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21 pages, 5860 KiB

Open AccessArticle

Analysis of Different Weighting Functions of Observations for GPS and Galileo Precise Point Positioning Performance

by Damian Kiliszek, Krzysztof Kroszczyński and Andrzej Araszkiewicz

Remote Sens. 2022, 14(9), 2223; https://doi.org/10.3390/rs14092223 - 6 May 2022

Cited by 6 | Viewed by 2776

Abstract

This research presents the analysis of using different weighting functions for the GPS and Galileo observations in Precise Point Positioning (PPP) performance for globally located stations for one week in 2021. Eight different weighting functions of observations dependent on the elevation angle have [...] Read more.

This research presents the analysis of using different weighting functions for the GPS and Galileo observations in Precise Point Positioning (PPP) performance for globally located stations for one week in 2021. Eight different weighting functions of observations dependent on the elevation angle have been selected. It was shown that the use of different weighting functions has no impact on the horizontal component but has a visible impact on the vertical component, the tropospheric delay and the convergence time. Depending on the solutions, i.e., GPS-only, Galileo-only or GPS+Galileo, various weighting functions turned out to the best. The obtained results confirm that the Galileo solution has comparable accuracy to the GPS solution. Also, with the Galileo solution, the best results were obtained for functions with a smaller dependence on the elevation angle than for GPS, since Galileo observations at lower elevation angles have better performance than GPS observations. Finally, a new weighting approach was proposed, using two different weighting functions from the best GPS-only and Galileo-only for GPS+Galileo solution. This approach improves the results by 5% for convergence time and 30% for the troposphere delay when compared to using the same function. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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19 pages, 5648 KiB

Open AccessArticle

Improving the Orbits of the BDS-2 IGSO and MEO Satellites with Compensating Thermal Radiation Pressure Parameters

by Chen Wang, Jing Guo, Qile Zhao and Maorong Ge

Remote Sens. 2022, 14(3), 641; https://doi.org/10.3390/rs14030641 - 28 Jan 2022

Cited by 8 | Viewed by 2909

Abstract

The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou [...] Read more.

The orbit accuracy of the navigation satellites relies on the accurate knowledge of the forces on the spacecraft, in particular the non-conservative perturbations. This study focuses on the Inclined Geosynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites of the regional Chinese BeiDou Navigation Satellite System (BDS-2), for which apparent deficiencies of non-conservative models are identified and evidenced in the Satellite Laser Ranging (SLR) residuals. The orbit errors derived from the empirical 5-parameter Extended CODE Orbit Model (ECOM) as well as a semi-analytical adjustable box-wing model show prominent dependency on the Sun elongation angle, even in the yaw-steering attitude mode. Hence, a periodic acceleration in the normal direction of the +X surface, presumably generated by the mismodeled thermal radiation pressure, is introduced. The SLR validations reveal that the Sun elongation angle-dependent systematic errors were significantly reduced, and the orbit accuracy was improved by 10–30% to approximately 4.5 cm and 3.0 cm for the BDS-2 IGSO and MEO satellites, respectively. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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17 pages, 6730 KiB

Open AccessArticle

Performance Assessment of BDS-2/BDS-3/GPS/Galileo Attitude Determination Based on the Single-Differenced Model with Common-Clock Receivers

by Mingkui Wu, Shuai Luo, Wang Wang and Wanke Liu

Remote Sens. 2021, 13(23), 4845; https://doi.org/10.3390/rs13234845 - 29 Nov 2021

Cited by 7 | Viewed by 2196

Abstract

Global navigation satellite system (GNSS)-based attitude determination has been widely applied in a variety of fields due to its high precision, no error accumulation, low power consumption, and low cost. Recently, the emergence of common-clock receivers and construction of GNSS systems have brought [...] Read more.

Global navigation satellite system (GNSS)-based attitude determination has been widely applied in a variety of fields due to its high precision, no error accumulation, low power consumption, and low cost. Recently, the emergence of common-clock receivers and construction of GNSS systems have brought new opportunities for high-precision GNSS-based attitude determination. In this contribution, we focus on evaluating the performance of the BeiDou regional navigation satellite system (BDS-2)/BeiDou global navigation satellite system (BDS-3)/Global Positioning System (GPS)/Galileo navigation satellite system (Galileo) attitude determination based on the single-differenced (SD) model with a common-clock receiver. We first investigate the time-varying characteristics of BDS-2/BDS-3/GPS/Galileo line bias (LB) with two different types of common-clock receivers. The results have confirmed that both the phase and code LBs are relatively stable in the time domain once the receivers have started. However, the phase LB is expected to change to an arbitrary value after each restart of the common-clock receivers. For the first time, it is also found that the phase LBs of overlapping frequencies shared by different GNSS systems are identical. Then, we primarily evaluated the performance of BDS-2/BDS-3/GPS/Galileo precise relative positioning and attitude determination based on the SD model with a common-clock receiver, using a static dataset collected at Wuhan. Experimental results demonstrated that, compared with the double-differenced (DD) model, the SD model can deliver a comparable root–mean–square (RMS) error of yaw but a significantly smaller RMS error of pitch, whether for BDS-2, BDS-3, GPS, or Galileo alone or a combination of them. The improvements of pitch accuracy are approximately 20.8–47.5% and 40.7–57.5% with single- and dual-frequency observations, respectively. Additionally, BDS-3 can deliver relatively superior positioning and attitude accuracy with respect to GPS and Galileo, due to its better geometry. The three-dimensional positioning and attitude (including yaw and pitch) accuracy for both the DD and SD models can be remarkably improved by the BDS-2, BDS-3, GPS, and Galileo combination with respect to a single system alone. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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44 pages, 7500 KiB

Open AccessArticle

Broadcast Ephemeris with Centimetric Accuracy: Test Results for GPS, Galileo, Beidou and Glonass

by Alessandro Caporali and Joaquin Zurutuza

Remote Sens. 2021, 13(20), 4185; https://doi.org/10.3390/rs13204185 - 19 Oct 2021

Cited by 5 | Viewed by 3611

Abstract

Here we test the capability of the Broadcast Ephemeris Message, in both its GPS-like (Keplerian ellipse with secular and periodic perturbations) and Glonass-like (numerical integration of a 9D state vector) formats, to reproduce a corresponding precise ephemeris. We start from a daily Rinex [...] Read more.

Here we test the capability of the Broadcast Ephemeris Message, in both its GPS-like (Keplerian ellipse with secular and periodic perturbations) and Glonass-like (numerical integration of a 9D state vector) formats, to reproduce a corresponding precise ephemeris. We start from a daily Rinex 3.04 navigation file for multiple GNSS and the corresponding SP3 precise orbits computed by CNES (Centre National d’Etudes Spatiales) for GPS, Glonass, Galileo and CODE (Center for Orbit Determination in Europe) for Beidou, and compute broadcast ECEF coordinates and clocks. The pre-fit discrepancies are converted by least squares to corrections to the broadcast ephemeris parameters in two-hour consecutive arcs (for GPS, Galileo and Beidou) and to a set of seven Helmert parameters for the entire day, to align in origin, orientation and scale to the common GNSS IGS14 Reference Frame. The test cases suggest that the Broadcast Ephemeris Message, complemented with Reference Frame information, can reproduce the precise ephemeris and clocks with centimetric accuracy for intervals at least equal to the respective validity times, typically 2 h. The broadcast ephemeris of Glonass consists of three initial positions and velocities at epoch, three constant Lunisolar accelerations for the satellite position, and of three polynomial coefficients for the satellite clock. The 9D vector of state is numerically integrated to generate position and velocity data within the validity time (0.5 h) of the message. To test the capability of this model to reproduce the corresponding values of a precise ephemeris, the 9D vector of state and clock polynomials are adjusted until the rms (root mean squared spread) of the post-fit residuals relative to a precise orbit (CNES’s in our case) is minimum. We show in one example (one satellite for one day) that the Glonass type of message can reproduce a precise ephemeris and clock with a rms spread of 0.025 m over one-hour arcs. Volume computations on one month of data with all available satellites confirm the test results. For GPS, Glonass, Galileo and Beidou, the best fitting clock values predicted by our second order polynomials, based on a 15 min sampling, are shown to fit the corresponding high rate clocks (30 s sampling) of MGEX with zero bias and a rms spread of 0.062 ns (GPS G01), 0.023 ns (Galileo E01), 0.43 ns (Glonass R01), 0.086 ns (Beidou C07) and 0.086 ns (Beidou C12). Modifications to the GPS-like message structure and Glonass algorithm are proposed to increase the validity time by including the effect of the 3rd zonal harmonic of the Earth’s gravity field. The potential of the RTCM messages for broadcasting the improved navigation message is reviewed. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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18 pages, 3789 KiB

Open AccessArticle

Impact of Tropospheric Mismodelling in GNSS Precise Point Positioning: A Simulation Study Utilizing Ray-Traced Tropospheric Delays from a High-Resolution NWM

by Florian Zus, Kyriakos Balidakis, Galina Dick, Karina Wilgan and Jens Wickert

Remote Sens. 2021, 13(19), 3944; https://doi.org/10.3390/rs13193944 - 2 Oct 2021

Cited by 7 | Viewed by 3431

Abstract

In GNSS analysis, the tropospheric delay is parameterized by applying mapping functions (MFs), zenith delays, and tropospheric gradients. Thereby, the wet and hydrostatic MF are derived under the assumption of a spherically layered atmosphere. The coefficients of the closed-form expression are computed utilizing [...] Read more.

In GNSS analysis, the tropospheric delay is parameterized by applying mapping functions (MFs), zenith delays, and tropospheric gradients. Thereby, the wet and hydrostatic MF are derived under the assumption of a spherically layered atmosphere. The coefficients of the closed-form expression are computed utilizing a climatology or numerical weather model (NWM) data. In this study, we analyze the impact of tropospheric mismodelling on estimated parameters in precise point positioning (PPP). To do so, we mimic PPP in an artificial environment, i.e., we make use of a linearized observation equation, where the observed minus modelled term equals ray-traced tropospheric delays from a high-resolution NWM. The estimated parameters (station coordinates, clocks, zenith delays, and tropospheric gradients) are then compared with the known values. The simulation study utilized a cut-off elevation angle of 3° and the standard downweighting of low elevation angle observations. The results are representative of a station located in central Europe and the warm season. In essence, when climatology is utilized in GNSS analysis, the root mean square error (RMSE) of the estimated zenith delay and station up-component equal about 2.9 mm and 5.7 mm, respectively. The error of the GNSS estimates can be reduced significantly if the correct zenith hydrostatic delay and the correct hydrostatic MF are utilized in the GNSS analysis. In this case, the RMSE of the estimated zenith delay and station up-component is reduced to about 2.0 mm and 2.9 mm, respectively. The simulation study revealed that the choice of wet MF, when calculated under the assumption of a spherically layered troposphere, does not matter too much. In essence, when the ‘correct’ wet MF is utilized in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component remain at about 1.8 mm and 2.4 mm, respectively. Finally, as a by-product of the simulation study, we developed a modified wet MF, which is no longer based on the assumption of a spherically layered atmosphere. We show that with this modified wet MF in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component can be reduced to about 0.5 mm and 1.0 mm, respectively. In practice, its success depends on the ability of current (future) NWM to predict the fourth coefficient of the developed closed-form expression. We provide some evidence that current NWMs are able to do so. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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23 pages, 74104 KiB

Open AccessArticle

Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series

by Sorin Nistor, Norbert-Szabolcs Suba, Ahmed El-Mowafy, Michal Apollo, Zinovy Malkin, Eduard Ilie Nastase, Jacek Kudrys and Kamil Maciuk

Remote Sens. 2021, 13(17), 3478; https://doi.org/10.3390/rs13173478 - 2 Sep 2021

Cited by 3 | Viewed by 3286

Abstract

The seasonal signal determined by the Global Navigation Satellite System (GNSS), which is captured in the coordinate time series, exhibits annual and semi-annual periods. This signal is frequently modelled by two periodic signals with constant amplitude and phase-lag. The purpose of this study [...] Read more.

The seasonal signal determined by the Global Navigation Satellite System (GNSS), which is captured in the coordinate time series, exhibits annual and semi-annual periods. This signal is frequently modelled by two periodic signals with constant amplitude and phase-lag. The purpose of this study is to explore the implication of different types of geophysical events on the seasonal signal in three stages—in the time span that contains the geophysical events, before and after the geophysical event, but also the stationarity phenomena, which is analysed on approximately 200 reference stations from the EPN network since 1995. The novelty of the article is demonstrated by correlating three different types of geophysical events, such as earthquakes with a magnitude greater than 6° on the Richter scale, landslides, and volcanic activity, and analysing the variation in amplitude of the seasonal signal. The geophysical events situated within a radius of 30 km from the epicentre showed a higher seasonal value than when the timespan did not contain a geophysical event. The presence of flicker and random walk noise was computed using overlapping Hadamard variance (OHVAR) and the non-stationary behaviour of the time series of the CORS coordinates in the time frequency analysis was done using continuous wavelet transform (CWT). Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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23 pages, 7132 KiB

Open AccessArticle

Earth Rotation Parameters Estimation Using GPS and SLR Measurements to Multiple LEO Satellites

by Xingxing Li, Hongmin Zhang, Keke Zhang, Yongqiang Yuan, Wei Zhang and Yujie Qin

Remote Sens. 2021, 13(15), 3046; https://doi.org/10.3390/rs13153046 - 3 Aug 2021

Cited by 8 | Viewed by 3839

Abstract

Earth rotation parameters (ERP) are one of the key parameters in realization of the International Terrestrial Reference Frames (ITRF). At present, the International Laser Ranging Service (ILRS) generates the satellite laser ranging (SLR)-based ERP products only using SLR observations to Laser Geodynamics Satellite [...] Read more.

Earth rotation parameters (ERP) are one of the key parameters in realization of the International Terrestrial Reference Frames (ITRF). At present, the International Laser Ranging Service (ILRS) generates the satellite laser ranging (SLR)-based ERP products only using SLR observations to Laser Geodynamics Satellite (LAGEOS) and Etalon satellites. Apart from these geodetic satellites, many low Earth orbit (LEO) satellites of Earth observation missions are also equipped with laser retroreflector arrays, and produce a large number of SLR observations, which are only used for orbit validation. In this study, we focus on the contribution of multiple LEO satellites to ERP estimation. The SLR and Global Positioning System (GPS) observations of the current seven LEO satellites (Swarm-A/B/C, Gravity Recovery and Climate Experiment (GRACE)-C/D, and Sentinel-3A/B) are used. Several schemes are designed to investigate the impact of LEO orbit improvement, the ERP quality of the single-LEO solutions, and the contribution of multiple LEO combinations. We find that ERP estimation using an ambiguity-fixed orbit can attain a better result than that using ambiguity-float orbit. The introduction of an ambiguity-fixed orbit contributes to an accuracy improvement of 0.5%, 1.1% and 15% for X pole, Y pole and station coordinates, respectively. In the multiple LEO satellite solutions, the quality of ERP and station coordinates can be improved gradually with the increase in the involved LEO satellites. The accuracy of X pole, Y pole and length-of-day (LOD) is improved by 57.5%, 57.6% and 43.8%, respectively, when the LEO number increases from three to seven. Moreover, the combination of multiple LEO satellites is able to weaken the orbit-related signal existing in the single-LEO solution. We also investigate the combination of LEO satellites and LAGEOS satellites in the ERP estimation. Compared to the LAGEOS solution, the combination leads to an accuracy improvement of 0.6445 ms, 0.6288 ms and 0.0276 ms for X pole, Y pole and LOD, respectively. In addition, we explore the feasibility of a one-step method, in which ERP and the orbit parameters are jointly determined, based on SLR and GPS observations, and present a detailed comparison between the one-step solution and two-step solution. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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21 pages, 2849 KiB

Open AccessArticle

An Improved Single-Epoch Attitude Determination Method for Low-Cost Single-Frequency GNSS Receivers

by Xinzhe Wang, Yibin Yao, Chaoqian Xu, Yinzhi Zhao and Huan Zhang

Remote Sens. 2021, 13(14), 2746; https://doi.org/10.3390/rs13142746 - 13 Jul 2021

Cited by 8 | Viewed by 2552

Abstract

GNSS attitude determination has been widely used in various navigation and positioning applications, due to its advantages of low cost and high efficiency. The navigation positioning and attitude determination modules in the consumer market mostly use low-cost receivers and face many problems such [...] Read more.

GNSS attitude determination has been widely used in various navigation and positioning applications, due to its advantages of low cost and high efficiency. The navigation positioning and attitude determination modules in the consumer market mostly use low-cost receivers and face many problems such as large multipath effects, frequent cycle slips and even loss of locks. Ambiguity fixing is the key to GNSS attitude determination and will face more challenges in the complex urban environment. Based on the CLAMBDA algorithm, this paper proposes a CLAMBDA-search algorithm based on the multi-baseline GNSS model. This algorithm improves the existing CLAMBDA method through a fixed geometry constraint among baselines in the vehicle coordinate system. A fixed single-baseline solution reduces two degrees of freedom of vehicle rigid body, and a global minimization search for the ambiguity objective function in the other degree of freedom is conducted to calculate the baseline vector and its Euler angles. In addition, in order to make up for the shortcomings of short baseline ambiguity in complex environments, this paper proposes different validation strategies. Using three low-cost receivers (ublox M8T) and patch antennas, static and dynamic on-board experiments with different baseline length set-ups were carried out in different environments. Both the experiments prove that the method proposed in this paper has greatly improved the ambiguity fixing performance and also the Euler angle calculation accuracy, with an acceptable calculation burden. It is a practical vehicle-mounted attitude determination algorithm. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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22 pages, 5960 KiB

Open AccessArticle

TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere

by Di Zhang, Jiming Guo, Tianye Fang, Na Wei, Wensheng Mei, Lv Zhou, Fei Yang and Yinzhi Zhao

Remote Sens. 2021, 13(13), 2568; https://doi.org/10.3390/rs13132568 - 30 Jun 2021

Cited by 4 | Viewed by 3188

Abstract

Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity [...] Read more.

Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles—Tilting Mapping Function (TMF)—was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg–Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay’s accuracy by 73%, 54% and 29% at the 5° elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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22 pages, 2180 KiB

Open AccessArticle

Enhanced Neural Network Model for Worldwide Estimation of Weighted Mean Temperature

by Fengyang Long, Chengfa Gao, Yuxiang Yan and Jinling Wang

Remote Sens. 2021, 13(12), 2405; https://doi.org/10.3390/rs13122405 - 19 Jun 2021

Cited by 5 | Viewed by 2455

Abstract

Precise modeling of weighted mean temperature (

T_{m}

) is critical for realizing real-time conversion from zenith wet delay (ZWD) to precipitation water vapor (PWV) in Global Navigation Satellite System (GNSS) meteorology applications. The empirical

T_{m}

models developed by neural network [...] Read more.

Precise modeling of weighted mean temperature (

T_{m}

) is critical for realizing real-time conversion from zenith wet delay (ZWD) to precipitation water vapor (PWV) in Global Navigation Satellite System (GNSS) meteorology applications. The empirical

T_{m}

models developed by neural network techniques have been proved to have better performances on the global scale; they also have fewer model parameters and are thus easy to operate. This paper aims to further deepen the research of

T_{m}

modeling with the neural network, and expand the application scope of

T_{m}

models and provide global users with more solutions for the real-time acquisition of

T_{m}

. An enhanced neural network

T_{m}

model (ENNTm) has been developed with the radiosonde data distributed globally. Compared with other empirical models, the ENNTm has some advanced features in both model design and model performance, Firstly, the data for modeling cover the whole troposphere rather than just near the Earth’s surface; secondly, the ensemble learning was employed to weaken the impact of sample disturbance on model performance and elaborate data preprocessing, including up-sampling and down-sampling, which was adopted to achieve better model performance on the global scale; furthermore, the ENNTm was designed to meet the requirements of three different application conditions by providing three sets of model parameters, i.e.,

T_{m}

estimating without measured meteorological elements,

T_{m}

estimating with only measured temperature and

T_{m}

estimating with both measured temperature and water vapor pressure. The validation work is carried out by using the radiosonde data of global distribution, and results show that the ENNTm has better performance compared with other competing models from different perspectives under the same application conditions, the proposed model expanded the application scope of

T_{m}

estimation and provided the global users with more choices in the applications of real-time GNSS-PWV retrival. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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23 pages, 5737 KiB

Open AccessArticle

Analysis of the Impact of Multipath on Galileo System Measurements

by Dominik Prochniewicz and Maciej Grzymala

Remote Sens. 2021, 13(12), 2295; https://doi.org/10.3390/rs13122295 - 11 Jun 2021

Cited by 22 | Viewed by 3730

Abstract

Multipath is one of the major source of errors in precise Global Navigation Satellite System positioning. With the emergence of new navigation systems, such as Galileo, upgraded signals are progressively being used and are expected to provide greater resistance to the effects of [...] Read more.

Multipath is one of the major source of errors in precise Global Navigation Satellite System positioning. With the emergence of new navigation systems, such as Galileo, upgraded signals are progressively being used and are expected to provide greater resistance to the effects of multipath compared to legacy Global Positioning System (GPS) signals. The high quality of Galileo observations along with recent development of the Galileo space segment can therefore offer significant advantages to Galileo users in terms of the accuracy and reliability of positioning. The aim of this paper is to verify this hypothesis. The multipath impact was determined both for code and phase measurements as well as for positioning results. The code multipath error was determined using the Code-Minus-Carrier combination. The influence of multipath on phase observations and positioning error was determined using measurements on a very short baseline. In addition, the multipath was classified into two different types: specular and diffuse, using wavelet transform. The results confirm that the Galileo code observations are more resistant to the multipath effect than GPS observations. Among all of the observations examined, the lowest values of code multipath errors were recorded for the Galileo E5 signal. However, no advantage of Galileo over GPS was observed for phase observations and for the analysis of positioning results. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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18 pages, 3948 KiB

Open AccessArticle

An Improved Multipath Mitigation Method and Its Application in Real-Time Bridge Deformation Monitoring

by Ruicheng Zhang, Chengfa Gao, Qing Zhao, Zihan Peng and Rui Shang

Remote Sens. 2021, 13(12), 2259; https://doi.org/10.3390/rs13122259 - 9 Jun 2021

Cited by 4 | Viewed by 2601

Abstract

A multipath is a major error source in bridge deformation monitoring and the key to achieving millimeter-level monitoring. Although the traditional MHM (multipath hemispherical map) algorithm can be applied to multipath mitigation in real-time scenarios, accuracy needs to be further improved due to [...] Read more.

A multipath is a major error source in bridge deformation monitoring and the key to achieving millimeter-level monitoring. Although the traditional MHM (multipath hemispherical map) algorithm can be applied to multipath mitigation in real-time scenarios, accuracy needs to be further improved due to the influence of observation noise and the multipath differences between different satellites. Aiming at the insufficiency of MHM in dealing with the adverse impact of observation noise, we proposed the MHM_V model, based on Variational Mode Decomposition (VMD) and the MHM algorithm. Utilizing the VMD algorithm to extract the multipath from single-difference (SD) residuals, and according to the principle of the closest elevation and azimuth, the original observation of carrier phase in the few days following the implementation are corrected to mitigate the influence of the multipath. The MHM_V model proposed in this paper is verified and compared with the traditional MHM algorithm by using the observed data of the Forth Road Bridge with a seven day and 10 s sampling rate. The results show that the correlation coefficient of the multipath on two adjacent days was increased by about 10% after residual denoising with the VMD algorithm; the standard deviations of residual error in the L1/L2 frequencies were improved by 37.8% and 40.7%, respectively, which were better than the scores of 26.1% and 31.0% for the MHM algorithm. Taking a ratio equal to three as the threshold value, the fixed success rates of ambiguity were 88.0% without multipath mitigation and 99.4% after mitigating the multipath with MHM_V. The MHM_V algorithm can effectively improve the success rate, reliability, and convergence rate of ambiguity resolution in a bridge multipath environment and perform better than the MHM algorithm. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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25 pages, 15587 KiB

Open AccessArticle

Algorithm for Real-Time Cycle Slip Detection and Repair for Low Elevation GPS Undifferenced Data in Different Environments

by Ning Liu, Qin Zhang, Shuangcheng Zhang and Xiaoli Wu

Remote Sens. 2021, 13(11), 2078; https://doi.org/10.3390/rs13112078 - 25 May 2021

Cited by 8 | Viewed by 3261

Abstract

Real-time cycle slip detection and repair is one of the key issues in global positioning system (GPS) high precision data processing and application. In particular, when GPS stations are in special environments, such as strong ionospheric disturbance, sea, and high-voltage transmission line interference, [...] Read more.

Real-time cycle slip detection and repair is one of the key issues in global positioning system (GPS) high precision data processing and application. In particular, when GPS stations are in special environments, such as strong ionospheric disturbance, sea, and high-voltage transmission line interference, cycle slip detection and repair in low elevation GPS observation data are more complicated than those in normal environments. For low elevation GPS undifferenced carrier phase data in different environments, a combined cycle slip detection algorithm is proposed. This method uses the first-order Gauss–Markov stochastic process to model the pseudorange multipath in the wide-lane phase minus narrow-lane pseudorange observation equation, and establishes the state equation of the wide-lane ambiguity with the pseudorange multipath as a parameter, and it uses the Kalman filter for real-time estimation and detects cycle slips based on statistical hypothesis testing with a predicted residual sequence. Meanwhile, considering there are certain correlations among low elevation, observation epoch interval, and ionospheric delay error, a second-order difference geometry-free combination cycle slip test is constructed that takes into account the elevation. By combining the two methods, real-time cycle slip detection for GPS low elevation satellite undifferenced data is achieved. A cycle slip repair method based on spatial search and objective function minimization criterion is further proposed to determine the correct solution of the cycle slips after they are detected. The whole algorithm is experimentally verified using the static and kinematic measured data of low elevation satellites under four different environments: normal condition, high-voltage transmission lines, dynamic condition in the sea, and ionospheric disturbances. The experimental results show that the algorithm can detect and repair cycle slips accurately for low elevation GPS undifferenced data, the difference between the float solution and the true value for the cycle slip does not exceed 0.5 cycle, and the differences obey the normal distribution overall. At the same time, the wide-lane ambiguity and second-order difference GF combination sequence calculated by the algorithm is smoother, which give further evidence that the algorithm for cycle slip detection and repair is feasible and effective, and has the advantage of being immune to the special observation environments. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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15 pages, 83382 KiB

Open AccessTechnical Note

Performance of Multi-GNSS Real-Time UTC(NTSC) Time and Frequency Transfer Service Using Carrier Phase Observations

by Pengfei Zhang, Rui Tu, Xiaochun Lu, Lihong Fan and Rui Zhang

Remote Sens. 2021, 13(20), 4184; https://doi.org/10.3390/rs13204184 - 19 Oct 2021

Viewed by 2086

Abstract

The technique of carrier phase (CP), based on the global navigation satellite system (GNSS), has proven to be a highly effective spatial tool in the field of time and frequency transfer with sub-nanosecond accuracy. The rapid development of real-time GNSS satellite orbit and [...] Read more.

The technique of carrier phase (CP), based on the global navigation satellite system (GNSS), has proven to be a highly effective spatial tool in the field of time and frequency transfer with sub-nanosecond accuracy. The rapid development of real-time GNSS satellite orbit and clock determinations has enabled GNSS time and frequency transfer using the CP technique to be performed in real-time mode, without any issues associated with latency. In this contribution, we preliminarily built the prototype system of real-time multi-GNSS time and frequency transfer service in National Time Service Center (NTSC) of the Chinese Academy of Sciences (CAS), which undertakes the task to generate, maintains and transmits the national standard of time and frequency UTC(NTSC). The comprehensive assessment of the availability and quality of the service system were provided. First, we assessed the multi-GNSS state space representation (SSR) correction generated in real-time multi-GNSS prototype system by combining broadcast ephemeris through a comparison with the GeoForschungsZentrum (GFZ) final products. The statistical results showed that the orbit precision in three directions was smaller than 6 cm for global positioning system (GPS) and smaller than approximately 10 cm for BeiDou satellite system (BDS). The root mean square (RMS) values of clock differences for GPS were approximately 2.74 and 6.74 ns for the GEO constellation of BDS, 3.24 ns for IGSO, and 1.39 ns for MEO. The addition, the GLObal NAvigation Satellite System (GLONASS) and Galileo satellite navigation system (Galileo) were 4.34 and 1.32 ns, respectively. In order to assess the performance of real-time multi-GNSS time and frequency transfer in a prototype system, the four real-time time transfer links, which used UTC(NTSC) as the reference, were employed to evaluate the performance by comparing with the solution determined using the GFZ final products. The RMS could reach sub-nanosecond accuracy in the two solutions, either in the SSR or GFZ solution, or in GPS, BDS, GLONASS, and Galileo. The frequency stability within 10,000 s was 3.52 × 10⁻¹² for SSR and 3.47 × 10⁻¹² for GFZ and GPS, 3.63 × 10⁻¹² for SSR and 3.53 × 10⁻¹² for GFZ for BDS, 3.57 × 10⁻¹² for SSR and 3.52 × 10⁻¹² for GFZ for GLONASS, and 3.56 × 10⁻¹² for SSR and 3.48 × 10⁻¹² for GFZ for Galileo. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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17 pages, 3087 KiB

Open AccessTechnical Note

A Method to Accelerate the Convergence of Satellite Clock Offset Estimation Considering the Time-Varying Code Biases

by Shuai Liu and Yunbin Yuan

Remote Sens. 2021, 13(14), 2714; https://doi.org/10.3390/rs13142714 - 9 Jul 2021

Cited by 7 | Viewed by 2113

Abstract

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time [...] Read more.

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior. Full article

(This article belongs to the Special Issue High-Precision GNSS: Methods, Open Problems and Geoscience Applications—Part II)

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