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We used Precise Point Positioning, a well-established GPS carrier-phasefrequency transfer method to perform a direct remote comparison of two opticalfrequency standards based on single laser-cooled $^{171}$Yb$^+$ ions operatedat NPL, UK and PTB, Germany. At both institutes an active hydrogen maser servesas a flywheel oscillator; it is connected to a GPS receiver as an externalfrequency reference and compared simultaneously to a realization of theunperturbed frequency of the ${{}^2S_{1/2}(F=0)-{}^2D_{3/2}(F=2)}$ electricquadrupole transition in ${}^{171}$Yb${}^+$ via an optical femtosecondfrequency comb. To profit from long coherent GPS link measurements weextrapolate over the various data gaps in the optical clock to masercomparisons which introduces maser noise to the frequency comparison butimproves the uncertainty from the GPS link. We determined the total statisticaluncertainty consisting of the GPS link uncertainty and the extrapolationuncertainties for several extrapolation schemes. Using the extrapolation schemewith the smallest combined uncertainty, we find a fractional frequencydifference $y(\mathrm{PTB})-y(\mathrm{NPL})$ of $-1.3(1.2)\times 10^{-15}$ fora total measurement time of 67 h. This result is consistent with an agreementof both optical clocks and with recent absolute frequency measurements againstcaesium fountain clocks.

Frequency comparison of ${}^{171}$Yb${}^+$ ion optical clocks at PTB and NPL via GPS PPP