The effect of introducing continuity conditions in the constrained sinusoidal crossover adjustment method to reduce satellite orbit errors

The constrained sinusoidal crossover adjustment method [Tai, 1988] is one of the most efficient and frequently used method to remove the orbit error in satellite altimetry. In this method, the orbit error for each different satellite revolution is represented by a different sine wave, with wavelength equal to the circumference of the earth. One drawback of this method is that the orbit error function is theoretically not forced to be continuous between every two successive revolutions. In this short note, we study the effect of introducing rigorous continuity conditions between every two successive revolutions, and constraints to avoid an offset from a probable variation datum level. To achieve the continuity, the orbit error for each revolution is modelled as a temporal function composed of a sinusoidal function and a second‐order polynomial. Examples using ERS‐1 data show that for local studies, when one demands the geoid height in the neighbourhood of the junction between every two successive cycles, it is recommended to fulfill the continuity conditions. Otherwise, the simple constrained sinusoidal crossover adjustment method must be preferred.