Precise long-range kinematic GPS positioning requires the use of carrier phase measurements, the data processing of which suffers from the technical challenges of ambiguity resolution and cycle slip repair. In this paper, the combination of an ambiguity recovery technique and a linear bias correction method has been used to overcome such problems. An experiment was conducted to test the utility of this technique to determine aircraft height to high accuracy, over very long baselines (of the order of one thousand kilometres), in support of the Laser Airborne Depth Sounder (LADS). From a comparison of four independently derived trajectories, this airborne GPS kinematic positioning experiment has confirmed that the sea surface can be determined to centimetre accuracy. The sea surface profiles thus obtained can be used to correct the errors introduced by long period ocean swells.