Evaluation of improved solutions for MOLA laser altimeter profiles based on HRSC and Evolution Strategy, and prospects for joint data analysis and data products
Authors: Gwinner Klaus , Willner Konrad , Stark Alexander , Elgner Stephan , Hussmann Hauke 
Published: July 2024

Introduction: The laser altimeter data of Mars Global Surveyors (MGS) Mars Orbiter Laser Altimeter (MOLA) [1] instrument provide a global network of laser shots with high height precision for planet Mars. In practice, the global data products derived from these data have largely replaced the use of the VIKING-based global ground control point network [2] as a main geometric reference for Mars cartography. The determination of planetary radii (i.e. 3D coordinates of points at the surface), requires knowledge of spacecraft trajectory and the instrument&#8217;s orientation in space that is often limited, leading to inconsistencies between the nominal ground profiles obtained, as is observed in the original (not adjusted) MOLA mission data record at cross-over points. In general, the horizontal coordinates of MOLA footprints are estimated as about 100 m, while vertical accuracy is on the scale of few meters and below. Occasionally, substantially offset outlier profiles are found. In the final mission data products such discrepancies are reduced by applying adjustment techniques to minimize cross-over residuals [3]. Also, outlier tracks have been partially removed for the production of the gridded MEGDR data product, but when compared to digital terrain models (DTM) of similar resolution such as HRSC Mars quadrangle DTMs [4], single MOLA tracks still show considerable variability in terms of height differences.Being based on an areally extended measurement principle, the near-global coverage of High Resolution Stereo Camera (HRSC) images is an obvious complement to MOLA profile data. HRSC on ESA&#8217;s MarsExpress (MEX) [5] spacecraft with its capabilities for multi-stereo and simultaneous stereo observations provides a unique data set to derive a global Mars DTM through stereo photogrammetry [4], at improved spatial resolution. While the HRSC DEM is already co-registered with the MOLA DEM through a photogrammetric bundle adjustment using MOLA height control, HRSC&#8217;s higher spatial resolution and the laterally continuous height information can also be exploited for improving the 3D accuracy of MOLA profiles by co-registration techniques. A new adjustment technique based on Evolution Strategy (ES) optimization [6,7] has been tested succesfully for this purpose [8].&#160;Methods: In this contribution, we report on and discuss the setup, performance and validation of ES adjustment for the area of the HRSC DEM used as a reference, but also beyond, i.e. when applying the locally-derived adjustment results to a hemispheric extent of the laser tracks. The ES method allows to derive improvements to the extrinsic observation parameters (orbit position and instrument pointing) and therefore allows for more complex, physically-based adjustment results than previous co-registration approaches relying on rigid geometric transformation in object space only.Using ES, we minimize the height residuals between the HRSC and MOLA DEMs by optimizing a MOLA observational parameter vector comprising the bore-sight vector of MOLA and an 3-D orbital shift for each laser segment. Segments are defined as continuous sections of the laser orbital track data that can reach from North Pole to South Pole. Segments are co-registered to HRSC DTMs for low-latitude areas of different extent while laser data points of the same segment outside the DTM area will inherit the optimized parameter values. &#160;&#160;Systematic variation of the extent of the reference DTM allows us to analyze the reliability of &#8220;extrapolating&#8221; parameter results beyond the reference area. We apply two independent measures for the quality of the adjustment results: height residuals at MOLA cross-over points, and height deviation with HRSC DEMs that were not included in the reference area used for optimization.Results: ES-based adjustment of MOLA tracks was applied using HRSC DTMs covering four different half-quadrangles and combinations of these, and the laser track segments intersecting these areas. Our results show significant improvements of cross-over and DEM-to-DEM residuals for both the reference area and adjacent areas, amounting to a reduction of the residuals shown by the original profile data set by a factor of up to five. In absolute numbers, the final average cross-over residuals are smaller than 1 m for all latitudes (0.15 m to 0.65 m after outlier removal at the 3s level). The quality of the adjustment was evaluated also by visual inspection of gridded DTM data products, which shows that the ES technique successfully adjusted tracks that appear as outliers in the MEGDR data product. However, outlier tracks also do still appear in the crossover adjusted version, suggesting that for some profiles the estimated parameters cannot be generalized to the entire extent of the segments. This could be caused by rapid changes of the spacecraft orientation, e.g. associated with manouvers.Based on these encouraging results, we performed processing tests for both the generation of an updated MOLA gridded data product and for a seamless joint HRSC-MOLA DEM to be generated without need to draw on purely numeric blending procedures which might generally limit the physical significance of geodetic data products. We also will discuss implications of the new profile solutions concerning science applications such as the observed temporal variability of MOLA profile heights at the poles and their possible association with deposition and sublimation processes in theses areas.Acknowledgments: The authors thank the Mars Express Project teams at ESTEC, ESOC, and ESAC, and DLR for their successful planning and acquisition of data and for making processed data available.References: [1] Smith, D. E. et al. JGR 106, 23689-23722 (2001). Doi:10.1029/2000JE001364[2] Archinal, B. A. et al.,, XXth Congr. ISPRS, Comm. IV, WG IV/9, 2004.[3] Smith, D. E. et al. NASA PDS (2003). MGS-M-MOLA-5-MEGDR-L3-V1.0.[4] Gwinner, K. et al. PSS 126, 93-138 (2016). Doi: 10.1016/j.pss.2016.02.014[5] Jaumann, R. et al.&#160; PSS 55, 928-952 (2007). Doi:10.1016/j.pss.2006.12.003[6] Hansen, N. 75-102 (Springer Berlin Heidelberg, 2006).[7] Rechenberg, I. Evolutionsstrategie 94. Vol. 1 (Frommann-Holzboog, 1994).[8] Willner, K. et al., this conference.