A geometric approach to Low Earth Orbiter (LEO) precision orbit determination (POD) based exclusively on triple-differenced GPS carrier phase observables is presented. The algorithm is fast and efficient because there is no ambiguity-resolution requirement, which is a complicated and time-consuming task for long-range kinematic GPS. However, the triple-difference kinematic LEO POD requires careful screening for cycle slips, as the orbit quality depends on the accuracy and the geometry of the observations. It is shown that the signal-to-noise-ratio (SNR) combined with residual screening offers a good approach to data cleaning. Data from a CHAMP (Challenging Minisatellite Payload, altitude ~450 km) mission are used to present the accuracy, speed and efficiency of the processing algorithms. The methods of data screening and the effects of geometry on the orbit quality are discussed and the final achievable accuracy including the limitations and benefits of this method are quantified. It is demonstrated that the triple-difference method offers short processing times and is currently capable of achieving a 3D RMS fit to the dynamic orbit of 15–30 cm and 1 mm/s to the velocity.