The SLR/LLR Double-Difference Baseline

Abstract

Here we present a novel SLR double-difference approach with GNSS satellites. It is shown how forming double-differences of SLR measurements between Herstmonceux (HERL) and Graz (GRZL) ILRS stations and two Galileo satellites removes common SLR biases: i.e., ILRS station range biases and common retro-reflector effects. By using the orbits of GNSS satellites from IGS as fixed in the parameter estimation, the double-difference SLR approach offers a bias-free estimation of relative coordinates with the mm-accuracy between two ILRS stations (SLR baseline) that are separated by about 5000 km. In this way, we obtain SLR observables of utmost precision and accuracy at sub-millimeter level with the standard deviation σ = 0.5 – 1.0 mm. We show that after differencing the remaining noise in the SLR measurements nicely averages out, leading to estimation of station coordinates, local ties between different space geodesy techniques and precise comparison of optical/microwave tropospheric effects. Considering that relative station coordinates between ILRS stations can be estimated in a similar way between collocated GNSS stations using the GNSS double-differences, the SLR approach allows direct estimation of local ties between SLR and GNSS ground stations. We extend the common-view SLR and make double-differences over time by considering the different observation times for all SLR measurements between all SLR stations. SLR range biases and small biases between SLR sessions are removed. The scale is preserved when double-differencing SLR and free of range biases (at mm-level), making this approach very attractive to combine ILRS network with IGS network in the global GNSS solution. We show that LLR offers estimation of UT0 and with differential SLR the global GNSS can estimate a complete terrestrial frame. For the un-differenced SLR we refer to Pearlman et al. (2002).

When a LEO satellite is observed by two SLR stations quasi-simultaneously with a GNSS satellite, one can calculate the “vertical SLR baseline” (vector) between the GNSS and the LAGEOS (LEO) satellite as well as the “vertical SLR range” (GNSS-LEO range) derived from geometry. This provides radial orbit information that can be used for altimetry and gravity field missions as well as reference frame satellites. At the end we extend the double-difference approach to other space geodesy techniques such as lunar laser ranging, VLBI and DORIS and discuss estimation of local ties and global reference frame parameters. We also derive a relationship between a possible bias in LAGEOS center of mass correction and radial bias in GNSS orbits. At the end we extend the concept of SLR double-differencing to lunar laser ranging (LLR) and present first results for the LLR double-difference baseline. We succeeded in processing LLR measurements to Apollo and Luna retro-reflectors on the Moon, and, in a similar way, have processed SLR measurements to GPS satellites considering only the geocentric frame in order to model the uplink and downlink for lunar laser ranges.