A Study on Along-Track and Cross-Track Noise of Altimetry Data by Maximum Likelihood: Mars Orbiter Laser Altimetry (Mola) Example

Abstract The work investigates the spatial correlation of the data collected along orbital tracks of Mars Orbiter Laser Altimeter (MOLA) with a special focus on the noise variance problem in the covariance matrix. The problem of different correlation parameters in along-track and crosstrack directions of orbital or profile data is still under discussion in relation to Least Squares Collocation (LSC). Different spacing in along-track and transverse directions and anisotropy problem are frequently considered in the context of this kind of data. Therefore the problem is analyzed in this work, using MOLA data samples. The analysis in this paper is focused on a priori errors that correspond to the white noise present in the data and is performed by maximum likelihood (ML) estimation in two, perpendicular directions. Additionally, correlation lengths of assumed planar covariance model are determined by ML and by fitting it into the empirical covariance function (ECF). All estimates considered together confirm substantial influence of different data resolution in along-track and transverse directions on the covariance parameters.