# Journal of Geodesy

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### Divergence-free spherical harmonic gravity field modelling based on the Runge–Krarup theorem: a case study for the Moon

Mon, 04/01/2019 - 00:00
Abstract

Recent numerical studies on external gravity field modelling show that external spherical harmonic series may diverge near or on planetary surfaces. This paper investigates an alternative solution that is still based on external spherical harmonic series, but capable of avoiding the divergence effect. The approach relies on the Runge–Krarup theorem and the iterative downward continuation. In theory, Runge–Krarup-type solutions are able to approximate the true potential within the entire space external to the masses with an arbitrary $$\varepsilon$$ -accuracy, $$\varepsilon >0$$ . Using gravity implied by the lunar topography, we show numerically that this technique avoids indeed the divergence effect, at least at the studied 5 arc-min resolution. In the context of the iterative scheme, we show that a function expressed as a truncated solid spherical harmonic expansion on a general star-shaped surface possesses an infinite surface spherical harmonic spectrum after it is mapped onto a sphere. We also study the convergence of the gradient approach, which is a technique for efficient grid-wise synthesis on irregular surfaces. We show that the resulting Taylor series may converge slowly when analytically upward continuing from points inside the masses. The continuation from the mass-free space should therefore be preferred. As an underlying topic of the paper, spherical harmonic coefficients from spectral gravity forward modelling and their Runge–Krarup counterpart are numerically studied. Regarding their different nature, we formulate some research topics that might contribute to a deeper understanding of the current methodologies used to develop combined high-degree spherical harmonic gravity models.

### Atmospheric refraction and system stability investigations in short-baseline VLBI observations

Mon, 04/01/2019 - 00:00
Abstract

Geodetic very long baseline interferometry observations of radio telescopes, which are located in an immediate neighborhood, provide an optimal experimental setup for investigations in atmospheric refraction and system stability issues. In this study, a series of dedicated VLBI sessions with very short baselines, referred to as WHISP (Wettzell HIgh SPeed) sessions, has been designed. Six sessions were observed, three on a 123-m baseline only and another three adding to the short baseline the VLBI telescope at Onsala in Sweden. New is that these sessions and their analysis benefit from the high velocities of the radio telescopes in changing from radio source to radio source providing an unprecedented number of observations on such a short baseline and consequently an extremely reliable parameter estimation. The resulting European triangle is used to compare atmospheric time series derived by two adjacent baselines. Before this could be done, the stability of the observing system, in particular the noise contributions induced by the stability of the hydrogen maser clocks and the correlation process, is investigated to separate the individual uncertainty components. We determined the uncertainty level of the observing systems to be on the order of 10 ps. We were also able to quantify the effect of applying manual phase calibration instead of scan-by-scan system calibration, which is on the order of about 20 ps in this specific example and therefore not negligible. It could be substantiated that estimating clock parameters in geodetic VLBI absorb other effects because direct H-Maser comparisons produce variations at the 5–10 ps level while clock estimates are a factor of 3–6 times larger. Atmospheric refraction has been investigated at different stages: Zenith wet delays were estimated in a differential model for one station relative to the other station and in an absolute sense using two adjacent baselines between the two Wettzell antennas and the Onsala telescope. In both cases, the variations in the estimated atmospheric parameters are found to be of the order of only 1–3 mm and the remaining variations are assigned to unmodeled random effects, particularly refractivity fluctuations in the neutral atmosphere. This was confirmed by introducing an atmospheric turbulence model yielding WRMS post-fit residuals between 7 and 20 ps when clock and correlator effects have been subtracted.

### Assessment of spatial and temporal TEC variations derived from ionospheric models over the polar regions

Mon, 04/01/2019 - 00:00
Abstract

A comprehensive evaluation of Global Positioning System (GPS) Klobuchar, Galileo broadcast NeQuick2, international reference ionosphere (IRI) and global ionospheric map (GIM) models in estimating ionospheric total electron content (TEC) is performed using GPS-derived, constellation observing system for meteorology, ionosphere, and climate and JASON-2 TECs under various solar conditions in the Arctic and Antarctic. The performances of the four ionospheric models are first analysed for the overall polar regions. In addition, according to the temporal and spatial characteristics of the polar regions, the accuracies of the four models are evaluated for the polar days and nights, the Antarctic ice sheet (AIS) and the Arctic Ocean (AO), the Weddell Sea Anomaly (WSA) as well as for ionospheric storm. The results show that Klobuchar, NeQuick2, IRI2016 and GIM can mitigate the ionospheric delay by 28.69–29.41%, 44.57–56.09%, 43.38–55.99% and 67.17–77.56%, respectively. The performances of the four models during the polar days are obviously worse than those during the polar nights. In the AIS and AO, the Galileo broadcast NeQuick outperforms the GPS broadcast Klobuchar, and the root-mean-square error of IRI2016 performs almost the same as NeQuick2, but IRI2016 has a greater deviation. In addition, the GIM model can only mitigate the ionospheric delay by 46.81–56.72%, which is lower than other regions due to the lack of GPS ground station observations. Under the WSA conditions, the four models underestimate the real TEC to varying degrees, and the night-time deviations of the Klobuchar, NeQuick2 and IRI2016 models are significantly greater than the daytime deviations. The relative accuracy of four ionospheric models is lower during the ionospheric storm period than that in the ionospheric quiet period, especially the NeQuick2 and IRI2016 over the Antarctic.

### Improved pitch-constrained ambiguity function method for integer ambiguity resolution in BDS/MIMU-integrated attitude determination

Mon, 04/01/2019 - 00:00
Abstract

The initialization is a critical step in the BeiDou Navigation Satellite System and microelectromechanical inertial measurement unit (MIMU)-integrated attitude determination. One of the primary tasks in the initializing process is integer ambiguity resolution. The rapidity and reliability of integer ambiguity resolution play a particularly important role in kinematic attitude determination. However, the common ambiguity function method (AFM) is time consuming and unreliable due to searching over the entire yaw and pitch range. In view of the fact that MIMU can provide initial pitch by self-alignment with the three-axis accelerometers, we present a pitch-constrained AFM (PCAFM) for single-epoch and single-frequency integer ambiguity resolution. Although only pitch information is available, both pitch and yaw search spaces can be constrained in PCAFM. The pitch search space is constrained by the initial pitch from MIMU, and then the yaw search candidates are reduced by the constrained pitch range with the mathematical relationship between yaw and pitch in the DD carrier-phase observation equation. Experimental results demonstrate that the yaw and pitch search candidates of PCAFM are greatly decreased by 67.55% and 97.51%, respectively. Meanwhile, the success rate of integer ambiguity resolution is improved compared with the AFM.

### Multi-GNSS satellite clock estimation constrained with oscillator noise model in the existence of data discontinuity

Mon, 04/01/2019 - 00:00
Abstract

During the past years, real-time precise point positioning has been proven to be an efficient tool in the applications of navigation, precise orbit determination of LEO as well as earthquake and tsunami early warning, etc. One of the most crucial issues of these applications is the high-precision real-time GNSS satellite clock. Though the performance and character of the GNSS onboard atomic frequency standard have been widely studied, the white noise model is still the most popular hypothesis that employed in the real-time GNSS satellite clock estimation. However, concerning the real-time applications, significant data discontinuity may arise either due to the fact that only regional stations involved, or the failure in the stations, satellites and network connections. These data discontinuity would result in an arbitrary clock jump between adjacent arcs when the clock offsets are modeled as white noise. In addition, it is also expected that the detection and identification of outliers would be benefited from the constrains of the satellite oscillator noise model. Thus in this contribution, based on the statistic analysis of almost 2-year multi-GNSS precise clock products, we developed the oscillator noise model for the satellites of GPS, GLONASS, BDS and Galileo according to the oscillator type as well as the block type. Then, the efficiency of this oscillator noise model in multi-GNSS satellite clock estimation is demonstrated with 2-months data for both regional and global networks in simultaneous real-time mode. For the regional network, the results suggest that compared with the traditional solution based on white noise model, the improvement is 44.4 and 12.1% on average for STD and RMS, respectively, and the improvement is mainly attributed to the efficiency of the oscillator noise model during the convergence period and the gross error resistance. Concerning the global experiment, since the stations guarantee the continuous tracking of the satellites with redundant observable, the improvement is not as evident as that of regional experiment for GPS, GLONASS and BDS. The STD of Galileo clock improves from 0.28 to 0.19 ns due to that, the satellites E14 and E18 still suffer significant data discontinuity during our experimental period.

### Refining ionospheric delay modeling for undifferenced and uncombined GNSS data processing

Mon, 04/01/2019 - 00:00
Abstract

To access the full capabilities of multi-frequency signals from the modernized GPS, GLONASS and newly deployed BDS, Galileo, the undifferenced and uncombined observable model in which the individual signal of each frequency is treated as independent observable has drawn increasing interest in GNSS community. The ionosphere delay is the major issue in the undifferenced and uncombined observable model. Though several ionosphere delay parameterization approaches have been promoted, we argue that the functional model with only deterministic characteristic may not follow the irregular spatial and temporal variations. On the contrary, when the ionosphere delay is estimated as random walk or even white noise with only stochastic characteristic, the ionosphere terms turn out to be non-estimable or not sensitive to their absolute value. In the authors’ previous study, we have developed the deterministic plus stochastic ionosphere model, denoted as DESIGN, in which the deterministic part expressed with second-order polynomial is estimated as piece-wise constant over 5 min and the stochastic part is estimated as random walk with constrains derived based on statistics of 4 weeks data in 2010. In this contribution, we further model the deterministic part with Fourier series and update the variogram of the stochastic part accordingly based on two-year data collected by about 150 stations. From the statistic studies, it is concluded that the main frequency components are identical for different coefficients, different stations, as well as different ionosphere activity status, but with varying amplitude. Thus, in the Fourier series expression of the deterministic part, we fix the frequency and estimate the amplitude as daily constant unknowns. Concerning the stochastic component, the variation of variogram is both, geomagnetic latitude and ionosphere activity status dependent. Thus, we use the Gaussian function and Epstein function to model the variation of geomagnetic latitude and ionosphere activity status, respectively. Based on the undifferenced and uncombined observable model with ionosphere constrained with DESIGN, both dual-frequency and single-frequency PPP are carried out to demonstrate its efficiency with three-month data collected in 2010, 2014, and 2017 with different ionosphere activity status. The experimental results suggest that compared with ionosphere-free model and our previous method, the averaged 3D improvement of our new method is 17.8 and 7.6% for dual-frequency PPP, respectively. While for single-frequency PPP, the averaged 3D improvement is 37.0 and 14%, respectively.

### GPS inter-frequency clock bias estimation for both uncombined and ionospheric-free combined triple-frequency precise point positioning

Mon, 04/01/2019 - 00:00
Abstract

The time-varying biases within carrier phase observations will be integrated with satellite clock offset parameters in the precise clock estimation. The inconsistency among signal-dependent phase biases within a satellite results in the inadequacy of the current L1/L2 ionospheric-free (IF) satellite clock products for the GPS precise point positioning (PPP) involving L5 signal. The inter-frequency clock bias (IFCB) estimation approaches for triple-frequency PPP based on either uncombined (UC) observations or IF combined observations within a single arbitrary combination are proposed in this study. The key feature of the IFCB estimation approaches is that we only need to obtain a set of phase-specific IFCB (PIFCB) estimates between the L1/L5 and L1/L2 IF satellite clocks, and then, we can directly convert the obtained L1/L5 IF PIFCBs into L5 UC PIFCBs and L1/L2/L5 IF PIFCBs by multiplying individual constants. The mathematical conversion formula is rigorously derived. The UC and IF triple-frequency PPP models are developed. Datasets from 171 stations with a globally even distribution on seven consecutive days were adopted for analysis. After 24-h observation, the UC and IF triple-frequency PPP without PIFCB corrections can achieve an accuracy of 8, 6 and 13 mm, and 8, 5 and 13 mm in east, north and up coordinate components, respectively, while the corresponding positioning accuracy of the cases with PIFCB consideration can be improved by 38, 33 and 31%, and 50, 40 and 23% to 5, 4 and 9 mm, and 4, 3 and 10 mm in the three components, respectively. The corresponding improvement in convergence time is 17, 1 and 22% in the three components in UC model, respectively. Moreover, the phase observation residuals on L5 frequency in UC triple-frequency PPP and of L1/L2/L5 IF combination in IF triple-frequency PPP are reduced by about 4 mm after applying PIFCB corrections. The performance improvement in UC triple-frequency PPP over UC dual-frequency PPP is 7, 4 and 2% in terms of convergence time in the three components, respectively. The daily solutions of UC triple-frequency PPP have a comparable positioning accuracy to the UC dual-frequency PPP.

### High-quality three-dimensional displacement fields from new-generation SAR imagery: application to the 2017 Ezgeleh, Iran, earthquake

Mon, 04/01/2019 - 00:00
Abstract

Mapping the three-dimensional (3D) displacement fields associated with a variety of geological phenomena has been widely performed by exploiting synthetic aperture radar (SAR) imagery, as the result is important for providing insight into the formation mechanisms and potential risks of geological hazards. New-generation SAR sensors, namely ALOS-2 and Sentinel-1, can capture surface deformation with a high coherence in wide-swath mode, thereby providing outstanding across-track displacement accuracies; however, this improvement partially sacrifices the azimuth resolution, which affects the retrieval of 3D surface deformation fields. To explore the feasibility of generating 3D deformation maps with new SAR imagery, we collect two pairs of ALOS-2 ScanSAR and four pairs of Sentinel-1 Terrain Observation by Progressive Scans (TOPS) images for the 12 November 2017 Ezgeleh earthquake. Furthermore, the differential interferometric SAR (DInSAR), pixel offset tracking (POT), multiple-aperture InSAR (MAI), and burst-overlap interferometry (BOI) methods are used to measure the across- and along-track displacements. Compared with the POT and MAI methods, the integration of DInSAR and BOI measurements provides high-quality 3D deformation maps with an accuracy of 4 cm, which is four times and two times better than the accuracies of the POT and MAI methods integrated with DInSAR, respectively. In addition, a significant north–south displacement of 0.76 m is found in our 3D deformation results that was underestimated in the slip distribution model constrained with seismic waveforms or InSAR measurements. Our 3D deformation map of the 2017 Ezgeleh earthquake indicates a southwestward horizontal motion and an upward motion without any corresponding surface rupture that effectively match the behavior of a blind rupture along a northeast-dipping reverse fault. We conclude that combining BOI with DInSAR would provide a better 3D deformation field and should be applied to study future earthquakes.

### A new relationship between the quality criteria for geodetic networks

Mon, 04/01/2019 - 00:00
Abstract

The goal of this paper is to present a new relationship between the quality criteria for geodetic networks. The quality criteria described here are fourfold: positional uncertainty of network points, considering both bias and precision (at a given confidence level); the maximum allowable number of undetected outliers; the level of reliability and its homogeneity for the observations; and the minimum power of the data snooping test procedure for multiple alternative hypotheses. The highlights consist of the use of advanced concepts, such as reliability measures for multiple outliers and the power of the test for multiple alternative hypotheses (instead of the single outlier and/or the single alternative hypothesis case); and a sequential computational procedure, wherein the quality criteria are mathematically related, instead of being treated as separate criteria. Its practical application is demonstrated numerically in the design of a real horizontal network. A satisfactory performance was achieved by means of simulations. Furthermore, Monte Carlo experiments were conducted to verify the power of the test and the positional uncertainty following the approach proposed. Results provide empirical evidence that the quality criteria present realistic outputs.

Mon, 04/01/2019 - 00:00

### The ILRS: approaching 20 years and planning for the future

Tue, 03/19/2019 - 00:00
Abstract

The International Laser Ranging Service (ILRS) was established by the International Association of Geodesy (IAG) in 1998 to support programs in geodesy, geophysics, fundamental constants and lunar research, and to provide the International Earth Rotation Service with data products that are essential to the maintenance and improvement in the International Terrestrial Reference Frame (ITRF), the basis for metric measurements of changes in the Earth and Earth–Moon system. Other scientific products derived from laser ranging include precise geocentric positions and motions of ground stations, satellite orbits, components of Earth’s gravity field and their temporal variations, Earth Orientation Parameters, precise lunar ephemerides and information about the internal structure of the Moon. Laser ranging systems are already measuring the one-way distance to remote optical receivers in space and are performing very accurate time transfer between remote sites in the Earth and in Space. The ILRS works closely with the IAG’s Global Geodetic Observing System. The ILRS develops (1) the standards and specifications necessary for product consistency, and (2) the priorities and tracking strategies required to maximize network efficiency. The service collects, merges, analyzes, archives and distributes satellite and lunar laser ranging data to satisfy a variety of scientific, engineering, and operational needs and encourages the application of new technologies to enhance the quality, quantity, and cost effectiveness of its data products. The ILRS works with (1) new satellite missions in the design and building of retroreflector targets to maximize data quality and quantity, and (2) science programs to optimize scientific data yield. Since its inception, the ILRS has grown to include forty laser ranging stations distributed around the world. The ILRS stations track more than ninety satellites from low Earth orbit (LEO) to the geosynchronous orbit altitude as well as retroreflector arrays on the surface of the Moon. Applications have been expanded to include time transfer, asynchronous ranging for targets at extended ranges, free space quantum telecommunications, and the tracking of space debris. Laser ranging technology is moving to lower energy, higher repetition rates (kHz), single-photon-sensitive detectors, shorter pulse widths, shorter normal point intervals for faster data acquisition, and increased pass interleaving, automated to autonomous operation with remote access, and embedded software for real-time updates and decision making. An example of pass interleaving is presented for the Yarragadee station (see Fig. 4); tracking of LEO satellites is often accommodated during break in LEO and GNSS passes. New satellites arrays provide more compact targets and work continues on the development of lighter less expensive arrays for satellites and the moon. The service now provides operational ITRF products including daily/weekly station positions and daily resolution Earth orientation products; the flow of weekly combination of satellite orbit files for LAGEOS/Etalon-1 and -2 has recently been established. New products are under testing through a pilot project on systematic error monitoring currently underway. The article will give an overview of activities underway within the service, paths forward presently envisioned, and current issues and challenges.

### Investigation of the noise properties at low frequencies in long GNSS time series

Thu, 03/14/2019 - 00:00
Abstract

The accuracy by which velocities can be estimated from GNSS time series is mainly determined by the low-frequency noise, below 0.2–0.1 cpy, which are normally described by a power-law model. As GNSS observations have now been recorded for over two decades, new information about the noise at these low frequencies has become available and we investigate whether alternative noise models should be considered using the log-likelihood, Akaike and Bayesian information criteria. Using 110 globally distributed IGS stations with at least 12 years of observations, we find that for 80–90% of them the preferred noise models are still the power law or flicker noise with white noise. For around 6% of the stations, we found the presence of random-walk noise, which increases the linear trend uncertainty when taken into account in the stochastic noise model of the time series by about a factor of 1.5 to 8.4, in agreement with previous studies. Next, the Generalised Gauss–Markov with white noise model describes the stochastic properties better for 4% and 5% of the stations for the East and North component, respectively, and 13% for the vertical component. For these stations, the uncertainty associated with the tectonic rate is about 2 times smaller compared to the case when the standard power-law plus white noise model is used.

### Apparent calibration shift of the Scintrex CG-5 gravimeter caused by reading-dependent scale factor and instrumental drift

Mon, 03/11/2019 - 00:00
Abstract

Calibration measurements of the Scintrex CG-5 gravimeter were conducted using absolute gravity stations of the Japan Gravity Standardization Net, to constrain the scale factor and its temporal changes. The calibration data were obtained from a total gravity interval of 1.4 Gal through six campaigns, conducted for over 5 years between years 2012 and 2017. The scale factors varied by 1500 ppm in a range from 0.9991 to 1.0006, according to station combinations of the six campaigns. The scale factor depends primarily on the gravity reading ranges: for similar gravity reading ranges, no significant differences in the estimated scale factors were recognised, even though station combinations and observed times are different. Therefore, the gravity readings can be corrected by introducing a gravity reading-dependent scale factor. Furthermore, even though the scale factor essentially depends on gravity readings and not on time, temporal changes were observed during repeated calibration measurements at the same station combinations. A long-term instrumental drift of the CG-5 gravimeter could explain this phenomenon. In conclusion, the calibration shifts recognised during repeated measurements were apparently caused by: (1) the scale factor dependence on the gravity reading ranges and (2) the shift of the gravity reading ranges due to the instrumental drift.

### Operating two SLR systems at the Geodetic Observatory Wettzell: from local survey to space ties

Mon, 03/11/2019 - 00:00
Abstract

The present paper provides an overview on the design of a new Satellite Laser Ranging (SLR) system, the Satellite Observing System Wettzell (SOS-W). It pays special attention on the local survey, the determination and monitoring of the ties between the established Wettzell Laser Ranging System (WLRS) and the SOS-W. We also introduce an alternative normal point algorithm, which demonstrated fewer systematics in the resulting normal point statistics compared to the standard approach of iterative data editing. Having two highly productive SLR stations on site allows for a rigorous comparison between local survey derived ties and space segment derived ties. One-year observations to the Laser Geodynamic Satellite (LAGEOS) have been processed, and a multitude of different solutions has been calculated. The results show agreement in the sub-millimeter range with respect to the local survey.

### Mapping ground displacement by a multiple phase difference-based InSAR approach: with stochastic model estimation and turbulent troposphere mitigation

Sat, 03/09/2019 - 00:00
Abstract

Tropospheric delay is one of the dominant error sources of interferometric synthetic aperture radar when measuring ground displacement. Although many methods have been presented for the correction of tropospheric effects, a large portion of them (such as the numerical weather models and the topography-correlated analysis methods) can only be used to correct the stratified delays (i.e., topography-related delays), and it is still intractable for mitigating the turbulent effects. Considering that the approximate displacement extent over an interested region often can be known based on some prior geophysical or geological information, we present here a new method to mitigate the effects of atmospheric turbulence by fusing multiple phase differences (MPDs) between the pixel of interest and those pixels whose displacement can be ignored or can be known based on external displacement datasets (e.g., from other geodetic observations). Our method involves estimating the stochastic model, i.e., variance–covariance matrix, of the MPDs for each pixel and then reconstructing the ground displacement pixel by pixel using a proposed minimum variance-based linear estimator. Two advantages of the proposed method are that: (1) no external atmospheric data are required; (2) uncertainties of the reconstructed displacements can be provided as well. In addition, our method is implemented interferogram by interferogram, so we do not need time series of InSAR datasets. The performance of the proposed approach is tested by using both simulated datasets and the real data over Mexico City regions, and the experimental results show that our method can mitigate the turbulent atmosphere efficiently and robustly, which is of great interest to a wide community of geodesists and geophysicists.

### Improving reliability and efficiency of RTK ambiguity resolution with reference antenna array: BDS + GPS analysis and test

Sat, 03/09/2019 - 00:00
Abstract

Rapid and reliable ambiguity resolution is the key to high-precision global navigation satellite system-based applications. To improve the efficiency and reliability of ambiguity resolution, one effective method is equipping the reference station with an antenna array of known geometry instead of a single antenna. In this contribution, the benefits of reference antenna array-aided real-time kinematic (RTK) positioning are investigated. The mathematical relations between the number of reference antennas and the float baseline and ambiguity solutions are explored, and the closed-form formula of ambiguity dilution of precision (ADOP) is further presented. It is demonstrated that the maximum decrease in ADOP or the improvement in precision of float solutions is approximately 29.29% with the increase in the number of reference antennas. Then, we analyze the impact of errors (noises or biases) on the float baseline and ambiguity solutions. Finally, the performance of the array-aided RTK is evaluated with raw BDS and GPS observations in terms of the ambiguity resolution success rate, false alarm, wrong detection alarm, and the time-to-first-fix (TTFF). It is demonstrated that the array-aided RTK can deliver improved ambiguity success rates with respect to the standard one-reference-antenna RTK, especially when only single-frequency, single-system observations from fewer satellites are available. Moreover, the array-aided RTK can provide much more robust ambiguity resolution in the presence of biases. And the performance of suppressing false alarm and wrong detection alarm is improved as well. Additionally, the TTFF with single-frequency observations is also significantly shortened. One order of magnitude improvements in TTFF are achieved for most of the cases from the standard one-reference-antenna solutions to the three-reference-antenna solutions. The results confirm that the array-aided RTK ensures more reliable and efficient ambiguity resolution.

### Improved 90-day Earth orientation predictions from angular momentum forecasts of atmosphere, ocean, and terrestrial hydrosphere

Fri, 03/01/2019 - 00:00
Abstract

Short-term forecasts of atmospheric, oceanic, and hydrological effective angular momentum functions (EAM) of Earth rotation excitation are combined with least-squares extrapolation and autoregressive modeling to routinely predict polar motion (PM) and $$\Delta \hbox {UT1}$$ for up to 90 days into the future. Based on hindcast experiments covering the years 2016 and 2017, a best performing parametrization was elaborated. At forecast horizons of 10 days, remaining prediction errors are 3.02 and 5.39 mas for PM and $$\Delta \hbox {UT1}$$ , respectively, corresponding to improvements of 34.5 and 44.7% when compared to predictions reported routinely in Bulletin A of the International Earth Rotation and Reference Systems Service. At forecast horizons of 60 days, prediction errors are 12.52 and 107.96 mas for PM and $$\Delta \hbox {UT1}$$ , corresponding to improvements of 34.5 and 8.2% over Bulletin A. The 90-day-long EAM forecasts leading to those improved EOP predictions are routinely published on a daily basis at isdc.gfz-potsdam.de/esmdata/eam.

### Towards thermospheric density estimation from SLR observations of LEO satellites: a case study with ANDE-Pollux satellite

Fri, 03/01/2019 - 00:00
Abstract

The present contribution investigates the possibility to obtain thermospheric neutral density estimates using satellite laser ranging (SLR) observations of low Earth orbiters (LEOs). This approach is based on the analysis of the satellite atmospheric drag, driven by the fact that the drag force is the largest non-gravitational perturbation acting on LEOs. Due to the uncertainty of current thermospheric models, it is the main error source in the LEO orbit determination process. Moreover, the drag is physically related to the thermospheric density distribution, the interaction of the satellite surface with the surrounding thermosphere and thermospheric winds. For this investigation, a spherical satellite called “Atmospheric Neutral Density Experiment-Pollux” (ANDE-P) developed by the Naval Research Laboratory (USA) is adopted as a case study. The satellite flew at the very low altitude of about 350 km. The most important perturbing acceleration at this altitude, the atmospheric drag, is easier to model for a spherical satellite like ANDE-P than for a satellite of complex geometry. A precise orbit determination of ANDE-P was performed with the DGFI Orbit and Geodetic parameter estimation Software (DOGS) over a period of 49 days (16 August 2009 until 3 October 2009) using SLR observations to this satellite and different thermospheric models. In total, we tested four thermospheric models, namely CIRA86, NRLMSISE00, JB2008 and DTM2013. Correspondingly, scale factors of these reference models are estimated with a 6-h resolution. The results confirm that the estimation of force model parameters from SLR measurements of the ANDE-P satellite is sensitive to differences in the density distributions provided by different models. As a consequence, information on the discrepancies between the various models and the true density can be derived from SLR measurements. Moreover, it is found that SLR observations to LEO satellites at very low altitudes are capable to estimate corrections to (scale factors of) the integrated thermospheric density if all other perturbing accelerations are modelled with sufficient accuracy. We derived time series of estimated scale factors of the thermospheric densities provided by the models and obtained the following mean values during the processed period of time at the ANDE-P altitude: $$0.65\pm 0.26$$ for CIRA86, $$0.65\pm 0.25$$ for NRLMSISE00, $$0.79\pm 0.24$$ for DTM2013, and $$0.89\pm 0.27$$ for JB2008. This suggests that all models overestimate the true thermospheric density along the ANDE-P trajectory during the processed period to a certain extent. The thermospheric densities need to be scaled downwards to fit ANDE-P SLR observations with JB2008 requiring the least amount of scaling.

### Performance analysis of dual-frequency receiver using combinations of GPS L1, L5, and L2 civil signals

Fri, 03/01/2019 - 00:00
Abstract

Processing of GNSS signals from more than one frequency band enhances the accuracy and integrity of a position solution in both standalone and differential positioning. The modern GPS program and newly launched GNSS systems such as GALILEO, BeiDou allow civilians to access signals from multiple frequencies in the L-band spectrum. While there are some advantages in triple-frequency processing in carrier phase applications, in general most of the standalone kinematic receivers get benefit from dual-frequency signals for ionosphere error correction. In implementing a dual-frequency receiver, it is necessary to select a combination of frequencies leading to an optimum performance of the existing civilian signals. In the current research work, we have analyzed the performance of dual-frequency receiver in terms of combined signal observation noise, sensitivity and robustness using analytical models by taking the combination of GPS L1, L2C and L5 signals as an example. Further, we have investigated the benefits of common Doppler estimate-based two-frequency signal tracking to reduce the noise in linear combination of observations. Through analytical and experimental results, it is confirmed that the L1/L5 signal combination in GPS system has low observation noise, which is suitable to use in high accuracy and precise positioning applications using standalone dual-frequency receiver. Further, it is shown that common Doppler estimate-based dual-frequency signal tracking has improved receiver tracking loop performance in terms of observation noise and multipath in linear combination of observations and enhanced receiver sensitivity and robustness. In GPS system, L1/L5 signals processed using common Doppler estimate-aided two-frequency signal tracking architecture, it is possible to effectively mitigate ionosphere delay and other receiver observation errors, to achieve less than 1 m position accuracy using unambiguous code phase observations. Proposed analysis is applicable of finding an optimal two-frequency signal combination in multi-frequency GNSS system and suitable signal processing architecture to obtain high accuracy and precise ionosphere-free position solution using code phase observations in standalone dual-frequency receiver.

### Geometry-based cycle slip and data gap repair for multi-GNSS and multi-frequency observations

Fri, 03/01/2019 - 00:00
Abstract

Carrier phase observations are commonly used in high-precision GNSS positioning applications, such as precise point positioning and real-time kinematic positioning, due to their millimeter precisions. Hence, it is a crucial module to handle cycle slips and short-time signal interruptions when phase observations are involved, which otherwise will lead to a time-consuming re-initialization. With the gradual GNSS modernization, jointly using observations from multi-GNSS and multi-frequency tends to be a hotspot application pattern for high-accuracy positioning. In this contribution, we will present a geometry-based ionosphere-weighted approach to estimate integer cycle slips in an integrated adjustment, which is universally applicable to arbitrary number of frequencies of GNSS systems. Different from the traditional methods, where cycle slips are processed in a satellite-by-satellite mode based on geometry-free combinations, we take full advantage of the mutual correlations between multi-frequency, between satellites and between systems embodied in the receiver coordinate parameters. When it is unable to effectively fix the full set of cycle slips, we further propose to partially fix the subset of cycle slips that can be reliably fixed. Performance of the proposed method is validated by extensive experiments using undifferenced dual/triple-frequency BDS data, dual-frequency GPS data and triple-frequency BDS  $$+$$  dual-frequency GPS data. The results show that the proposed method can effectively fix continuous cycle slips in case of small/large sampling intervals and connect the data gaps up to a few minutes with high success rates.

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