Limits on gravitational Einstein Equivalence Principle violation from monitoring atomic clock frequencies during a year

Sun's gravitation potential at earth varies during a year due to varying Earth-Sun distance. Comparing the results of very accurate measurements of atomic clock transitions performed at different time in the year allows us to study the dependence of the atomic frequencies on the gravitational potential. We examine the measurement data for the ratio of the frequencies in Hg$^+$ and Al$^+$ clock transitions and absolute frequency measurements (with respect to caesium frequency standard) for Dy, Sr, H, hyperfine transitions in Rb and H, and obtain significantly improved limits on the values of the gravity related parameter of the Einstein Equivalence Principle violating term in the Standard Model Extension Hamiltonian $c_{00} = (3.0 \pm 5.7) \times 10^{-7}$ and the parameter for the gravity-related variation of the fine structure constant $\kappa_{\alpha} = (-5.3 \pm 10) \times 10^{-8}$.