An earthmoving system including a bulldozer has a pair of GPS receivers mounted on the cutting blade of the bulldozer. The cutting blade is supported by a blade support extending from the frame. The blade support includes a pair of hydraulic cylinders for raising and lowering the blade in relation to the frame and a blade tilt cylinder for controlling the lateral tilt of the cutting blade. Sensors, including gyroscopic sensors and an accelerometer, sense rotation of the frame about three orthogonal axes and vertical movement of the bulldozer frame that would affect the position of the blade. A control is responsive to the pair of GPS receivers and to the gyroscopic sensors, for controlling the operation of the hydraulic cylinders and thereby the position of the cutting blade. The control monitors the position of the cutting blade with repeated calculations based on the outputs of the GPS receivers and with low-latency feed-forward correction of these repeated calculations, based on the outputs of the gyroscopic sensors and the accelerometer.