Earth Rotation Parameters Research Articles

Simulation of tracking scenarios to LAGEOS and Etalon satellites

The International Laser Ranging Service (ILRS) provides weekly solutions for coordinates of Satellite Laser Ranging (SLR) stations coordinates, geocenter coordinates, as well as Earth rotation parameters with a daily resolution. The ILRS standard solution is an important contribution to the International Terrestrial Reference Frame (ITRF). As of today, it is derived from SLR observations to the pairs of LAGEOS and Etalon satellites exclusively. In this paper, the effect of altering the tracking strategy for the LAGEOS and Etalon satellites on the weekly ILRS standard solution is studied. This is done by simulating various tracking scenarios and by comparing the parameters of the solutions for each scenario. In particular, the focus lies on redistributing observation time between the LAGEOS and Etalon satellites as a possible optimization for the tracking scheduling. By this, the current tracking capability of each station is taken into account with no change of the overall tracking activity to LAGEOS and Etalon. It is shown that the quality of the solution for the ITRF-relevant parameters is not significantly degraded when reducing the number of observations to LAGEOS by up to 20% with respect to the number of available normal points in 2016. The vacant tracking capability obtained from the reduction of LAGEOS observations may be used to increase the number of measurements to Etalon by a factor of three. This leads to nearly 10% improvement of the recovery of Earth rotation parameters within the combined LAGEOS–Etalon solution. With our study, we contribute to the ongoing discussions regarding tracking strategies for SLR stations within the ILRS. In particular, the stations could adjust their individual tracking priorities according to these results in the future without major investments or the need for new infrastructure.

Influence of the layered Moon and Earth’s orientation on lunar rotation

One of the most efficient ways to probe the lunar inner structure at present is through the study of its rotation. Range and range rate (Doppler) data between the Chang’E-3 lander and station on the Earth were collected from the beginning of the Chang’E-3 lunar mission in 2013. These observation data, taken together with the existing lunar laser ranging data, provide a new approach to extend research on the Earth-Moon system. The high precision of current observation data imposes exacting demands, making it necessary to include previously neglected factors. In this paper, motivated by progress of the Chinese lunar exploration project and to use its data in the near future, two lunar models: a one-layer model and a two-layer model with a fluid core, were applied to the rotational equations based on our implemented algorithm of the Moon’s motion. There was a difference of about 0.5″ in ϕ and ψ, but 0.2″ in θ between the two models. This result confirms that stratification of the inner structure of the Moon can be inferred from rotation data. We also added precise Earth rotation parameters in our model; the results show that this factor is negligible at present, due to the limited precision of the existing data. These results will help us understand the rotational process clearly and build a more realistic Earth-Moon model when we combine Lunar Laser Ranging data with high precision radio data to fit lunar motion in the near future.

Multi-constellation GNSS orbit combination based on MGEX products

Abstract. The mission of the International GNSS Service (IGS) is to deliver highly accurate GNSS data and products to the scientific users and the community. Among these products, precise orbits, and clocks for GPS and GLONASS are available to the public. These products are system-wise combinations based on solutions provided by the Analysis Centers (AC). Over the past years, the IGS has been putting efforts in extending the service to other navigation satellite systems within the Multi-GNSS Experiment and Pilot Project (MGEX). Several ACs contribute by providing solutions containing not only GPS and GLONASS but also Galileo, BeiDou, and QZSS. However, there is no official MGEX combination so far. Therefore, we started to develop a new combination algorithm aiming at a fully consistent multi-constellation solution. We apply two different strategies focusing on the alignment of the orbits to the International Terrestrial Reference Frame (ITRF). In the first strategy, we use the Earth Rotation Parameters (ERP) to align the orbits, whereas in the second strategy Helmert parameters provided by the Terrestrial Frame Combination Center (TFCC) are applied. Based on the alignment we compare the GPS orbit products from both strategies with the official IGS orbits. These preliminary results show that the ERP strategy agrees with the official orbits around by 30 mm whereas, with the second strategy, the agreement is around 15 mm.

ПРОГНОЗИРОВАНИЕ ПАРАМЕТРОВ ВРАЩЕНИЯ ЗЕМЛИ С ПОМОЩЬЮ АДАПТИВНЫХ ГАРМОНИЧЕСКИХ МОДЕЛЕЙ

The article discusses the methodology for predicting the Earth's rotation parameters (ERP), which differs from the generally accepted one's in that for constructing prognostic models, time series of initial data of various durations are used. At the same time, the estimation of the parameters of models of slow trend changes performed in the interval of the training sample of about 100 years. Intervals from 6 to 40 years are used to evaluate the parameters of the faster quasiperiodic and regular components. This method of dividing the time series into training sample intervals of different durations allows obtaining adaptive models of slow and fast changes in time series with their subsequent integration into a complete prognostic model. The practical implementation of the proposed methodology showed high stability of the forecasting results for all ERP regardless start date of the forecast, which was confirmed by the results of its testing in various international projects and programs.

Estimation of precise orbits and clock corrections of GLONASS and GPS navigation satellites in ultra-rapid regime based on observation data

The article presents the results on development of an algorithm and a program for calculation in ultra-rapid regime of ephemeris-time information for GLONASS and GPS navigation satellites, achieved by now in the Main metrological center of the state service of time and frequency and determination of earth rotation parameters of VNIIFTRI. Calculation of ephemeris-time information is carried out by data of code and phase measurements at two carrier frequencies. The measurement data are presented in the form of hourly RINEX observation files and navigation message files from tracking stations involved in the IGS (International GNSS Service) network. Results of test calculations of ephemeris and clock corrections of GLONASS and GPS navigation satellites are presented. The analysis of the accuracy of the obtained results compared to the aposteriori data of other analysis centers is given.

Combination of VLBI Intensive Sessions with GNSS for generating Low latency Earth Rotation Parameters

Abstract. The Earth Orientation Parameters (EOPs) are published by the Earth Orientation Centre of the International Earth Rotation and Reference Systems Service (IERS). They are provided as the low-latency Bulletin A and the 30 d latency long-term EOP time series IERS 14 C04. The EOPs are a combined product derived from different geodetic space techniques, namely Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR) and Lunar Laser Ranging (LLR), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) and Very Long Baseline Interferometry (VLBI). Since not all techniques are equally sensitive to every EOP, several parameters rely on specific observation techniques. As an example, dUT1 can only be estimated from VLBI observations. This means VLBI is an essential part of the estimation procedure for consistent EOPs. Within this paper, we are performing a combination of two low-latency space geodetic techniques as they enable the estimation of the full set of Earth Rotation Parameters (ERPs; polar motion, dUT1 and the corresponding rates). In particular, we focus on the development of a robust combination scheme of 1 h VLBI Intensive sessions with so-called GNSS Rapid solutions on the normal equation level of the Gauß-Markov model. The aim of the study is to provide highly accurate low-latency ERPs. So far, a latency of approximately only 1–3 d cold be reached since the main limiting factor is still the latency of the input data. The mathematical background of the applied algorithm is discussed in detail and evaluated by numerical results of empirical investigations. The combination yields a numerical stabilization of the equation system as well as an improvement (reduction) of the corresponding root mean square deviation of the epoch-wise estimated parameters w.r.t. the IERS 14 C04 reference time series.

An improved prediction algorithm for Earth’s polar motion with considering the retrograde annual and semi-annual wobbles based on least squares and autoregressive model

Earth Rotation Parameters (ERP) are indispensable in the transformation between the Celestial Reference Frame and the Terrestrial Reference Frame, and significant for high-precision space navigation and positioning. As a key parameter in ERP, Polar Motion (PM) is of great importance in analyzing and understanding the dynamic interaction between solid Earth, atmosphere, ocean and other geophysical fluids. The diverse excitations, as well as complex motion mechanisms of PM, make it more difficult for its high-precision prediction. In this study, the characteristics of PM from 1962 to 2018 are firstly analyzed. The main period term of the PM is extracted and reconstructed by the Fourier Transform Band-Pass Filter, which indicates Chandler’s amplitude has decayed to its lowest state in 2016 and then enters into the next growth stage. More importantly, a Retrograde Semi-annual Wobble (RSAW) is detected and confirmed for the first time. Secondly, the contributions of Retrograde Annual Wobble (RAW) and RSAW terms to PM are analyzed and compared. Results demonstrate that the magnitudes of RAW and RSAW terms to PM from 1962 to 2018 are about 3–8 mas. Finally, in view of the existence of RAW and RSAW in PM, an improved PM prediction algorithm with considering the influence of RAW and RSAW based on least squares and autoregressive model (LS + AR) is developed. The results show that the inclusion of RAW term can effectively improve the accuracy of the LS + AR model in the prediction span of 1–360 days for both components of PM. Besides, considering the RSAW term, the prediction accuracy can be further improved in the prediction spans of 50–310 days for x component of PM, and in the prediction spans of 50–180 days for y component of PM.

Future TRFs and GGOS – where to put the next SLR station?

Abstract. Satellite Laser Ranging (SLR) is one of the four geodetic space techniques contributing to the realisation of terrestrial reference frames (TRFs) as well as to the determination of Earth Rotation Parameters (ERPs). The current SLR tracking network suffers from an insufficient network geometry due to a lack of stations especially in the southern hemisphere. Previous simulation studies have shown that the extension of the global SLR tracking network is indispensable for reaching the target accuracy of future TRFs according to user requests and the ambitious goals of the Global Geodetic Observing System (GGOS). The simulation study presented here puts the focus on a determination of the locations where additional SLR stations are most valuable for an improved estimation of the geodetic parameters. Within the present study, we perform a simulation of a set of stations distributed homogeneously over the globe and compare different solutions, always adding one of these simulated stations to the real SLR station network. This approach has been chosen in order to be able to investigate the deficiencies of the existing SLR network and to judge in which regions on the globe an additional SLR station would be most valuable for the improvement of certain geodetic parameters of SLR-derived reference frames. It is shown that the optimum location of a future SLR station depends on the parameter of interest. In case of the ERPs, the main potential for improvement by a single additional station can be shown for locations in polar regions (improvement for ypole up to 7 %) and for locations along the equator for the lengh of day (LOD, improvement up to 1.5 %). The TRF parameters would benefit from an additional station around the pierce points of the axes of the terrestrial reference frame (improvement for ty up to 4 %), the Arctic and the Pacific Ocean region (tz improved by up to 4.5 %), and the Antarctic and the Indian Ocean region (scale improved by up to 2.2 %). As outcome of this study, it is concluded that an additional SLR site in the Antarctic region might be of first priority, enabling improvements in the pole coordinates and the scale of the TRF; potential further sites are recommended in the equatorial region, especially beneficial for the origin of the realised TRF as well as for LOD.

Earth rotation variations observed by VLBI and the Wettzell “G” ring laser during the CONT17 campaign

Abstract. The VLBI (Very Long Baseline Interferometry) technique can provide the full set of parameters needed for the transformation between celestial and terrestrial reference frames with high accuracy. Yet it has some limitations regarding temporal resolution and continuity, and the accuracy of the resulting Earth Orientation Parameters (EOP) varies depending on the network geometry. In this work we explore the benefit of combining VLBI observations with the measurements of the large ring laser gyroscope “G” in Wettzell for deriving highly resolved ERP (Earth Rotation Parameters, i.e. polar motion and universal time variations, δUT1). We examine the observations collected by two simultaneously operating VLBI networks during the 15 d of the CONT17 campaign. These two networks, of 14 globally distributed telescopes each, were designed for the estimation of Earth rotation variations, for which reason the resulting hourly ERP are appointed as benchmark in this investigation. To evaluate the advantage of a VLBI and ring laser combined solution, we create degraded versions of the original networks, containing only six stations. The ERP derived from those sparse networks and from the VLBI sparse plus ring laser solutions are then compared in terms of differences to the reference values. It should certainly be considered that these are relative numbers, since they are also determined by the number and selection of the stations remaining in the sparse networks. The root mean square of the difference to the benchmark is reduced by 24 % in case of δUT1 from one network. The polar motion yp component from the same network moves 14 % closer to the reference value due to the inclusion of the ring laser data. The impact on xp and on all ERP from the other network ranges between 2 % and 9 %. The research again confirms the feasibility and also the potential gain of a combined evaluation of VLBI and ring laser observations, but the full capacity of such a sensor fusion will emerge once the ring laser gyroscopes reach a level of accuracy similar to VLBI.

Impact of network constraining on the terrestrial reference frame realization based on SLR observations to LAGEOS

The Satellite Laser Ranging (SLR) network struggles with some major limitations including an inhomogeneous global station distribution and uneven performance of SLR sites. The International Laser Ranging Service (ILRS) prepares the time-variable list of the most well-performing stations denoted as ‘core sites’ and recommends using them for the terrestrial reference frame (TRF) datum realization in SLR processing. Here, we check how different approaches of the TRF datum realization using minimum constraint conditions (MCs) and the selection of datum-defining stations affect the estimated SLR station coordinates, the terrestrial scale, Earth rotation parameters (ERPs), and geocenter coordinates (GCC). The analyses are based on the processing of the SLR observations to LAGEOS-1/-2 collected between 2010 and 2018. We show that it is essential to reject outlying stations from the reference frame realization to maintain a high quality of SLR-based products. We test station selection criteria based on the Helmert transformation of the network w.r.t. the a priori SLRF2014 coordinates to reject misbehaving stations from the list of datum-defining stations. The 25 mm threshold is optimal to eliminate the epoch-wise temporal deviations and to provide a proper number of datum-defining stations. According to the station selection algorithm, we found that some of the stations that are not included in the list of ILRS core sites could be taken into account as potential core stations in the TRF datum realization. When using a robust station selection for the datum definition, we can improve the station coordinate repeatability by 8%, 4%, and 6%, for the North, East and Up components, respectively. The global distribution of datum-defining stations is also crucial for the estimation of ERPs and GCC. When excluding just two core stations from the SLR network, the amplitude of the annual signal in the GCC estimates is changed by up to 2.2 mm, and the noise of the estimated pole coordinates is substantially increased.

Determination of Global Geodetic Parameters Using Satellite Laser Ranging Measurements to Sentinel-3 Satellites

Sentinel-3A/3B (S3A/B) satellites are equipped with a number of precise instruments dedicated to the measurement of surface topography, sea and land surface temperatures and ocean and land surface color. The high-precision orbit is guaranteed by three instruments: Global Positioning System (GPS) receiver, laser retroreflector dedicated to Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) antenna. In this article, we check the possibility of using SLR observations and GPS-based reduced-dynamic orbits of active S3A/B satellites for the determination of global geodetic parameters, such as geocenter motion, Earth rotation parameters (ERPs) and the realization of the terrestrial reference frame, based on data from 2016-2018. The calculation process was preceded with the estimation of SLR site range biases, different network constraining tests and a different number of orbital arcs in the analyzed solutions. The repeatability of SLR station coordinates based solely on SLR observations to S3A/B is at the level of 8-16 mm by means of interquartile ranges even without network constraining in 7-day solutions. The combined S3A/B and LAGEOS solutions show a consistency of estimated station coordinates better than 13 mm, geocenter coordinates with a RMS of 6 mm, pole coordinates with a RMS of 0.19 mas and Length-of-day with a RMS of 0.07 ms/day when referred to the IERS-14-C04 series. The altimetry observations have to be corrected by the geocenter motion to obtain unbiased estimates of the mean sea level rise. The geocenter motion is typically derived from SLR measurements to passive LAGEOS cannonball-like satellites. We found, however, that SLR observations to active Sentinel satellites are well suited for the determination of global geodetic parameters, such as Earth rotation parameters and geocenter motion, which even further increases the potential applications of Sentinel missions for deriving geophysical parameters.

Troposphere delay modeling with horizontal gradients for satellite laser ranging

Satellite laser ranging (SLR) constitutes a fundamental space geodetic technique providing global geodetic parameters, such as geocenter coordinates, Earth rotation parameters, and low-degree gravity field coefficients. The tropospheric delay correction is one of the crucial corrections that have to be taken into account when processing SLR data. Current conventional models of the troposphere delays assume a full symmetry of the atmosphere above SLR stations. Neglecting horizontal gradients in SLR solutions introduces a systematic error in SLR products, especially for the observations at low elevation angles, and leads to a deterioration of the consistency between SLR and other space geodetic techniques, such as global navigational satellite systems and very-long-baseline interferometry. We derive new mapping function coefficients, as well as first- and second-order horizontal gradients, all of which are based on numerical weather models, in order to properly consider the azimuthal asymmetry in SLR solutions. We test the enhanced mapping function and horizontal gradients on the solutions based on 11 years of SLR observations to LAGEOS-1/2 satellites and 1 year of SLR observations to Sentinel-3A. The consideration of azimuthal asymmetry of the atmosphere above the SLR stations has a systematic effect on SLR-derived products, such as station and geocenter coordinates and pole coordinates. Horizontal gradients in SLR solutions improve the consistency between SLR-derived pole coordinates and the combined IERS-C04 series by means of reducing the offset for the X and Y pole coordinates by 20 {upmu }mathrm{as}. The second-order horizontal gradients are negligible in SLR solutions; thus, including first-order gradients is sufficient for SLR solutions.

Impact of the Atmospheric Non-tidal Pressure Loading on Global Geodetic Parameters Based on Satellite Laser Ranging to GNSS

Atmospheric pressure loading plays a crucial role in precise space geodesy, thus its omission, especially the nontidal loading (ANTL) part, leads to the inconsistency between solutions based on the microwave [Global Navigation Satellite Systems (GNSS)] and optical [satellite laser ranging (SLR)] observations. SLR observations are performed only during the cloudless conditions coincident with high values of air pressure that deforms the earth’s crust downward. The systematic shift of the estimated SLR station coordinates, which arises from the ANTL omission, is called the Blue-Sky effect. The offset is related to the long-term averaging of ANTL for SLR observations which are provided in sparse intervals, unlike GNSS, which observes continuously. Based on the ANTL model applied on SLR observations to GNSS, we determined the values of the Blue-Sky effect. The largest values of the Blue-Sky effect are observed for the inland stations, i.e., 2.3, 2.1, 2.0, and 1.9 mm for Svetloe, Potsdam, Baikonur, and Altay, respectively. We also investigate the impact of the omission of ANTL corrections on geodetic parameters, i.e., earth rotation parameters, geocenter motion, precise GNSS orbits, as well as on the global SLR network. The negligence of ANTL causes a systematic effect on geocenter coordinates with the amplitude of the annual signal at the level of 1.9 mm for the Z-component. The omission of ANTL corrections causes also a systematic shift of the multi-GNSS orbit constellation with the amplitude of the annual signal at the level of 2.7 mm for the Z-component.

Network Effects and Handling of the Geocenter Motion in Multi‐GNSS Processing

AbstractBoth, the network configuration and the way of terrestrial reference frame (TRF) realization, affect the global geodetic products delivered from the Global Navigation Satellite Systems (GNSS) data processing. The purpose of this study is to analyze the differences in GNSS products, such as station coordinates, Earth rotation parameters, geocenter coordinates (GCC), and satellite orbits delivered from the double‐difference multi‐GNSS (GPS, GLONASS, and Galileo) processing, which may arise from (1) using a homogeneous and inhomogeneous network of multi‐GNSS stations, (2) different approaches to the TRF realization using minimum constraint conditions, and (3) different approaches to handling of GCC in GNSS global processing. The questionable quality of GCC delivered from the global GNSS solutions is described with a special attention to network effects and system‐specific parameters. We found that Galileo can provide GCC, whose quality corresponds to the GPS series. Moreover, the GCC from Galileo is of a better quality than those based on GLONASS data, despite the same number of nominal orbital planes and a much lower number of active satellites. When the No‐Net‐Translation constraint is not applied on the GNSS network, the station coordinate repeatability is worsened by about 70%, 55%, and 25% for the north, east, and up components, respectively, compared to the solution when applying No‐Net‐Translation and when having the network origin consistent with the international TRF. We thus infer that the No‐Net‐Translation condition is mandatory in global GNSS solutions.

Future SLR station networks in the framework of simulated multi-technique terrestrial reference frames

Currently, the requirements of the Global Geodetic Observing System are not yet met by the latest global terrestrial reference frames (TRF). In this study, we assess potential TRF improvements by future SLR network designs partly already classified as “future stations” by the International Laser Ranging Service. We simulate the space geodetic techniques GPS, SLR, and VLBI within the time span 2008–2014 and evaluate the feasible improvements of the SLR-only and the multi-technique TRFs w.r.t. the current station networks. The station performance of the simulated 14 additional SLR stations is driven by the total cloud coverage from the numerical weather model ERA5. We find that the estimated station positions and velocities as well as the Earth rotation parameters, and the TRF-defining parameters origin and scale improve by 1–4% if a single additional station is added to the current SLR-only network. The solution with all 14 additional stations improves by about 22% in origin and 20% in scale w.r.t. the current SLR-only TRF. Single existing stations were excluded from the network resulting in deteriorations of 2–6%. Multi-technique TRFs improve by new co-located sites due to additional SLR stations by up to 1% for station positions, velocities, and the realization of the orientation.

Estimating global geodetic parameters using SLR observations to Galileo, GLONASS, BeiDou, GPS, and QZSS

All Galileo, GLONASS, QZSS, and BeiDou satellites are equipped with laser retroreflector arrays dedicated to satellite laser ranging (SLR). Using SLR data to new GNSS systems allows for estimating global geodetic parameters, such as Earth rotation parameters, global scale, and geocenter coordinates. In this study, we evaluate the quality of global geodetic parameters estimated on a basis of SLR tracking of new GNSS satellites and the combined solution based on SLR observations to GNSS and LAGEOS. We show that along with a progressive populating of Galileo orbital planes, the quality of geocenter components based on SLR–GNSS data has been improved to the level of 6 and 15 mm for equatorial and polar geocenter components, respectively. The scale of the reference frame and the geocenter coordinates in the combined LAGEOS + GNSS solutions are dominated by the LAGEOS data. Some noncore SLR stations provide by far more observations to GNSS than to LAGEOS, e.g., Russian and Chinese stations dedicated to supporting GLONASS and BeiDou constellations. The number of solutions for these stations can be increased by up to 40%, whereas the station coordinate repeatability can be improved from about 20–30 mm to the level of 15–20 mm when considering both SLR to LAGEOS and SLR to GNSS.

Random Optimization Algorithm on GNSS Monitoring Stations Selection for Ultra-Rapid Orbit Determination and Real-Time Satellite Clock Offset Estimation

Geographical distribution of global navigation satellite system (GNSS) ground monitoring stations affects the accuracy of satellite orbit, earth rotation parameters (ERP), and real-time satellite clock offset determination. The geometric dilution of precision (GDOP) is an important metric used to measure the uniformity of the stations distribution. However, it is difficult to find the optimal configuration with the lowest GDOP when taking the 71% ocean limitation into account, because the ground stations are hardly uniformly distributed on the whole of the Earth surface. The station distribution geometry needs to be optimized and besides the stability and observational quality of the stations should also be taken into account. Based on these considerations, a method of configuring global station tracking networks based on grid control probabilities is proposed to generate optimal configurations that approximately have the minimum GDOP. A random optimization algorithm method is proposed to perform the station selection. It is shown that an optimal subset of the total stations can be obtained in limited iterations by assigning selecting probabilities for the global stations and performing a Monte Carlo sampling. By applying the proposed algorithm for observation data of 201 International GNSS Service (IGS) stations for 3 consecutive days, an experiment of ultra-rapid orbit determination and real-time clock offset estimation is conducted. The distribution effects of stations on the products accuracy are analyzed. It shows that (1) the accuracies of GNSS ultra-rapid observed and predicted orbits and real-time clock offset achieved using the proposed algorithm are higher than those achieved with the traditional method having the drawbacks of lacking evaluation indicators and being time-consuming, corresponding to the improvements 17.15%, 19.30%, and 31.55%, respectively. Only using 30 stations selected by the proposed method, the accuracies achieved reach 2.01 cm (RMS), 4.93 cm (RMS), and 0.20 ns (STD), respectively. Using 60 stations, the accuracies are 1.47 cm, 3.50 cm, and 0.17 ns, respectively. (2) With the increasing number of stations, the accuracies of the Global Positioning System (GPS) orbit and clock offset improve continuously, but more than 60 stations, the improvement on the orbit determination becomes more gradual, while for more than 30 stations, there is no appreciable increase in the accuracy of the real-time clock offset.

陆态网络与IGS数据对地球自转参数的解算精度分析

陆态网络与IGS数据对地球自转参数的解算精度分析

A Method for Rapidly Determining the Optimal Distribution Locations of GNSS Stations for Orbit and ERP Measurement Based on Map Grid Zooming and Genetic Algorithm

Designing the optimal distribution of Global Navigation Satellite System (GNSS) ground stations is crucial for determining the satellite orbit, satellite clock and Earth Rotation Parameters (ERP) at a desired precision using a limited number of stations. In this work, a new criterion for the optimal GNSS station distribution for orbit and ERP determination is proposed, named the minimum Orbit and ERP Dilution of Precision Factor (OEDOP) criterion. To quickly identify the specific station locations for the optimal station distribution on a map, a method for the rapid determination of the selected station locations is developed, which is based on the map grid zooming and heuristic technique. Using the minimum OEDOP criterion and the proposed method for the rapid determination of optimal station locations, an optimal or near-optimal station distribution scheme for 17 newly built BeiDou Navigation Satellite System (BDS) global tracking stations is suggested. To verify the proposed criterion and method, real GNSS data are processed. The results show that the minimum OEDOP criterion is valid, as the smaller the value of OEDOP, the better the precision of the satellite orbit and ERP determination. Relative to the exhaustive method, the proposed method significantly improves the computational efficiency of the optimal station location determination. In the case of 3 newly built stations, the computational efficiency of the proposed method is 35 times greater than that of the exhaustive method. As the number of stations increases, the improvement in the computational efficiency becomes increasingly obvious.

Satellite laser ranging as a tool for the recovery of tropospheric gradients

Space geodetic techniques, such as Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI) have been extensively used for the recovery of the tropospheric parameters. Both techniques employ microwave observations, for which the troposphere is a non-dispersive medium and which are very sensitive to the water vapor content. Satellite laser ranging (SLR) is the only space geodetic technique used for the definition of the terrestrial reference frames which employs optical – laser observations. The SLR sensitivity to the hydrostatic part of the troposphere delay is similar to that of microwave observations, whereas the sensitivity of laser observations to non-hydrostatic part of the delay is about two orders of magnitude smaller than in the case of microwave observations. Troposphere is a dispersive medium for optical wavelengths, which means that the SLR tropospheric delay depends on the laser wavelength. This paper presents the sensitivity and capability of the SLR observations for the recovery of azimuthal asymmetry over the SLR stations, which can be described as horizontal gradients of the troposphere delay. For the first time, the horizontal gradients are estimated, together with other parameters typically estimated from the SLR observations to spherical LAGEOS satellites, i.e., station coordinates, earth rotation parameters, and satellite orbits. Most of the SLR stations are co-located with GNSS receivers, thus, a cross-correlation between both techniques is possible. We compare our SLR horizontal gradients to GNSS results and to the horizontal gradients derived from the numerical weather models (NWM). Due to a small number of the SLR observations, SLR is not capable of reconstructing short-period phenomena occurring in the atmosphere. However, the long-term analysis allows for the recovery of the atmosphere asymmetry using SLR. As a result, the mean offsets of the SLR-derived horizontal gradients agree to the level of 47%, 74%, 54% with GNSS, hydrostatic delay, and total delay from NWM, respectively. SLR can be thus employed as a tool for the recovery of the atmospheric parameters with a major sensitivity to the hydrostatic part of the delay.