An experimental combination of IGS repro3 campaign’s orbit products using a variance component estimation strategy

Over the past years, the International GNSS Service (IGS) has put efforts into reprocessing campaigns reanalyzing the full data collected by the IGS network since 1994. The goal is to provide a consistent set of orbits, station coordinates, and earth rotation parameters using state-of-the-art models. Different from the previous campaigns - namely: repro1 and repro2 - the repro3 includes not only GPS and GLONASS but also the Galileo constellation. The main repro3 objective is the contribution to the next realization of the International Terrestrial Reference Frame (ITRF2020). To achieve this goal, several Analysis Centers (AC) submitted their specific products, which are combined to provide the final solutions for each product type. In this contribution, we focus on the combination of the orbit products.We will present a consistent orbit solution based on a newly developed combination strategy where the weights are determined by a Least-Squares Variance Component Estimation (LSVCE). The orbits are combined in an iterative processing, first aligning all the products via a Helmert transformation, second defining which satellites will be used in the LSVCE, and finally normalizing the inverse of the variances as weights that are used to compute a weighted mean. Moreover, we will discuss the weight factors and their stability in the time evolution for each AC depending on the constellations. In addition, an external validation using a Satellite Laser Ranging (SLR) procedure will be shown for the combined solution.

An experimental combination of IGS repro3 campaign’s orbit products using a variance component estimation strategy

Over the past years, the International GNSS Service (IGS) has put efforts into reprocessing campaigns reanalyzing the full data collected by the IGS network since 1994. The goal is to provide a consistent set of orbits, station coordinates, and earth rotation parameters using state-of-the-art models. Different from the previous campaigns - namely: repro1 and repro2 - the repro3 includes not only GPS and GLONASS but also the Galileo constellation. The main repro3 objective is the contribution to the next realization of the International Terrestrial Reference Frame (ITRF2020). To achieve this goal, several Analysis Centers (AC) submitted their specific products, which are combined to provide the final solutions for each product type. In this contribution, we focus on the combination of the orbit products.We will present a consistent orbit solution based on a newly developed combination strategy where the weights are determined by a Least-Squares Variance Component Estimation (LSVCE). The orbits are combined in an iterative processing, first aligning all the products via a Helmert transformation, second defining which satellites will be used in the LSVCE, and finally normalizing the inverse of the variances as weights that are used to compute a weighted mean. Moreover, we will discuss the weight factors and their stability in the time evolution for each AC depending on the constellations. In addition, an external validation using a Satellite Laser Ranging (SLR) procedure will be shown for the combined solution.

A variance component estimation approach to infer associations between Mendelian polledness and quantitative production and female fertility traits in German Simmental cattle

Background Managing beneficial Mendelian characteristics in dairy cattle breeding programs implies that the correlated genetic effects are considered to avoid possible adverse effects in selection processes. The Mendelian trait polledness in cattle is traditionally associated with the belief that the polled locus has unfavorable effects on breeding goal traits. This may be due to the inferior breeding values of former polled bulls and cows in cattle breeds, such as German Simmental, or to pleiotropic or linkage effects of the polled locus. Methods We focused on a variance component estimation approach that uses a marker-based numerator relationship matrix reflecting gametic relationships at the polled locus to test for direct pleiotropic or linked quantitative trait loci (QTL) effects of the polled locus on relevant traits. We applied the approach to performance, health, and female fertility traits in German Simmental cattle. Results Our results showed no evidence for any pleiotropic QTL effects of the polled locus on test-day production traits milk yield and fat percentage, on the mastitis indicator ‘somatic cell score’, and on several female fertility traits, i.e. 56 days non return rate, days open and days to first service. We detected a significant and unfavorable QTL effect accounting for 6.6% of the genetic variance for protein percentage only. Conclusions Pleiotropy does not explain the lower breeding values and phenotypic inferiority of polled German Simmental sires and cows relative to the horned population in the breed. Thus, intensified selection in the polled population will contribute to increased selection response in breeding goal traits and genetic merit and will narrow the deficit in breeding values for production traits.

GPS-BDS-Galileo double-differenced stochastic model refinement based on least-squares variance component estimation

Stochastic models are essential for precise navigation and positioning of the global navigation satellite system (GNSS). A stochastic model can influence the resolution of ambiguity, which is a key step in GNSS positioning. Most of the existing multi-GNSS stochastic models are based on the GPS empirical model, while differences in the precision of observations among different systems are not considered. In this paper, three refined stochastic models, namely the variance components between systems (RSM1), the variances of different types of observations (RSM2) and the variances of observations for each satellite (RSM3) are proposed based on the least-squares variance component estimation (LS-VCE). Zero-baseline and short-baseline GNSS experimental data were used to verify the proposed three refined stochastic models. The results show that, compared with the traditional elevation-dependent model (EDM), though the proposed models do not significantly improve the ambiguity resolution success rate, the positioning precision of the three proposed models has been improved. RSM3, which is more realistic for the data itself, performs the best, and the precision at elevation mask angles 20°, 30°, 40°, 50° can be improved by 4⋅6%, 7⋅6%, 13⋅2%, 73⋅0% for L1-B1-E1 and 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5% for L2-B2-E5a, respectively.

Combination of GNSS orbits using variance component estimation

<p>The International GNSS Service (IGS) publishes operationally GPS and GLONASS orbit and clock products with the highest accuracy. These final products result from a combination using as input products determined by the IGS Analysis Centers (ACs). The method to perform the combination was developed in the early nineties by Springer and Beutler and is used until nowadays despite some updates made over the years mainly to improve the clock combination and the alignment with the current ITRF. Over the past years, towards the Multi-GNSS Experiment and Pilot Project (MGEX) the IGS has been putting efforts into extending its service. Several MGEX ACs contribute by providing solutions containing not only GPS and GLONASS but also Galileo, BeiDou, and QZSS. For MGEX an orbit and clock combination is still not consolidated inside the IGS and requires studies in order to provide a consistent solution.</p><p>We will present a least-squares framework for a multi-GNSS orbit combination, where the weights used to combine the ACs' orbits are determined by least-squares variance component estimation.  In this contribution, we will introduce and compare two weighting strategies, where either AC specific weights or AC plus constellation specific weights are used. Both strategies are tested using MGEX orbit solutions for a period of two and a half years. They yield similar results where the agreement between combined and individual products is around one centimeter for GPS and up to a few centimeters for the other constellations. The agreement is generally slightly better using the AC plus constellation weighting. A comparison of our combination approach with the official combined IGS final solution using three years of GPS, and GLONASS orbits from the regular IGS processing show an agreement of better than 5 mm and 12 mm for GPS and GLONASS, respectively. An external validation using Satellite Laser Ranging is performed for our combined MGEX orbit solutions with both weighting schemes and shows offsets values in the millimeter level for all constellations except to QZSS where the values reach a few centimeters.</p>