An asphalt milling machine control is provided for an asphalt milling machine of the type which mills an asphalt pavement surface over which the machine travels. The machine has a milling machine body, and a rotatable milling drum mounted on the lower portion of the milling machine body, the bottom surface of the milling drum contacting the asphalt pavement surface to mill the surface to a design elevation. The machine further includes a plurality of machine body supports which are adjusted to raise or lower the height of the milling machine body and the rotatable milling drum with respect to the asphalt pavement surface. This defines the elevation of the surface that results from milling with the drum. The control includes a floating plate, mounted to the side of the milling machine and the rotatable milling drum, or a pair of floating plates mounted to either side of the machine, for sliding over the surface adjacent to the area to be milled. The floating plates have associated sensors and are vertically movable with respect to the machine body and the rotatable milling drum. The control includes a GNSS receiver on the machine body for determining the two dimensional coordinates of the floating plate or plates. The control includes a memory which stores a map of the unmilled asphalt pavement surface, and data defining a desired design surface. The control includes a sensor for detecting the relative vertical position of the floating plate with respect to the machine body and an inclinometer. Finally, the control includes a processor, responsive to the GNSS receiver, the inclinometer, and the sensors. Cross checking of various measurements may be made to determine error conditions.