  We report on a new test of the gravitational redshift and thus of local
position invariance, an integral part of the Einstein equivalence principle,
which is the foundation of general relativity and all metric theories of
gravitation. We use data spanning 1008 days from two satellites of Galileo,
Europe's global satellite navigation system (GNSS), which were launched in
2014, but accidentally delivered on elliptic rather than circular orbits. The
resulting modulation of the gravitational redshift of the onboard atomic clocks
allows the redshift determination with high accuracy. Additionally specific
laser ranging campaigns to the two satellites have enabled a good estimation of
systematic effects related to orbit uncertainties. Together with a careful
conservative modelling and control of other systematic effects we measure the
fractional deviation of the gravitational redshift from the prediction by
general relativity to be $(+0.19 \pm 2.48)\times10^{-5}$ at 1 sigma, improving
the best previous test by a factor~5.6. To our knowledge, this represents the
first reported improvement on one of the longest standing results in
experimental gravitation, the Gravity Probe A hydrogen maser rocket experiment
back in 1976.

General Relativity and Quantum Cosmology