# GPS Solutions

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### Regional integration of long-term national dense GNSS network solutions

Fri, 10/04/2019 - 00:00
Abstract

The EUREF Permanent Network Densification is a collaborative effort of 26 European GNSS analysis centers providing series of daily or weekly station position estimates of dense national and regional GNSS networks, in order to combine them into one homogenized set of station positions and velocities. During the combination, the station meta-data, including station names, DOMES numbers, and position offset definitions were carefully homogenized, position outliers were efficiently eliminated, and the results were cross-checked for any remaining inconsistencies. The results cover the period from March 1999 to January 2017 (GPS week 1000-1933) and include 31 networks with positions and velocities for 3192 stations, well covering Europe. The positions and velocities are expressed in ITRF2014 and ETRF2014 reference frames based on the Minimum Constraint approach using a selected set of ITRF2014 reference stations. The position alignment with the ITRF2014 is at the level of 1.5, 1.2, and 3.2 mm RMS for the East, North, Up components, respectively, while the velocity RMS values are 0.17, 0.14, and 0.38 mm/year for the East, North, and Up components, respectively. The high quality of the combined solution is also reflected by the 1.1, 1.1, and 3.5 mm weighted RMS values for the East, North, and Up components, respectively.

### A comparison of three widely used GPS triple-frequency precise point positioning models

Sat, 09/28/2019 - 00:00
Abstract

Triple-frequency signals can be transmitted by the GPS Block IIF satellites. With triple-frequency integration, more choices are available for the implementation of precise point positioning (PPP), namely the PPP using L1/L2 and L1/L5 dual-frequency ionospheric-free (IF) combinations (IF-PPP1), the PPP using the triple-frequency IF combination (IF-PPP2), and the PPP with uncombined (UC) measurements (UC-PPP). A comprehensive comparison of the three GPS triple-frequency PPP models is carried out in this study. A total of 197 3-h datasets with pure triple-frequency observables are used for analysis in the static situation. The mathematical equivalence among the three PPP models in the converged stage is proven. Only an accuracy difference of smaller than 6 mm exists among the three triple-frequency PPP models. For all the three models, the positioning accuracies are 37.2–42.9, 11.6–13.0 and 36.2–40.6 mm in east, north and vertical directions, respectively. As to the average convergence time, IF-PPP2 shows the best performance, which is 29.7, 11.0 and 29.9 min in the three directions, respectively. The improvement for IF-PPP2 on the average convergence time is 6%, 3% and 1% over IF-PPP1, and 17%, 13% and 20% over UC-PPP in the three directions, respectively. These numerical differences may be attributed to the different parameterization and noise levels for the three triple-frequency PPP models.

### Field of coherence of GPS-measured earth tremors

Fri, 09/27/2019 - 00:00
Abstract

A new method for investigating the coherence field of the noise component of high-frequency GPS time series is proposed. The method is applied to the main territory of the USA, which is characterized by a dense network of GPS stations. The data are presented in steps of 5 min from February 28, 2013, until June 29, 2019, on the Nevada Geodetic Laboratory Web site. The proposed method estimates the spatial distribution of the mean values of multiple coherence, calculated within nodes of a regular grid, between GPS coordinates of a given number of nearest operable stations and the periods at which the maximum values of coherence are reached. The two-dimensional probability density of the positions of places where the coherence maximum is most often realized is estimated. These estimates can be obtained for the entire history of observations and also in a sliding time window of a given length, which makes it possible to trace the dynamics of changes in time in the coherence field of the earth’s tremor. The entropy of the two-dimensional probability density of places of concentration of maximum values of coherence allows us to distinguish seasonal changes in the structure of the coherence field of GPS noise. To study the temporal dynamics, we use the auxiliary time series of changes in the maximum multiple coherence at 50 reference points located throughout the study area. The study of the coherence properties of this auxiliary 50-dimensional time series (“secondary coherence”) in a 180-day sliding time window highlighted a series of synchronization bursts of earth’s surface tremors.

### Analysis of a federal Kalman filter-based tracking loop for GPS signals

Sat, 09/21/2019 - 00:00
Abstract

Kalman filter is widely used in modern GPS receivers. A traditional receiver based on Kalman filter (KF) tracks the GPS signals from each satellite separately, and so its tracking performance could be inferior in challenging situations. The vector delay frequency-locked loop (VDFLL) combines all tracking channels into one Kalman filter and so has a better tracking performance. But VDFLL has two primary drawbacks: high computational cost and low robustness. To solve this problem, the federal tracking loop is proposed. The single Kalman filter of the traditional federal loop is separated into a least-squares block and a master filter in consideration of reducing the computational complexity at the cost of a slight performance reduction. In this tracking loop, the GPS signal from each satellite is tracked independently in the subfilters. The master filter works as a navigation processor, which estimates the acceleration of the receiver and feeds it back to the subfilters. The thermal jitter and dynamic stress error of the federal tracking loop are analyzed theoretically and demonstrated with simulation data. The dynamic performance, robustness and computational complexity of the traditional KF loop, the proposed federal tracking loop and the VDFLL are compared. Analysis and simulation results show that the dynamic tracking performance of the federal loop is much better than that of the KF loop and is almost close to that of the VDFLL. Also, the federal loop has advantages over the VDFLL in terms of robustness and the computational complexity. Therefore, the federal tracking loop can be implemented as a new method in the practical implementation for high-performance applications in the future.

### Estimation of snow depth using pseudorange and carrier phase observations of GNSS single-frequency signal

Tue, 09/17/2019 - 00:00
Abstract

A new method is proposed to estimate snow depth by using observations of the GNSS single-frequency signal collected by a ground-based receiver. The proposed method utilizes the pseudorange and carrier phase observations to form the geometry-free combination. Based on mathematical formulas of the amplitude attenuation factor, the pseudorange multipath error, and the carrier phase multipath error, a function is derived serving as the theoretical model that describes the relationship between the antenna height and the peak frequency of a series of function values associated with the range of satellite elevation angles. In the observation data processing stage, the moving average filtering method is used to remove the ionospheric delay from the combined observation series, followed by spectrum analysis to obtain the peak frequency, which is used to determine the antenna height and hence snow depth based on the theoretical model. A weighting method is proposed to combine individual snow depth estimates related to the use of signals of individual satellites to enhance the estimation accuracy. Each weighting coefficient is proportional to the maximum of the power spectral density of the combined observation series. The proposed method is substantiated by simulations and observations from geodetic-grade receivers, which can process multi-constellations and multi-frequency GNSS signals. Two field GNSS data sets collected in Heilongjing, China, and Colorado, USA, were used to evaluate the method. The results show that the root-mean-square error of GPS, BDS, and Galileo-based snow depth estimations is in the range of 2–6 cm when the topography around the GNSS receiver is flat.

### Relativity effects of Galileo passive hydrogen maser satellite clocks

Wed, 09/04/2019 - 00:00
Abstract

As seen from comparisons of recent multi-GNSS experiment and pilot project (MGEX) clock solutions of November 23, 2018, and February 15, 2019, most Galileo satellite passive hydrogen maser (PHM) clocks, once corrected for daily drifts, can already show the small error of the conventional relativity correction (i.e., − 2 r.v/c2—negative twice the dot product of the satellite position and velocity vectors, divided by the light velocity squared). The Galileo satellite clock solutions, generated by the GRG and COD MGEX Analysis Centers, in most cases agree well with the simple analytical error approximation, based only on the most significant J2 term of the earth’s gravitational potential expansion. The analytical error approximation is periodical with half an orbit period, and for the Galileo satellites it has an amplitude of 0.064 ns. It is subjected to residual periodical errors with amplitudes of up to 0.025 ns, which also have about half an orbital period. The residual periodical errors are likely caused by orbit perturbations, mostly due to the lunar attraction, which were neglected in the development of the analytical error approximation. Nevertheless, the application of the analytical error approximation to Galileo satellite clocks, corrected for daily drift, resulted in a significant reduction in clock RMS, from the average of 0.095–0.083 ns for GRG MGEX clock solutions on November 23, 2018, and from 0.084 to 0.075 ns on February 15, 2019, for COD MGEX clock solutions. The analytical relativity error approximation improves the linearity of Galileo PHM clocks, which, when accounted for, can result in significant improvements in clock solution precision, clock distributions and predictions. Furthermore, unlike for GPS and GLONASS, Galileo satellite clocks with samplings of 5 or 15 min can be safely interpolated, as demonstrated by Galileo-only kinematic PPP solutions with the MGEX tracking data of Feb. 15, 2019, at the station BRUX. When using the interpolated COD and GRG MGEX SP3 satellite clocks, rather than the 30-s clocks included in the respective clock files, the North/East/Up repeatability sigma’s of 10/8/16 mm increased by less than 10% for COD 5-min SP3 clock sampling. In the case of GRG’s 15-min sampling, the repeatability sigma’s of 8/8/14 mm increased by less than 20%.

### An analysis of inter-system biases in BDS/GPS precise point positioning

Wed, 09/04/2019 - 00:00
Abstract

The ways of estimating the inter-system bias (ISB) have an important influence on BDS/GPS combined precise point positioning (PPP). Ordinarily, in data processing, the precise ephemeris and clock offset from the Center for Orbit Determination in Europe (CODE), Deutsches GeoForschungsZentrum (GFZ), and Wuhan University (WHU), respectively, are applied to obtain the ISB products ( $${\text{ISB}}_{\text{COD}}$$ , $${\text{ISB}}_{\text{GFZ}}$$ , and $${\text{ISB}}_{\text{WHU}}$$ ). Currently, in the case of BDS/GPS PPP, the ISB is generally considered to be a stable value in a given day and estimated as a constant. To better understand the mechanism underlying the generation of ISB in combined PPP, we deduce and establish the ISB estimation formulas and mathematical models and collect and process data from 19 multi-GNSS experimental stations. The results show that the ranges of $${\text{ISB}}_{\text{COD}}$$ and $${\text{ISB}}_{\text{WHU}}$$ at different times are within 0.3 m, while $${\text{ISB}}_{\text{GFZ}}$$ can change up to 6.5 m. An interesting phenomenon is that the $${\text{ISB}}_{\text{GFZ}}$$ for different stations has a similar variation trend in a day, and in some days, the ISBs of all stations show a linear trend which may mainly be influenced by satellite clock offset. In addition, the temporal stability of ISB is independent of receiver software version number and antenna type, while the receiver type has little influence on the stability of ISB. Therefore, it is reasonable to estimate $${\text{ISB}}_{\text{COD}}$$ and $${\text{ISB}}_{\text{WHU}}$$ as constant in a day and use a random walk to obtain $${\text{ISB}}_{\text{GFZ}}$$ . The results show that the convergence speed and accuracy of BDS/GPS PPP obtained by the random walk method are higher than those using the constant method, no matter whether $${\text{ISB}}_{\text{GFZ}}$$ , $${\text{ISB}}_{\text{COD}}$$ , or $${\text{ISB}}_{\text{WHU}}$$ is used.

### Regularization and particle filtering estimation of phase inter-system biases (ISB) and the lookup table for Galileo E1-GPS L1 phase ISB calibration

Sat, 08/31/2019 - 00:00
Abstract

The between-receiver phase inter-system bias (ISB) in multi-GNSS integration needs to be calibrated when fixing the inter-system double difference (DD) ambiguities. As a result, the DD ambiguity fixing performance is affected by the accuracy of the ISB calibration; however, those effects have not been investigated until now. Also, the knowledge about the ISB characteristics is not enough which can lead to failure of ambiguity fixing with ISB calibration value such as obtained by the lookup table method. Our study first integrates the regularization method to the existing particle filtering fractional ISB (F-ISB) estimation to derive more precise F-ISB estimates. Afterward, the effects of the F-ISB accuracy on DD ambiguity fixing in single-epoch GPS L1-Galileo E1 integration are investigated. We show that the errors of F-ISB can degrade the success rate of single-epoch ambiguity fixing, and thus, more precise F-ISB values lead to higher empirical success rates. Finally, the characteristics of the F-ISB are investigated based on baselines shorter than 20 km from the GNSS network of International GNSS Services. According to the 132 F-ISB estimates obtained using data collected from day of year 001 2016 to DOY 001, 2019, the F-ISB values for 4 receiver brands including Leica, Septentrio, Trimble and Javad are analyzed. The receiver-type and software-version combinations from the same manufacturer and with similar F-ISB values are regarded as one group and all the receivers can be classified into 6 groups. With F-ISB of Leica receiver group set to zero value, the other groups have F-ISB values of 0.000 m, + 0.055 m and + 0.095 m and the L1-E1 F-ISBs between different groups are provided in a lookup table for practical use.

### CASSIOPE orbit and attitude determination using commercial off-the-shelf GPS receivers

Thu, 08/29/2019 - 00:00
Abstract

As part of the “GPS Attitude, Positioning, and Profiling experiment (GAP)” of the Canadian CASSIOPE science and technology mission, a set of four geodetic GPS receivers connected to independent antennas on the top-panel of the spacecraft can be operated concurrently to collect dual-frequency code and phase measurements on both the L1 and L2 frequencies. The qualification of the commercial off-the-shelf (COTS) GPS receivers is discussed, and flight results of precise orbit and attitude determination are presented. Pseudorange and carrier phase errors amount to roughly 65 cm and 8 mm for the ionosphere-free dual-frequency combination, which compares favorably with other missions using fully qualified space GPS receivers and is mainly limited by choice of simple patch antennas without choke rings. Precise orbit determination of CASSIOPE using GPS observations can achieve decimeter-level accuracy during continued operations but suffers from onboard and mission restrictions that limit the typical data availability to less than 50% of each day and induce regular long-duration gaps of 4–10 h. Based on overlap analyses, daily peak orbit determination errors can, however, be confined to 1 m 3D on 84% of all days, which fulfills the mission needs for science data processing of other instruments. The attitude of CASSIOPE can be determined with a representative precision of about 0.2° in the individual axes using three GAP receivers and antennas. Availability of dual-frequency measurements is particularly beneficial and enables single-epoch ambiguity fixing in about 97% of all epochs. Overall, the GAP experiment demonstrates the feasibility of using COTS-based global navigation satellite system receivers in space and the benefits they can bring for small-scale science missions.

### Performance evaluation of real-time global ionospheric maps provided by different IGS analysis centers

Wed, 08/28/2019 - 00:00
Abstract

With the development of real-time precise clock and orbit products, high-precision real-time ionospheric products have become one of the most critical resources for real-time single-frequency precise point positioning. Fortunately, there are several international GNSS service (IGS) analysis centers, e.g., UPC, WHU, and CAS, that are providing real-time global ionospheric maps (RT-GIMs). We evaluate these maps in detail over 2 years for different aspects. First, the RT-GIMs and 1-day predicted ionospheric products (C1PG GIM) differenced with the IGS final GIMs (IGSG GIM) are performed. Second, ionospheric vertical total electron content from Jason-2/3 data is set as a reference to evaluate the quality of RT-GIMs over oceanic regions. Third, 22 stations, which are not used in the generation of RT-GIMs, C1PG GIM, and IGSG GIM, are selected and the difference of slant total electron content (dSTEC) method is used to assess the accuracy and consistency of RT-GIMs over continental regions. Finally, the performance of RT-GIMs in the position domain is demonstrated based on SF-PPP solutions. The results show that the accuracy of the RT-GIMs is slightly worse than that of C1PG GIM and IGSG GIM. All RT-GIMs and the C1PG GIM have a smaller mean difference compared to the IGSG GIM by (−0.97, − 0.90, − 0.77, − 0.80) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM). Over oceanic regions, the RT-GIMs perform nearly the same as the C1PG GIM, but a slightly worse than IGSG GIM. The STDs are (3.96, 3.05, 3.25, 3.12, 2.54) TECU relative to Jason-2 and (4.94, 3.24, 3.38, 3.24, 2.65) TECU relative to Jason-3 for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM), respectively. Comparing with dSTEC values observed from the selected ground stations over continental regions, the RMS is (4.02, 2.16, 2.29, 1.86, 1.49) TECU for (UPC RT-GIM, CAS RT-GIM, WHU RT-GIM, C1PG GIM, IGSG GIM). In the position domain, the positioning accuracy of SF-PPP solution corrected by the RT-GIMs and C1PG GIM can reach decimeter level in the horizontal direction and meter level in the vertical direction, which is worse than obtained by IGSG GIM. Meanwhile, the positioning accuracy of SF-PPP corrected by RT-GIMs is almost the same as that obtained using C1PG GIM. For RT-GIMs, the accuracy of the CAS RT-GIM is slightly better than that of the other two RT-GIMs.

### A GNSS/INS-integrated system for an arbitrarily mounted land vehicle navigation device

Fri, 08/23/2019 - 00:00
Abstract

For the traditional implementation of inertial navigation system, aligning the inertial sensor axes with the vehicle body frame is a necessary process. While the development of micro-electromechanical system brings considerable cost and size advantages, the undesirable alignment process is still a challenge for widespread civil use of portable inertial devices. Aimed to avoid complicated manual mounting of an inertial device used in land vehicle navigation systems, an algorithm is proposed to automatically estimate the misalignment angles between the sensor platform and the vehicle body frame, which enables the device to be mounted in an arbitrary orientation. The foundation of this method is formed by two facts. The first is that the accelerometer can exactly estimate its own posture when it is stationary on the platform. The second is the yaw calculated from the horizontally aligned device has a constant error when the horizontal component of the angular velocity is zero. A robust motion mode recognition technique, which compares the statistical characteristics of the measurements with an empirical threshold, is applied to detect whether the vehicle is parking, turning, or moving straight. Validation experiments show that the error of the coarse estimation algorithm is within 2° when the heading misalignment is less than 45°. This guarantees that the arbitrarily mounted device achieves the equivalent performance as the well-aligned one, whenever the global navigation satellite system (GNSS) signal is available. In addition, the positioning error of the misaligned device during short GNSS signal blockage is within 7 m with the application of auxiliary velocity updates.

### Initial assessment of BeiDou-3 global navigation satellite system: signal quality, RTK and PPP

Mon, 08/19/2019 - 00:00
Abstract

China has recently established the primary constellation of BeiDou-3 global navigation satellite system (BDS-3). It is necessary to conduct a comprehensive assessment about its performance. The signal quality, ambiguity resolution efficiency and real-time kinematic (RTK) performance are assessed based on the datasets collected with two Trimble Alloy receivers that can track all open signals of BDS-3. Then, the precise point positioning (PPP) using combined BDS-2 and BDS-3 measurements is compared with the PPP using BDS-2 only, where the precise satellite orbits and clocks are determined using 116 globally distributed monitor stations. The results show that the signal quality of BDS-3 is generally better than that of BDS-2. Also, the ambiguity resolution efficiency of RTK is improved by incorporating the BDS-3 measurements with success rate improving from 88.5 to 91.4%. Regarding PPP, the convergence time is shortened from about an hour to less than half an hour, while the positioning accuracy is also improved significantly.

### Extraction of electron density profiles with geostationary satellite-based GPS side lobe occultation signals

Wed, 08/14/2019 - 00:00
Abstract

GPS radio occultation (RO) measurements recorded on the geostationary earth orbit (GEO) satellite TJS-2 have been investigated for electron density profile (EDP) retrieval. The total electron content derived from TJS-2 single-frequency excess phase is refined by a moving average filter to smooth high-frequency errors, which outperforms the single-difference technique. The side lobe GPS RO signals have been used to estimate electron densities up to several thousand kilometers in height for the first time. By comparison with the ground-based digisonde, the IRI 2016 model and the Constellation Observing System for Meteorology, Ionosphere, and Climate satellite (COSMIC) EDPs, the TJS-2 ionospheric EDPs show good agreement with correlation coefficients exceeding 0.8. The TJS-2 average NmF2 differences compared to digisondes and COSMIC results are 12.9% and 1.4%, respectively, while the hmF2 differences are 1.65 km and 1.76 km, respectively. Our results reveal that GEO-based RO signals can estimate EDPs to altitudes up to several thousand kilometers at specific locations with daily repeatability, which makes it a very suitable technique for routinely monitoring EDP variations.

### Improving LEO precise orbit determination with BDS PCV calibration

Sat, 08/10/2019 - 00:00
Abstract

As the new members of the Chinese Fengyun-3 meteorological satellites series, the Fengyun-3C (FY-3C) and Fengyun-3D (FY-3D) satellites were launched in 2013 and 2017, respectively. For the first time, both FY-3C and FY-3D satellites carry a high-precision BDS and GPS dual-system space-borne receiver to fulfill their stringent requirement of precise orbit determination (POD). The fusion of BDS and GPS onboard observations can significantly improve the spatial geometry, robustness and reliability of low earth orbit (LEO) POD. In order to achieve high-quality orbit recovery from the onboard GNSS observations, the in-flight calibration of phase center variation (PCV) is a prerequisite. In this contribution, we calibrate the BDS PCV for improving the orbit precision of both FY-3C and FY-3D satellites for the first time. The results show that with the GPS PCV corrections, the residuals of GPS carrier phase observations present a reduction of about 17.6% and 21.9% for FY-3C and FY-3D satellites, respectively, and overlap differences of the GPS-only orbit are reduced on average by 3 and 5 mm. After correcting for BDS PCV, the GPS and BDS combined (GC) POD achieves a better orbit precision for both FY-3C and FY-3D satellites. The application of BDS PCV corrections can contribute to a reduction of up to 12% in BDS phase residuals and a decrease of up to 3 mm in orbit overlap differences in 1-dimension. It indicates that the introduction of the BDS PCV model can significantly improve the orbit precision. Similar orbit precision can be achieved when using the GPS PCV model to replace the BDS PCV model in the GC POD. It demonstrates that for onboard receivers, the GPS PCV model can be used to correct PCV errors of BDS signals, which is commonly used in precise point positioning of ground stations when the BDS PCV is not available. Furthermore, we find that it is feasible to generate an integrated PCV model from both onboard BDS and GPS observations. After application of the integrated PCV model, the FY-3C and FY-3D orbits of GC POD present a better precision than the solution using the single-system PCV model and the largest precision improvement of about 1 mm can be recognized in the radial component. With such a high-quality orbit, FY-3C and FY-3D satellites can be expected to make more contributions to meteorological studies and applications.

### Performance of Galileo-only dual-frequency absolute positioning using the fully serviceable Galileo constellation

Wed, 08/07/2019 - 00:00
Abstract

The recent development of the Galileo space segment and the accompanying support of the International GNSS Service (IGS) allows for worldwide Galileo-only positioning. In this study, different techniques of dual-frequency absolute positioning using the fully serviceable Galileo constellation are evaluated for the first time and compared to the performance of GPS positioning. The daily static positioning based on the broadcast ephemeris using Galileo pseudoranges is significantly more accurate than the corresponding GPS solutions, obtaining the accuracy of a few decimeters. In the kinematic mode, the accuracy is better than 10 m and 20 m for the horizontal and vertical components, respectively, which is comparable to that of GPS. Precise absolute positioning using pseudorange and carrier phase Galileo observations combined with IGS Real-Time Service (RTS) or Multi-GNSS Experiment products is not yet as good as the corresponding GPS solutions. In the static mode, the root mean squared error (RMSE) between estimated and reference coordinates does not exceed 0.05 m and 0.06 m for the horizontal and vertical components, respectively. In the kinematic mode, the respective accuracies are better than 0.17 m and 0.21 m. Moreover, we show that both GPS and Galileo pseudorange solutions benefit from the RTS when compared to the broadcast solutions with the improvement in the accuracy between 10 and 59%. Remarkable results are achieved for Galileo Precise Point Positioning (PPP) solutions based on the broadcast ephemeris. In the static mode, the RMSE is 0.07 and 0.10 m for the horizontal and vertical components which is three and two times better, respectively, then the corresponding solutions based on GPS.

### GEO-pivoted carrier ambiguity resolution: a method for instantaneous ambiguity resolution in mid-low-latitude regions

Tue, 08/06/2019 - 00:00
Abstract

The effect of DD ionospheric delays can be unexpectedly large in the range of the equatorial anomaly, that is, in mid-low-latitude regions near noon and/or afternoon, and the large delays cause instantaneous AR to fail even over short baselines. Ionospheric delays can be represented by a function of vertical total electron content values, which often have significant latitudinal gradients in mid-low-latitude regions near noon and/or afternoon. Therefore, a short separation between the pivot and secondary satellites in the latitudinal direction indicates smaller effects of DD ionosphere. In the BeiDou system (BDS), five geostationary earth orbit (GEO) satellites are nearly motionless over the equator. We can use adjacent GEO satellites to form a DD pair whose pivot and secondary satellites are close in latitude (< 4°). Moreover, when inclined geosynchronous orbit or medium earth orbit (IGSO/MEO) satellites approach the equator, the separations between the IGSO/MEO and GEO satellites in the latitudinal direction will be minimal. Therefore, this study proposes a method called GEO-pivoted carrier AR (GEOCAR) for instantaneous AR. This method mitigates the influence of DD ionospheric delays by pivoting GEO satellites in BDS DD pairs and uses a trade-off design between the ionosphere-fixed and ionosphere-weighting models to resolve integer ambiguities of dual-frequency phases. Experimental short-baseline data (< 10 km) collected in mid-low-latitude regions near noon and afternoon are tested with conventional AR and GEOCAR methods. The results show that the GEOCAR can effectively produce higher success percentages than the conventional AR with improvements reaching 68.62% for BDS and 42.55% for BDS/GPS.

### Computationally efficient dual-frequency uncombined precise orbit determination based on IGS clock datum

Fri, 08/02/2019 - 00:00
Abstract

Using uncombined (UC) or undifferenced original observations has become a research topic in the global navigation satellite system (GNSS) community. This far, precise orbit determination (POD) with ionospheric-free (IF) observation combination has been favored. Using the uncombined strategy, i.e., using the raw observations to perform POD, the slant ionospheric delay is regarded as an unknown epoch parameter. We assume that the slant ionospheric delay depends on the frequency having the same magnitude for pseudoranges and carrier phases but opposite sign. Since there are, at each station and each epoch, as many ionospheric delay parameters as the observed satellites, a large number of ionospheric parameters need to be estimated for uncombined POD. The usual approch is that, when the observations at an epoch are accumulated, the epoch parameters consisting of clock and ionospheric parameters are eliminated simultaneously, which results in low computational efficiency. We develop a high-efficiency method by eliminating ionospheric parameters one by one, where each of them is eliminated when the observations of a station and a satellite are accumulated and no matrix inversion is required. In this uncombined POD algorithm, the IF-combined clock datum adopted by the international GNSS service (IGS) clock products is used to keep compatibility with existing IGS products by using the re-parameterized observation equations. We deduce the ambiguity resolution strategy for uncombined POD. In the experimental part, the modified parameter elimination method is first validated. With GPS observations from 58 global IGS stations, the first iteration processing time of parameter estimation for IF POD, UC POD and modified UC POD are 3.6, 62.5 and 9.2 min, respectively. The computational efficiency of modified UC POD strategy is greatly improved compared to UC POD. Then, the IF POD and the improved UC POD strategies with ambiguity float and fixed solutions are analyzed by comparing orbits, clocks, station coordinates and tropospheric delays with respect to IGS products. Results show that the accuracy of UC and IF solutions is comparable. Afterward, the repeatability of station coordinates is analyzed. With the solutions of 13 POD arcs, the repeatability over 13 days is consistent for UC and IF strategy. In addition, the ambiguity fixing rate, data usage rate, as well as residuals of code and phase observations, is analyzed. It is concluded that the slight difference between UC and IF strategy may be related to the data usage rate.

### GNSS metadata and data validation in the EUREF Permanent Network

Fri, 08/02/2019 - 00:00
Abstract

The EUREF Permanent Network (EPN) is a network of continuously operating GNSS stations installed throughout the European continent. The EPN Central Bureau (CB) performs the day-to-day EPN coordination, acts as liaison between station operators, data centers, and analysis centers, and maintains the EPN Information System. Over the last years, the EPN CB has accommodated the enhancements required by the new EU General Data Protection Regulation, new multi-GNSS signals, new RINEX formats, increased usage of real-time GNSS data, and the new GeodesyML metadata exchange format. We will discuss how the EPN CB validates and provides access to EPN station metadata and monitors EPN data sets in terms of availability, latency, and quality to ensure they meet the user requirements. The analysis of 23 years of EPN GNSS data quality checks demonstrates some of the most frequently encountered tracking problems affecting EPN stations, and specific GNSS receiver types, throughout the years.

### Use of modified carrier-to-code leveling to analyze temperature dependence of multi-GNSS receiver DCB and to retrieve ionospheric TEC

Fri, 07/26/2019 - 00:00
Abstract

Deriving the ionospheric total electron content (TEC) from the global navigation satellite systems (GNSS) measurements typically assumes the receiver differential code biases (RDCBs) to remain unchanged within at least 1 day. However, the RDCBs sometimes can exhibit remarkable intraday variability, probably due to the ambient temperature fluctuation. The modified carrier-to-code leveling (MCCL) method enables one to eliminate the adverse impact of the short-term variations of RDCBs (called RDCB offsets) on the retrieval of ionospheric TECs. In this study, we extend the GPS-only MCCL method to the multi-GNSS case and further carry out a series of investigations. First, in terms of the Pearson correlation coefficient (PCC), the dependence of multi-GNSS RDCB offsets upon ambient temperature is verified. As suggested by the results, a strong linear correlation exists between the estimated RDCB offsets and measured temperature values. The percentages of the stations analyzed with the absolute PCC values above 0.5 are 76.5%, 94.1% and 64.2% for GPS, BDS and Galileo, respectively. Second, the global ionospheric map provided by the center for orbit determination in Europe (CODE), the JASON altimeter and the difference of slant TEC (dSTEC) are chosen as the references for evaluating the performance of MCCL-derived TECs. After removing the significant RDCB offsets, an improvement of 69.7%, 93.4% and 87.6% for GPS, BDS and Galileo has been achieved in the dSTEC validation, respectively.

### Multipath mitigation based on trend surface analysis applied to dual-antenna receiver with common clock

Fri, 07/26/2019 - 00:00
Abstract

Multipath mitigation methods based on the intrinsic spatiotemporal repeatability of multipath effect are commonly applied in high-precision Global Navigation Satellite System positioning. Among which multipath hemispherical map (MHM) has the advantages of simplicity of calculation and real-time multipath reduction of static environment or some dynamic environment. However, utilizing the average of residuals as the calibration values will inevitably lead to insufficient or excessive modification of multipath in the lattice. We proposed an advanced multipath elimination method named trend surface analysis-based multipath hemispherical map (T-MHM), which extends the primary MHM by combining the trend surface analysis method to investigate the multipath spatial distribution and trend in each lattice. A short baseline experiment was carried out using a dual-antenna receiver with common clock in campus of East China Normal University. Single-difference carrier residuals were used for relative multipath modeling. The multipath elimination results indicate that, compared with the original approach, the T-MHM improves the dispersion and accuracy of the baseline solution and increases the phase observation residuals reduction rate. It also enhances the modeling of multipath information in both low- and high-frequency bands. Meanwhile, T-MHM is less sensitive to lattice size. In practical applications, larger lattice size can be adopted to improve the computational efficiency and spatial coverage with little loss of accuracy.

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