Constancy of any signal velocity in all inertial frames

If isotropy of space and homogeneity of space and time are the valid laws of nature then one can show that velocity of any signal (whether it is light in a vacuum or in a medium or something having constant velocity in the rest frame of the observer and by using which we can perform all (but not partial) measurements of all physical quantities related with the particular experiment) is constant in all inertial frames. To verify this constancy for other signals apart from light in vacuum (which is well-known) we have proposed particularly one experiment in which all measurements can be done using light in water as signal. If we perform experiment in a medium then the signal connecting the measurements of an event in two inertial frames can not be light in vacuum rather it is light in the medium. In such cases where signal used for measurement is not light in vacuum, relativistic relationships of various physical quantities in Special Theory of Relativity (in which light in vacuum has been used as signal) require modifications. This work might be verified from the analysis related with the number of cosmic muons reaching earth through atmosphere or that related with the amount of oscillation of atmospheric neutrinos as in both these cases signal for our measurement can not be light in vacuum but it is light in air.