$, a factor of five more sensitive than the limit set in 2001., Comment: To be published in Physical Review Letters. arXiv admin note: substantial text overlap with arXiv:1902.02864