Processing of laser altimeter time-of-flight measurements to geodetic coordinates

Laser altimeters are commonly used in planetary research for their high geodetic accuracy. A key procedure in processing of laser altimeter data is the geolocation. In this process, the time-of-flight measurements are converted to coordinates of laser pulse footprints on the surface of the target body. Here, we present a consistent and systematic formulation of three commonly used geolocation models with increasing complexity: static model, spacecraft motion model, pointing aberration model and special relativity model. We show that for small velocities of the spacecraft relative to the target the special relativity model can be reduced to the pointing aberration model without significant loss in the geolocation accuracy. We then discuss the respective accuracies of the proposed models and apply them to time-of-flight measurements from the Mars Orbiter Laser Altimeter (MOLA) onboard the Mars Global Surveyor (MGS) spacecraft and the Mercury Laser Altimeter (MLA) onboard the MErcury Surface, Space ENvironment, GEochemistry and Ranging spacecraft (MESSENGER). While, the archived datasets had not considered the effect of pointing aberration, we demonstrate that a correction due to pointing aberration makes insignificant improvements of 4-5 m laterally and up to +/- 3 cm radially for MOLA profiles, these figures enormously increase to up to about 150 m laterally and +/- 25 m radially when applied to the MLA orbital profiles.