Study on Optimal Broadcast Ephemeris Parameters for GEO/IGSO Navigation Satellites

This paper proposes new sets of suitable broadcast ephemeris parameters for geosynchronous (GEO) and inclined geosynchronous (IGSO) navigation satellites (NSs). Despite the increasing number of GEO and IGSO NSs, global positioning system (GPS)-type ephemeris parameters are still widely used for them. In an effort to provide higher fit accuracy, we analyze a variety of broadcast ephemeris parameters for GEO and IGSO satellites along with their orbital characteristics and propose optimal sets of parameters. Nonsingular elements and orbital plane rotation are adopted for alleviating/avoiding the singularity issues of GEO satellites. On the basis of 16 parameters of GPS LNAV, we add one to four parameters out of 28 correction ones to determine optimal sets of ephemeris parameters providing higher accuracy. All possible parameter sets are tested with the least-square curve fit for four BeiDou GEOs and six BeiDou IGSOs. Their fit accuracies are compared to determine the optimal broadcast ephemeris parameters that provide minimum fit errors. The set of optimal ephemeris parameters depends on the type of orbit. User range error (URE) accuracies of the proposed optimal ephemeris parameters ensure results within 2.4 cm for IGSO and 3.8 cm for GEO NSs. Moreover, the experimental results present common parameter sets for both IGSO and GEO for compatibility and uniformity. Compared with four conventional/well-known sets of ephemeris parameters for BeiDou, our proposed parameters can enhance accuracies of up to 34.5% in terms of URE. We also apply the proposed optimal parameter sets to one GEO and three IGSO satellites of QZSS. The effects of fitting intervals, number of parameters, total bits, and orbit types on the fit accuracy are addressed in detail.

Processing of GRACE FO satellite to satellite tracking data using the GRACE SIGMA software

<p>At our Institute we compute monthly gravity potential solutions from GRACE/GRACE-FO level 1B data by using the variational equations approach. The gravity field is recovered with our own MATLAB software "GRACE-SIGMA" that was recently updated in order to reduce the calculation time with parallel computing approach by approx. 80%. Also the processing chain has changed to update the background modeling and we made tests with different orbit types and different parametrizations. We discuss progress to include laser ranging interferometer data in gravity field solutions. We present validation results and analyze the properties of postfit range-rate residuals.</p>

A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems

Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via local operations with a non-vanishing probability. The classes obtained in this way are called SLOCC classes. They can be categorized into three disjoint types: the null-cone, the polystable states and strictly semistable states. Whereas the former two are well characterized, not much is known about strictly semistable states. We derive a criterion for the existence of the latter. In particular, we show that there exists a strictly semistable state if and only if there exist two polystable states whose orbits have different dimensions. We illustrate the usefulness of this criterion by applying it to tripartite states where one of the systems is a qubit. Moreover, we scrutinize all SLOCC classes of these systems and derive a complete characterization of the corresponding orbit types. We present representatives of strictly semistable classes and show to which polystable state they converge via local regular operators.

Accelerated methods for direct computation of fusion alpha particle losses within, stellarator optimization

Accelerated statistical computation of collisionless fusion alpha particle losses in stellarator configurations is presented based on direct guiding-centre orbit tracing. The approach relies on the combination of recently developed symplectic integrators in canonicalized magnetic flux coordinates and early classification into regular and chaotic orbit types. Only chaotic orbits have to be traced up to the end, as their behaviour is unpredictable. An implementation of this technique is provided in the code SIMPLE (symplectic integration methods for particle loss estimation, Albert et al., 2020b, doi:10.5281/zenodo.3666820). Reliable results were obtained for an ensemble of 1000 orbits in a quasi-isodynamic, a quasi-helical and a quasi-axisymmetric configuration. Overall, a computational speed up of approximately one order of magnitude is achieved compared to direct integration via adaptive Runge–Kutta methods. This reduces run times to the range of typical magnetic equilibrium computations and makes direct alpha particle loss computation adequate for use within a stellarator optimization loop.

Processing of GRACE-FO satellite-to-satellite tracking data using the GRACE-SIGMA software

<p>The dual-satellite mission GRACE Follow-On (GRACE-FO) was launched in May 2018 as the successor of the Gravity Recovery And Climate Experiment (GRACE). In May 2019 first level 1 data products were made available to the community and are now published regularly. These products, among others, include orbits, accelerometer measurements, star camera data and micron and sub-micron precise inter-satellite range measurements. The data products are used by different groups to compute estimates of monthly gravity fields of the Earth. The in-house developed GRACE-SIGMA software is used at the Institut of Geodesy/Leibniz University Hannover for the estimation of monthly gravity fields. Several parts of the software’s processing chain, such as background modeling, were updated recently and different parametrization scenarios were tested. First solutions were estimated based on laser ranging interferometer measurements. Moreover, different orbit types, such as reduced-dynamic and kinematic, were tested. In this contribution, we present the influence of these updates and tests on the quality of the gravity fields. The obtained solutions are assessed in terms of error degree standard deviations and post-fit residuals of the inter-satellite measurements.</p>

High-Rate Monitoring of Satellite Clocks Using Two Methods of Averaging Time

Knowledge of the global navigation satellite system (GNSS) satellite clock error is crucial in real-time precise point positioning (PPP), seismology, and many other high-rate GNSS applications. In this work, the authors show the characterisation of the atomic GNSS clock’s stability and its dependency on the adopted orbit type using Allan deviation with two methods of averaging time. Four International GNSS Service (IGS) orbit types were used: broadcast, ultra-rapid, rapid and final orbit. The calculations were made using high-rate 1 Hz observations from the IGS stations equipped with external clocks (oscillators). The most stable receiver oscillator was chosen as a reference clock. The results show the advantage of the newest GPS satellite block with respect to the other satellites. Significant differences in the results based on the orbit type used have not been recorded. Many averaging time methods used in Allan deviation (ADEV) show the clock’s fluctuations, usually smoothed in 2n s averaging times.

An Improved BDS Satellite-Induced Code Bias Correction Model Considering the Consistency of Multipath Combinations

The satellite-induced systematic biases were identified to exist in the code observations from BeiDou navigation satellite system (BDS) satellites using multipath (MP) combinations. The current correction model for satellite-induced code bias (SICB) does not take into account the consistency of MP combinations, which limits the accuracy of the developed model. Both the cycle slips and different tracking of a satellite at different stations can affect the absolute values of MP combinations, although the variations remain unchanged. An improved SICB piecewise linear correction model as a function of elevations is proposed. We estimate the model parameters for each frequency and for each satellite. The single-difference of MP combinations in the domain of elevation angles is carried out to remove the unknown ambiguities and stable hardware delays so that the SICB modeling is free of the effects of MP combination inconsistency. In addition, a denser elevation node separation of 1°, rather than the 10° usually employed by the traditional model, is used to describe the more precise SICB variations. The SICB corrections show significant differences among orbit types and frequency bands. The SICB variations have much less effect on Inclined Geosynchronous Orbit (IGSO) satellites than on Medium Earth Orbit (MEO) satellites for the regional BDS (BDS-2). The B1 signal has the largest SICB corrections, which can be up to 0.9 m close to zenith for BDS-2 MEO satellites, and the B2 signal follows. After adding the SICB corrections to the code observations, the elevation-dependent code biases vanish, and we can obtain improved code observations. After applying the improved SICB correction model, the root mean square (RMS) values of MP combination time series are reduced by 7%, 6% and 2%, and 18%, 14% and 5% on the B1, B2 and B3 frequencies for the BDS-2 IGSO and MEO satellites, respectively. For comparison, we also establish the traditional SICB correction model. With the traditional SICB correction model, the corresponding RMS MP combinations are smaller than those of uncorrected MP series, but slightly larger than those of corrected MP series using the improved SICB correction model. To validate the effectiveness and correctness of our proposed model, single-frequency precise point positioning (PPP) processing with BDS-2 MEO and IGSO satellites is conducted. An accuracy improvement of 24%, 19% and 89%, and 7%, 7% and 6% for the single-frequency PPP applying the improved SICB corrections over the case without SICB corrections and the case using the traditional SICB corrections in east, north and vertical directions is achieved, respectively. Although only centimeter-level SICB variations could be observed for the two legacy signals B1 and B3 and the three new navigation signals B1C, B2a and B2b transmitted by the satellites of global BDS demonstration system (BDS-3S), we still establish an effective SICB correction model on the B1 and B3 frequencies for BDS-3S IGSO satellites, and the RMS MP combinations are reduced by 1–4% after applying the improved SICB corrections.

A distribution model of the GNSS code noise and multipath error considering both elevation angle and orbit type

Commonly, the code noise and multipath error is considered to fully obey the Gaussian distribution. While in the cases with different elevation angles and orbit types, the assumption may be inappropriate. Based on an empirical study, by considering both the elevation angle and the orbit type, a new code noise and multipath distribution model is proposed to describe a more accurate code noise and multipath distribution in this paper. Actual code noise and multipath data from 10 observation stations during two months are researched, and the parameters and elevation angle range of code noise and multipath distribution model are determined. The code noise and multipath distribution model is verified to be more accurate than the model presented in the Global Navigation Satellite System Evolutionary Architecture Study report, according to the analysis on the code noise and multipath overbounding, position error overbounding, and the availability of receiver autonomous integrity monitoring. This model provides more accurate prior information for receiver autonomous integrity monitoring, especially its availability.

On the Stratifications of 2-Qubits X-State Space

The 7-dimensional family ℬX of the so-called mixed X-states of 2-qubits is considered. Two versions of stratifications of ℬX , i.e., its decomposition into strata according to orbit types of the adjoint actions of two groups, are described. The first stratification is due to the action of global unitary group GX ⊂ S U(4), while the second one corresponds to the action of the local unitary group LGX ⊂ GX . The equations and in-equalities in the invariants of the corresponding groups, determining each stratification component, are given.