Theoretically there is no sensor that is currently available in any phone that could measure absolute height/altitude to the degree you're asking (less than +/- 0.2 meters). Most likely candidates:
-GPS has error range of about 3m
-Barometer measurements are relative to sea level and doubtful consumer grade e-barometers have anywhere near the level of sensitivity needed
You could measure relative distance however, if user were to say, drop his phone on the ground. The Accelerometer could be used to calculate the distance using some approximation of g = 9.8 m/s²