Showing papers in "Gps Solutions in 2017"

Assessment of precise orbit and clock products for Galileo, BeiDou, and QZSS from IGS Multi-GNSS Experiment (MGEX)

Abstract: The focus is on the quality assessment of precise orbit and clock products for the emerging Galileo, BeiDou, and QZSS systems. Products provided by Multi-GNSS Experiment (MGEX) over 2 years are used for evaluation. First, the products are assessed by orbit and clock comparisons among individual analysis centers (ACs), which give us an objective impression of their consistency. In addition, the precise orbits are verified by satellite laser ranging (SLR) residuals, which can be regarded as indicators of orbit accuracy. Moreover, precise point positioning (PPP) tests are conducted to further verify the quality of MGEX precise orbits and clocks. Orbit comparisons show agreements of about 0.1---0.25 m for Galileo, 0.1---0.2 m for BeiDou MEOs, 0.2---0.3 m for BeiDou IGSOs, and 0.2---0.4 m for QZSS. The BeiDou GEO orbits, however, have the worst agreements having a few meters differences. Clock comparisons of individual ACs have a consistency of 0.2---0.4 ns for Galileo, 0.2---0.3 ns for BeiDou IGSOs, 0.15---0.2 ns for BeiDou MEOs, 0.5---0.8 ns for BeiDou GEOs, and 0.4---0.8 ns for QZSS in general. The SLR validations demonstrate an accuracy of about 0.1 m for the current Galileo, BeiDou IGSO/MEO orbits, and about 0.2 m for QZSS orbits. However, the SLR residuals of BeiDou GEO orbits show a systematic bias of about ź0.5 m together with a standard deviation of 0.3 m. Solutions of PPP with different products mostly agree well with each other, which further confirms the good consistency of orbits and clocks among ACs. After convergence, an accuracy of 1 mm to 1 cm for static PPP and a few centimeters for kinematic PPP is achieved using multi-GNSS observations and MGEX orbit and clock products. However, it should be noted that a few exceptions may exist throughout the evaluations due to the insufficient models, different processing strategies, and ongoing updates applied by individual ACs.

Galileo status: orbits, clocks, and positioning

Abstract: The European Global Navigation Satellite System Galileo is close to declaration of initial services. The current constellation comprises a total of 12 active satellites, four of them belonging to the first generation of In-Orbit Validation satellites, while the other eight are Full Operational Capability (FOC) satellites. Although the first pair of FOC satellites suffered from a launch anomaly resulting in an elliptical orbit, these satellites can be used for scientific applications without relevant limitations. The quality of broadcast orbits and clocks has significantly improved since the beginning of routine transmissions and has reached a signal-in-space range error of 30 cm. Precise orbit products generated by the scientific community achieve an accuracy of about 5 cm if appropriate models for the solar radiation pressure are applied. The latter is also important for an assessment of the clock stability as orbit errors are mapped to the apparent clock. Dual-frequency single point positioning with broadcast orbits and clocks of nine Galileo satellites that have so far been declared healthy already enables an accuracy at a few meters. Galileo-only precise point positioning approaches a precision of 2 cm in static mode using daily solutions.

GPS, Galileo, QZSS and IRNSS differential ISBs: estimation and application

Abstract: Knowledge of inter-system biases (ISBs) is essential to combine observations of multiple global and regional navigation satellite systems (GNSS/RNSS) in an optimal way. Earlier studies based on GPS, Galileo, BDS and QZSS have demonstrated that the performance of multi-GNSS real-time kinematic positioning is improved when the differential ISBs (DISBs) corresponding to signals of different constellations but transmitted at identical frequencies can be calibrated, such that only one common pivot satellite is sufficient for inter-system ambiguity resolution at that particular frequency. Recently, many new GNSS satellites have been launched. At the beginning of 2016, there were 12 Galileo IOV/FOC satellites and 12 GPS Block IIF satellites in orbit, while the Indian Regional Navigation Satellite System (IRNSS) had five satellites launched of which four are operational. More launches are scheduled for the coming years. As a continuation of the earlier studies, we analyze the magnitude and stability of the DISBs corresponding to these new satellites. For IRNSS this article presents for the first time DISBs with respect to the L5/E5a signals of GPS, Galileo and QZSS for a mixed-receiver baseline. It is furthermore demonstrated that single-frequency (L5/E5a) ambiguity resolution is tremendously improved when the multi-GNSS observations are all differenced with respect to a common pivot satellite, compared to classical differencing for which a pivot satellite is selected for each constellation.

Review of code and phase biases in multi-GNSS positioning

Abstract: A review of the research conducted until present on the subject of Global Navigation Satellite System (GNSS) hardware-induced phase and code biases is here provided. Biases in GNSS positioning occu ...

Uncovering common misconceptions in GNSS Precise Point Positioning and its future prospect

Abstract: Within the last decade, GNSS Precise Point Positioning (PPP) has generated unprecedented interest among the GNSS community and is being used for a number of scientific and commercial applications today. Similar to the conventional relative positioning technique, PPP could provide positioning solutions at centimeter-level precision by making use of the precise carrier phase measurements and high-accuracy satellite orbits and clock corrections provided by, for example, the International GNSS Service. The PPP technique is attractive as it is computationally efficient; it eliminates the need for simultaneous observations at both the reference and rover receivers; it also eliminates the needs for the rover receiver to operate within the vicinity of the reference receiver; and it provides homogenous positioning quality within a consistent global frame anywhere in the world with a single GNSS receiver. Although PPP has definite advantages for many applications, its merits and widespread adoption are significantly limited by the long convergence time, which restricts the use of the PPP technique for many real-time GNSS applications. We provide an overview of the current performance of PPP as well as attempt to address some of the common misconceptions of this positioning technique--considered by many as the future of satellite positioning and navigation. Given the upcoming modernization and deployment of GNSS satellites over the next few years, it would be appropriate to address the potential impacts of these signals and constellations on the future prospect of PPP.

Maintaining real-time precise point positioning during outages of orbit and clock corrections

Abstract: The precise point positioning (PPP) is a popular positioning technique that is dependent on the use of precise orbits and clock corrections. One serious problem for real-time PPP applications such as natural hazard early warning systems and hydrographic surveying is when a sudden communication break takes place resulting in a discontinuity in receiving these orbit and clock corrections for a period that may extend from a few minutes to hours. A method is presented to maintain real-time PPP with 3D accuracy less than a decimeter when such a break takes place. We focus on the open-access International GNSS Service (IGS) real-time service (RTS) products and propose predicting the precise orbit and clock corrections as time series. For a short corrections outage of a few minutes, we predict the IGS-RTS orbits using a high-order polynomial, and for longer outages up to 3 h, the most recent IGS ultra-rapid orbits are used. The IGS-RTS clock corrections are predicted using a second-order polynomial and sinusoidal terms. The model parameters are estimated sequentially using a sliding time window such that they are available when needed. The prediction model of the clock correction is built based on the analysis of their properties, including their temporal behavior and stability. Evaluation of the proposed method in static and kinematic testing shows that positioning precision of less than 10 cm can be maintained for up to 2 h after the break. When PPP re-initialization is needed during the break, the solution convergence time increases; however, positioning precision remains less than a decimeter after convergence.

Low-cost, high-precision, single-frequency GPS---BDS RTK positioning

Abstract: The integration of the Chinese BDS with other systems, such as the American GPS, makes precise RTK positioning possible with low-cost receivers. We investigate the performance of low-cost ublox receivers, which cost a few hundred USDs, while making use of L1 GPS + B1 BDS data in Dunedin, New Zealand. Comparisons will be made to L1 + L2 GPS and survey-grade receivers which cost several thousand USDs. The least-squares variance component estimation procedure is used to determine the code and phase variances and covariances of the receivers and thus formulate a realistic stochastic model. Otherwise, the ambiguity resolution and hence positioning performance would deteriorate. For the same reasons, the existence of receiver-induced time correlation is also investigated. The low-cost RTK performance is then evaluated by formal and empirical ambiguity success rates and positioning precisions. It will be shown that the code and phase precision of the low-cost receivers can be significantly improved by using survey-grade antennas, since they have better signal reception and multipath suppression abilities in comparison with low-cost patch antennas. It will also be demonstrated that the low-cost receivers can achieve competitive ambiguity resolution and positioning performance to survey-grade dual-frequency GPS receivers.

Assessment of code bias variations of BDS triple-frequency signals and their impacts on ambiguity resolution for long baselines

Abstract: Carrier phase ambiguity resolution over long baselines is challenging in BDS data processing. This is partially due to the variations of the hardware biases in BDS code signals and its dependence on elevation angles. We present an assessment of satellite-induced code bias variations in BDS triple-frequency signals and the ambiguity resolutions procedures involving both geometry-free and geometry-based models. First, since the elevation of a GEO satellite remains unchanged, we propose to model the single-differenced fractional cycle bias with widespread ground stations. Second, the effects of code bias variations induced by GEO, IGSO and MEO satellites on ambiguity resolution of extra-wide-lane, wide-lane and narrow-lane combinations are analyzed. Third, together with the IGSO and MEO code bias variations models, the effects of code bias variations on ambiguity resolution are examined using 30-day data collected over the baselines ranging from 500 to 2600 km in 2014. The results suggest that although the effect of code bias variations on the extra-wide-lane integer solution is almost ignorable due to its long wavelength, the wide-lane integer solutions are rather sensitive to the code bias variations. Wide-lane ambiguity resolution success rates are evidently improved when code bias variations are corrected. However, the improvement of narrow-lane ambiguity resolution is not obvious since it is based on geometry-based model and there is only an indirect impact on the narrow-lane ambiguity solutions.

Tightly coupled integration of multi-GNSS PPP and MEMS inertial measurement unit data

Abstract: Precise point positioning (PPP) using the Global Positioning System (GPS) is widely recognized as an efficient approach for providing precise positioning services. However, its accuracy and reliability could be significantly degraded by unexpected observation discontinuities and unfavorable tracking geometry which are unavoidable, especially in severe environments such as city canyons. Therefore, in the last decades inertial navigation system (INS) has been integrated to overcome such drawbacks. Recently, multi-Global Navigation Satellite Systems (GNSS) were applied to enhance the PPP performance by appropriate usage of the increased number of satellites. We present a new approach to tightly integrate the multi-GNSS PPP and INS together in the observation level. The inter-system bias and inter-frequency bias of multi-GNSS and the hardware errors of INS sensors are estimated to improve the position accuracy and to shorten the convergence time of PPP. In order to demonstrate the impact of multi-GNSS observations and INS data on the derived position, velocity, attitude, and the convergence time of PPP, the new approach is validated through an experimental test with a set of land vehicle data. The results show that the position accuracy can be improved by multi-GNSS and INS significantly, but very little improvement in velocity and attitude is achieved. The position root-mean-square improves from 23.3, 19.8, and 14.9 cm of the GPS PPP/INS tightly coupled integration (TCI) solution to 7.9, 3.3, and 5.1 cm of multi-GNSS PPP/INS TCI in north, east, and up components, respectively. Furthermore, GNSS outages are simulated and their effect on the performance of multi-GNSS PPP/INS TCI is investigated to demonstrate the contribution of the multi-GNSS PPP/INS TCI during GNSS outages. In addition, the convergence test also shows that both multi-GNSS and INS can improve the PPP convergence performance noticeably.

Remote leveling of tide gauges using GNSS reflectometry: case study at Spring Bay, Australia

Abstract: We further developed a new approach using GNSS reflectometry to determine the leveling connection between a tide gauge and a GNSS antenna. This approach includes the optimization of the unknown receiver bandwidth and the estimation of frequency changes in the signal-to-noise ratio (SNR) oscillation through an extended Kalman filter/smoother algorithm. We also corrected the geometric bending of the GNSS signals due to tropospheric refraction using local meteorological observations. Using 3 weeks of SNR data in Spring Bay, Australia, from a GNSS antenna placed sideways (i.e., ground plane orientated vertically and directed in azimuth toward the sea surface) to improve the SNR interference near the horizon, we obtained mean leveling differences of approximately 5 mm, with an RMS of approximately 3 cm level with respect to the nominal leveling from classical surveying techniques. SNR data from three different receiver manufacturers, coupled to the same antenna, provided similar leveling results. With a second antenna in the usual upright configuration, we obtained mean leveling differences of 1---2 cm and a RMS of about 10 cm. In the upright configuration, the leveling differences may include errors in the GNSS antenna phase center calibration, which are avoided in our technique but not in the classical surveying techniques. These results demonstrate the usefulness of the reflectometry technique to obtain precisely and remotely the leveling between a GNSS antenna and a tide gauge. In addition, this technique can be applied continuously, providing an independent and economical means to monitor the stability of the tide gauge zero.

Globalization highlight: orbit determination using BeiDou inter-satellite ranging measurements

Abstract: The BeiDou Navigation Satellite System is expected to provide a global positioning and navigation service by 2020. To achieve this goal, the new-generation navigation satellites that have been launched since March 2015 are equipped with inter-satellite links (ISLs), with the objective of testing new navigation signals and the ISLs themselves. Using these new-generation navigation satellites and several ground facilities in China, a combined orbit determination experiment was carried out during August 2016. The orbit mechanical model, orbit determination method, and accuracy evaluation method used in this experiment are presented here. The accuracy of the combined orbit determination method is evaluated, and the performance-related improvements resulting from the ISLs are analyzed. The performance of orbit determination has been increased about 37–76% for different satellites in orbit-only signal-in-space range error (orbit-only SISRE).

Modeling tropospheric wet delays with dense and sparse network configurations for PPP-RTK

Abstract: Precise Point Positioning (PPP) is a well-known technique of positioning by Global Navigation Satellite Systems (GNSS) that provides accurate solutions. With the availability of real-time precise orbit and clock products provided by the International GNSS Service (IGS) and by individual analysis centers such as Centre National d'Etudes Spatiales through the IGS Real-Time Project, PPP in real time is achievable. With such orbit and clock products and using dual-frequency receivers, first-order ionospheric effects can be eliminated by the ionospheric-free combination. Concerning the tropospheric delays, the Zenith Hydrostatic Delays can be quite well modeled, although the Zenith Wet Delays (ZWDs) have to be estimated because they cannot be mitigated by, for instance, observable combinations. However, adding ZWD estimates in PPP processing increases the time to achieve accurate positions. In order to reduce this convergence time, we (1) model the behavior of troposphere over France using ZWD estimates at Orpheon GNSS reference network stations and (2) send the modeling parameters to the GNSS users to be introduced as a priori ZWDs, with an appropriate uncertainty. At the user level, float PPP-RTK is achieved; that is, GNSS data are performed in kinematic mode and ambiguities are kept float. The quality of the modeling is assessed by comparison with tropospheric products published by Institut National de l'Information Geographique et Forestiere. Finally, the improvements in terms of required time to achieve 10-cm accuracy for the rover position (simulated float PPP-RTK) are quantified and discussed. Results for 68 % quantiles of absolute errors convergence show that gains for GPS-only positioning with ZWDs derived from the assessed tropospheric modeling are about: 1 % (East), 20 % (North), and 5 % (Up). Since ZWD estimation is correlated with satellite geometry, we also investigated the positioning when processing GPS + GLONASS data, which increases significantly the number of available satellites. The improvements achieved by adding tropospheric corrections in this case are about: 2 % (East), 5 % (North), and 13 % (Up). Finally, a reduction in the number of reference stations by using a sparser network configuration to perform the tropospheric modeling does not degrade the generated tropospheric corrections, and similar performances are achieved.

Characteristics of inter-frequency clock bias for Block IIF satellites and its effect on triple-frequency GPS precise point positioning

Abstract: The latest generation of GPS satellites, termed Block IIF, provides a new L5 signal. Multi-frequency signals open new prospects for precise positioning and fast ambiguity resolution and have become the trend in Global Navigation Satellite System (GNSS) development. However, a new type of inter-frequency clock bias (IFCB), i.e., the difference between the current clock products computed with L1/L2 and the satellite clocks computed with L1/L5, was noticed. Consequently, the L1/L2 clock products cannot be used for L1/L5 precise point positioning (PPP). In order to solve this issue, the IFCB should be estimated with a high accuracy. Datasets collected at 129 globally distributed Multi-GNSS Experiment (MGEX) stations from 2015 are employed to investigate the IFCB. The results indicate that the IFCB is satellite dependent and varies with the relative sun---spacecraft---earth geometry. Other factors, however, may also contribute to the IFCB variations according to the harmonic analysis of the single-day IFCB time series. In addition, the results show that the IFCB exhibits periodic signal with a notable period of 43,080 s and the peak-to-peak amplitude is 0.023---0.269 m. After considering a time lag of 240 s, the average cross-correlation coefficient between the IFCB series of two consecutive days is 0.943, and the prediction accuracy of IFCB is 0.006 m. A triple-frequency PPP model that takes the IFCB into account is proposed. When using 3-h datasets, the positioning accuracy of triple-frequency PPP can be improved by 19, 13 and 21 % compared with the L1/L2-based PPP in the east, north and up directions, respectively.

Likelihood-based GNSS positioning using LOS/NLOS predictions from 3D mapping and pseudoranges

Abstract: The accuracy of conventional global navigation satellite systems (GNSS) positioning in dense urban areas is severely degraded due to blockage and reflection of the signals by the surrounding buildings. By using 3D mapping of the buildings to aid GNSS positioning, the accuracy can be substantially improved. However, positioning performance must be balanced against computational load. Here, a likelihood-based 3D-mapping-aided (3DMA) GNSS ranging algorithm is demonstrated that enables signals predicted to be non-line-of-sight (NLOS) to contribute to the position solution without explicitly computing the additional path delay due to NLOS reception, which is computationally expensive. Likelihoods for an array of candidate positions are computed based on the difference between the measured and predicted pseudoranges. However, a skewed distribution is assumed for those signals predicted to be NLOS on the basis that the ensuing ranging errors are always positive. An overall position solution is then extracted from the likelihood surface. GNSS measurement data have been collected at several locations in both traditional and modern dense urban environments. Horizontal root-mean-square single-epoch position accuracies of 4.7, 5.6 and 6.5 m are obtained using, respectively, a Leica Viva geodetic receiver, a u-blox EVK M8T consumer-grade receiver and a Nexus 9 tablet incorporating a smartphone GNSS antenna and a GNSS chipset that outputs pseudoranges. The corresponding accuracies using single-epoch conventional GNSS positioning are 20.5, 23.0 and 28.4 m, about a factor of four larger. The 3DMA GNSS algorithms have also been implemented in real time on a Raspberry Pi 3 at a 1-Hz update rate.

Real-time multi-GNSS single-frequency precise point positioning

Abstract: Precise Point Positioning (PPP) is a popular Global Positioning System (GPS) processing strategy, thanks to its high precision without requiring additional GPS infrastructure. Single-Frequency PPP (SF-PPP) takes this one step further by no longer relying on expensive dual-frequency GPS receivers, while maintaining a relatively high positioning accuracy. The use of GPS-only SF-PPP for lane identification and mapping on a motorway has previously been demonstrated successfully. However, the performance was shown to depend strongly on the number of available satellites, limiting the application of SF-PPP to relatively open areas. We investigate whether the applicability can be extended by moving from using only GPS to using multiple Global Navigation Satellite Systems (GNSS). Next to GPS, the Russian GLONASS system is at present the only fully functional GNSS and was selected for this reason. We introduce our approach to multi-GNSS SF-PPP and demonstrate its performance by means of several experiments. Results show that multi-GNSS SF-PPP indeed outperforms GPS-only SF-PPP in particular in case of reduced sky visibility.

Wavelet packets based denoising method for measurement domain repeat-time multipath filtering in GPS static high-precision positioning

Abstract: Repeatable satellite orbits can be used for multipath mitigation in GPS-based deformation monitoring and other high-precision GPS applications that involve continuous observation with static antennas. Multipath signals at a static station repeat when the GPS constellation repeats given the same site environment. Repeat-time multipath filtering techniques need noise reduction methods to remove the white noise in carrier phase measurement residuals in order to retrieve the carrier phase multipath corrections for the next day. We propose a generic and robust three-level wavelet packets based denoising method for repeat-time-based carrier phase multipath filtering in relative positioning; the method does not need tuning to work with different data sets. The proposed denoising method is tested rigorously and compared with two other denoising methods. Three rooftop data sets collected at the University of Nottingham Ningbo China and two data sets collected at three Southern California Integrated GPS Network high-rate stations are used in the performance assessment. Test results of the wavelet packets denoising method are compared with the results of the resistor---capacitor (RC) low-pass filter and the single-level discrete wavelet transform (DWT) denoising method. Multipath mitigation efficiency in carrier phase measurement domain is shown by spectrum analysis of two selected satellites in two data sets. The positioning performance of the repeat-time-based multipath filtering techniques is assessed. The results show that the performance of the three noise reduction techniques is about 1---46 % improvement on positioning accuracy when compared with no multipath filtering. The statistical results show that the wavelet packets based denoising method is always better than the RC filter by 2---4 %, and better than the DWT method by 6---15 %. These results suggest that the proposed wavelet packets based denoising method is better than both the DWT method and the relatively simple RC low-pass filter for noise reduction in multipath filtering. However, the wavelet packets based denoising method is not significantly better than the RC filter.

Improving prediction performance of GPS satellite clock bias based on wavelet neural network

Abstract: As one of the IGS ultra-rapid predicted (IGU-P) products, the orbit precision has been remarkably improved since late 2007. However, because satellite atomic clocks in space show complicated time---frequency characteristics and are easily influenced by many external factors such as temperature and environment, the IGU-P clock products have not shown sufficient high-quality prediction performance. An improved prediction model is proposed in order to enhance the prediction performance of satellite clock bias (SCB) by employing a wavelet neural network (WNN) model based on the data characteristic of SCB. Specifically, two SCB values of adjacent epoch subtract each other to get the corresponding single difference sequence of SCB, and then, the sequence is preprocessed through using the preprocessing method designed for the single difference sequence. The subsequent step is to model the WNN based on the preprocessed sequence. After the WNN model is determined, the next single difference values at the back of the modeling sequence are predicted. Lastly, the predicted single difference values are restored to the corresponding predicted SCB values. The simulation results have shown that the proposed prediction principle based on the single difference sequence of SCB can make the WNN model simple in architecture and the predicting precision higher than that of the general SCB prediction modeling. The designed preprocessing method specific to the single difference of SCB is able to further improve the prediction performance of the WNN model by reducing the effect from outliers. The proposed SCB prediction model outperforms the IGU-P solutions at least on a daily basis. Specifically, the average prediction precisions for 6, 12 and 24 h based on the proposed model have improved by about 13.53, 31.56 and 49.46 % compared with the IGU-P clock products, and the corresponding average prediction stabilities for 12 and 24 h have increased by about 13.89 and 27.22 %, while the average prediction stability of 6 h is nearly equal.

GPS/BDS short-term ISB modelling and prediction

Abstract: The Chinese BeiDou Navigation Satellite System (BDS) has completed its first milestone by providing coverage of the Asia---Pacific area navigation service since December 27, 2012. With the combination of BDS, the GNSS precise point positioning (PPP) can improve its positioning accuracy, availability and reliability. However, in order to achieve the best positioning solutions, the inter-system bias (ISB) between GPS and BDS must be resolved as precisely as possible. In this study, a 1-week period (GPS week 1810) of GPS/BDS observations for 18 distributed stations from the International GNSS Service Multi-GNSS Experiment are processed. Primarily, the ISB is estimated by an extended Kalman filter as a piece-wise parameter every 30 min. Then we generate a smoothed ISB series (ISB_s) with a sliding window median filter to reject the outliers from the original estimated ISB series (ISB_o). After analysing the characteristics of the ISB_s, a short-term station-dependent ISB model based on a 1-week period is proposed in this study. This model consists of a quadratic polynomial in time and two or three periodic functions with diurnal and semi-diurnal periods. Frequency spectrum analysis is used to determine the periods of the periodic functions, and the coefficients of the quadratic function and the periodic functions are estimated by least squares. For model verification, we compare the ISB derived from the model (ISB_m) with ISB_s (assumed the true values). The comparisons indicate an almost normal distribution. It is found that the proposed model is consistent with the true values: the root-mean-square (RMS) values being about 0.7 ns, and some stations are even better. This means that the short-term ISB model proposed has a high fitting accuracy. Hence, it can be used for ISB prediction. Comparing the prediction ISB series (ISB_p) with ISB_s in the following week (GPS week 1811), we can draw the conclusion that the accuracy of the prediction declines with an increase in the time period. The 1-day period precision can achieve 0.57---1.21 ns, while the accuracy of the 2-day prediction decreases to 0.77---1.72 ns. Hence, we recommend a predicting duration of 1 day. The proposed model will be beneficial for subsequent GPS/BDS PPP or precise orbit determination (POD) since the ISB derived from this model can be considered as a priori constraint in the PPP/POD solutions. With this a priori constraint, the convergence time can be shortened by 19.6, 16.1 and 2.4 % in N, E and U components, respectively. The accuracy of result in the E component is remarkably improved by 11.9 %.

Feasibility analysis of baseband architectures for multi-GNSS receivers

Abstract: Receiver design challenges arising from new GNSS signals include required intermediate frequency, sampling rate, modulation type, spreading code, and secondary code. Several architectures are examined here aiming at a best model for multi-GNSS implementation, especially the underlying baseband and software realization platform. In this pursuit, it is found that the multi-core and multiple processor architectures are promising candidates. General purpose processors or digital signal processors demand excessive resources and power consumption. Alternative architectures are presented along with the general cost function, used to evaluate architecture efficiency. Taking into account (1) the superiority of a hardware time-interleaving technique, (2) RAM-based design versus register-based design, and (3) careful consideration of modern GNSS signal attributes, the proposed programmable custom pipeline correlator core provides flexibility and significantly reduces resources and power.

GPS real-time precise point positioning for aerial triangulation

Abstract: We extend the application of real-time kinematic PPP to aerial triangulation using GPS to determine coordinates of the antenna installed on the airplane, using real-time satellite products from IGS and the CNES Analysis Center. In order to verify the performance of real-time kinematic PPP for aerial triangulation, three tests with varying aerial and ground conditions are assessed. Numerical results show that real-time kinematic PPP using IGS real-time products of 5-cm orbit accuracy and 0.1- to 0.3-ns clock precision can provide comparable accuracy for aerial photogrammetric mapping at the scale of 1:1000 as does post-mission kinematic PPP using IGS final products. Millimeter-to-centimeter-level differences and centimeter-to-2-decimeter differences are identified for horizontal and vertical coordinates of ground check points, respectively, in the three tests. The comparison between real-time IGS and CNES products for GPS positioning and aerial triangulation unveils that real-time products with a better clock precision can result in better performance of GPS real-time kinematic PPP as applied to aerial triangulation.

Comparison of solar radiation pressure models for BDS IGSO and MEO satellites with emphasis on improving orbit quality

Abstract: In order to simplify the attitude control for inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites of the BeiDou Navigation Satellite System (BDS) in eclipse seasons, two attitude modes, namely yaw-steering (YS) and orbit-normal (ON) mode are used. Significant accuracy degradation is observed for the orbits determined with the purely empirical CODE solar radiation pressure (SRP) model when these satellites switch to the ON mode. In addition, even though BDS IGSO satellites are in the YS mode, the orbits determined with the CODE SRP model show undesirable systematic errors that depend on the elevation angle β of the sun above the satellite orbit plane and on the argument angle μ of satellite with respect to the midnight point in the orbit plane as identified from satellite laser ranging residuals. We present the yaw attitude model used for the bus of BDS IGSO and MEO satellites, and constrain the mode-switch conditions by the β and μ angles. In order to overcome the deficiency of the purely empirical CODE SRP model for precise orbit determination (POD) of BDS IGSO and MEO satellites in the ON mode, an additional constant acceleration bias with tight constraint of 1.0 × 10ź10 m/s2 in the along-track direction has been introduced to the CODE SRP model, and it is denoted as the C5a model. Although the orbit accuracy of IGSO and MEO satellites is significantly improved in the ON mode, the β- and μ-dependent systematic orbit errors of BDS IGSO are not reduced. Hence, with the presented yaw attitude model of the satellite bus and two assumed orientations of solar panels, the adjustable box-wing (ABW) model has been modified. Two modified ABW models are compared with the purely empirical CODE and C5a model. Based on the analysis of real data of 2014, the C5a model shows the best performance in the ON mode among the four SRP models. Although two modified ABW models show a rather worse performance for POD in the ON mode, particularly in the cross-track and radial direction, the β- and μ-dependent systematic orbit errors of BDS IGSO satellites are reduced. This provides a new insight and a possible way to improve the orbits of BDS IGSO and MEO satellites.

Real-time precise point positioning augmented with high-resolution numerical weather prediction model

Abstract: The tropospheric delay is one of the major error sources in precise point positioning (PPP), affecting the accuracy and precision of estimated coordinates and convergence time, which raises demand for a reliable tropospheric model, suitable to support PPP. In this study, we investigate the impact of three tropospheric models and mapping functions regarding position accuracy and convergence time. We propose a routine to constrain the tropospheric estimates, which we implemented in the in-house developed real-time PPP software. We take advantage of the high spatial resolution (4 × 4 km2) numerical weather prediction Weather Research and Forecasting (WRF) model and near real-time GNSS data combined by the least-squares collocation estimation to reconstruct the tropospheric delays. We also present mapping functions calculated from the WRF model using the ray-tracing technique. The performance tests are conducted on 14 Polish EUREF Permanent Network (EPN) stations during 3 weeks of different tropospheric conditions: calm, standard and severe. We consider six GNSS data processing variants, including two commonly used variants using a priori ZTD and mapping functions from UNB3m and VMF1-FC models, one with a priori ZTD and mapping functions calculated directly from WRF model and three variants using the aforementioned mapping functions but with ZTD model based on GNSS and WRF data used as a priori troposphere and to constrain tropospheric estimates. The application of a high-resolution GNSS/WRF-based ZTD model and mapping functions results in the best agreement with the official EPN coordinates. In both static and kinematic modes, this approach results in an average reduction of 3D bias by 20 and 10 mm, respectively, but an increase of 3D SDs by 1.5 and 4 mm, respectively. The application of high-resolution tropospheric model also shortens the convergence time, for example, for a 10 cm convergence level, from 67 to 58 min for the horizontal components and from 79 to 63 min for the vertical component.

Integrating GPS and BDS to shorten the initialization time for ambiguity-fixed PPP

Abstract: The main challenge of ambiguity resolution in precise point positioning (PPP) is that it requires 30 min or more to succeed in the first fixing of ambiguities. With the full operation of the BeiDou (BDS) satellite system in East Asia, it is worthwhile to investigate the performance of GPS + BDS PPP ambiguity resolution, especially the improvements of the initial fixing time and ambiguity-fixing rate compared to GPS-only solutions. We estimated the wide- and narrow-lane fractional-cycle biases (FCBs) for BDS with a regional network, and PPP ambiguity resolution was carried out at each station to assess the contribution of BDS. The across-satellite single-difference (ASSD) GPS + BDS combined ambiguity-fixed PPP model was used, in which the ASSD is applied within each system. We used a two-day data set from 48 stations. For kinematic PPP, the percentage of fixing within 10 min for GPS only (Model A) is 17.6 %, when adding IGSO and MEO of BDS (Model B), the percentage improves significantly to 42.8 %, whereas it is only 23.2 % if GEO is added (Model C) due to the low precision of GEO orbits. For static PPP, the fixing percentage is 32.9, 53.3 and 28.0 % for Model A, B and C, respectively. In order to overcome the limitation of the poor precision of GEO satellites, we also used a small network of 10 stations to analyze the contribution of GEO satellites to kinematic PPP. We took advantage of the fact that for stations of a small network the GEO satellites appear at almost the same direction, such that the GEO orbit error can be absorbed by its FCB estimates. The results show that the percentage of fixing improves from 39.5 to 57.7 % by adding GEO satellites.

Reliable partial ambiguity resolution for single-frequency GPS/BDS and INS integration

Abstract: Correctly fixing carrier phase integer ambiguities is a prerequisite to achieve high-precision positioning solutions from global navigation satellite system (GNSS). However, for the single-frequency dynamic users, a low ambiguity resolution (AR) success rate is usually associated with the small number of visible satellites. It is expected that the instantaneous single-frequency AR performance will be significantly improved by combining the observations from both global positioning system (GPS) and Chinese BeiDou navigation satellite system (BDS) for enhanced geometric strength. We develop an inertially aided AR technique using single-frequency GPS/BDS observations. With the addition of inertial navigation system (INS) measurements, a highly reliable fixing of ambiguities right after the GNSS signal blockages is possible because of the improved accuracy of the float ambiguities based on the calibrated inertial navigation solutions before the GNSS signal blockages. In addition, a new partial ambiguity resolution (PAR) technique is proposed, which is of great benefit when full ambiguity resolution fails under challenging conditions. The subset of ambiguities is ordered according to the maximum rounding fixing rate ordering method. An a priori decorrelation procedure is applied to the original observations that aim to obtain an optimal subset ordering. A further AR procedure is conducted to resolve the remaining unfixed ambiguities using the ambiguity-fixed phase observations, with the objective of improving the probability of fixing more ambiguities. In order to test the proposed algorithm, a field vehicular test was performed. The results show the availability and reliability of ambiguity resolution for the INS-aided single-frequency GPS/BDS using PAR technique are significantly improved compared to that of GNSS-only, and a success rate greater than 90 % can be obtained for the single-GNSS/INS system as well as combined GPS/BDS/INS system. In terms of positioning accuracy, the best performance is achievable for the single-frequency GPS/BDS/INS system, the RMSs for position difference stay below 1 cm for GPS/INS and GPS/BDS/INS single-epoch solutions; however, the worst positioning performance is from the BDS/INS system. In terms of INS bridging capability, a fast ambiguity recovery within 5 s becomes feasible for a 19-s outage using INS-aided PAR scheme after a long calibration period.

Timeslot scheduling of inter-satellite links based on a system of a narrow beam with time division

Abstract: An inter-satellite link (ISL) can enhance the performance of a global navigation satellite system. The system of narrow beams with time division is being increasingly used for ISLs. ISLs improve the performance of global navigation satellite systems via ranging and communication between satellites. When there are fewer antenna beams than targets, how to schedule timeslots for inter-satellite links to better perform the function of ISLs can become a problem. We describe the timeslot scheduling problem and propose a new method based on grouping to solve this problem of obtaining more range observations in a short time and communicating with a short delay between satellites and facilities. A series of 10,080 benchmarks of a typical constellation of a global navigation satellite system was run to demonstrate the feasibility of the proposed method. The regression cycle of constellations under test lasted approximately 7 days. The proposed schedule has a communication delay of less than 10 s and obtains more than nine different range observations in 60 s. Results show that the method effectively solves the scheduling problem and increases the scheduling success ratio remarkably.

Global ionosphere maps based on GNSS, satellite altimetry, radio occultation and DORIS

Abstract: Global ionosphere maps (GIMs) provided by the global navigation satellite systems (GNSS) data are essential in ionospheric research as the source of the global vertical total electron content (VTEC). However, conventional GIMs experience lower accuracy and reliability from uneven distribution of GNSS tracking stations, especially in ocean areas with few tracking stations. The orbits of ocean altimetry satellite cover vast ocean areas and can directly provide VTEC at nadir with two different wavelengths of radio waves. Radio occultation observations and the beacons of Doppler orbitography and radio positioning integrated by satellite (DORIS) are evenly distributed globally. Satellite altimetry, radio occultation and DORIS can compensate GNSS data in ocean areas, allowing a more accurate and reliable GIMs to be formed with the integration of these observations. This study builds GIMs with temporal intervals of 2 h by the integration of GNSS, satellite altimetry, radio occultation and DORIS data. We investigate the integration method for multi-source data and used the data in May 2013 to validate the effectiveness of integration. Result shows that VTEC changes by ź11.0 to ź7.0 TECU after the integration of satellite altimetry, radio occultation and DORIS data. The maximum root mean square decreases by 5.5 TECU, and the accuracy of GIMs in ocean areas improves significantly.

Ionospheric delay gradient model for GBAS in the Asia-Pacific region

Abstract: We investigated characteristics of anomalous spatial gradients in ionospheric delay on GNSS signals in the Asia-Pacific (APAC) low-magnetic latitude region in the context of the ground-based augmentation system (GBAS). The ionospheric studies task force established under the Communications, Navigation, and Surveillance subgroup of International Civil Aviation Organization (ICAO) Asia-Pacific Air Navigation Planning and Implementation Regional Group, analyzed GNSS observation data from the Asia-Pacific region to establish a regionally specified ionospheric threat model for GBAS. The largest ionospheric delay gradient value in the analyzed data was 518 mm/km at the L1 frequency (1.57542 GHz), observed at Ishigaki, Japan in April 2008. The upper bound on the ionospheric delay gradient for a common ionospheric threat model for GBAS in the ICAO APAC region was determined to be 600 mm/km, irrespective of satellite elevation angle.

Optimum stochastic modeling for GNSS tropospheric delay estimation in real-time

Abstract: In GNSS data processing, the station height, receiver clock and tropospheric delay (ZTD) are highly correlated to each other. Although the zenith hydrostatic delay of the troposphere can be provided with sufficient accuracy, zenith wet delay (ZWD) has to be estimated, which is usually done in a random walk process. Since ZWD temporal variation depends on the water vapor content in the atmosphere, it seems to be reasonable that ZWD constraints in GNSS processing should be geographically and/or time dependent. We propose to take benefit from numerical weather prediction models to define optimum random walk process noise. In the first approach, we used archived VMF1-G data to calculate a grid of yearly and monthly means of the difference of ZWD between two consecutive epochs divided by the root square of the time lapsed, which can be considered as a random walk process noise. Alternatively, we used the Global Forecast System model from National Centres for Environmental Prediction to calculate random walk process noise dynamically in real-time. We performed two representative experimental campaigns with 20 globally distributed International GNSS Service (IGS) stations and compared real-time ZTD estimates with the official ZTD product from the IGS. With both our approaches, we obtained an improvement of up to 10% in accuracy of the ZTD estimates compared to any uniformly fixed random walk process noise applied for all stations.

Cycle slip detection and repair of undifferenced single-frequency GPS carrier phase observations

Abstract: Cycle slip detection and repair is an important issue in the GPS data processing. Different methods have been developed to detect and repair cycle slips on undifferenced , single- or double-differenced observations. The issue is still crucial for high-precision GPS positioning, especially for the undifferenced GPS observations. A method is proposed to fix cycle slips based on the generalized likelihood ratio (GLR) test. The method has a good performance on cycle slip fixing of undifferenced carrier phase observations on individual frequencies, either on L1 or on L2, without making a linear combination among the observables. The functional model is a piecewise cubic curve fitted to a number of consecutive data using the least squares cubic spline approximation (LS-CSA). For fixing the cycle slips, an integer estimation technique is employed to determine the integer values from the float solution. The performance of the proposed method is then compared with the existing two methods using simulated data. The results on a few GPS data sets with sampling rate of 1 Hz or higher confirm that this method can detect and correct all simulated cycle slips regardless of the size of the cycle slip or the satellite elevation angle. The efficacy of the method is then investigated on the GPS data sets with lower sampling rates of 5, 10, and 30 s. The results indicate that the proposed method always performs the best for the data sets considered. This is thus an appropriate method for cycle slip detection and repair of single-frequency GPS observations.

Contributions of thermoelastic deformation to seasonal variations in GPS station position

Abstract: We investigate surface displacements due to land temperature variation with the 2014 global thermoelastic model, which is a solution on a uniformly elastic sphere under the constraint that the geocenter remains stationary. In this research, the seasonal variations of global surface displacements are numerically simulated based on 0---10 cm underground land surface temperatures from National Oceanic and Atmospheric Administration. The displacements include vertical and horizontal components for the first time. Meanwhile, the annual contributions of geophysical sources, which are mainly due to atmosphere, ocean, snow and continental water, are also estimated. For comparative analyses, the partial displacement by annual mass-loading and the total displacement by the combined annual of thermoelasticity and mass-loading are calculated, respectively, and displayed against the annual displacements at stations of global positioning system network. Results of the numerical simulation show that the amplitude of surface thermoelastic deformation is at the millimeter level on the global scale, topped at about 3 mm for radial displacement and about 1.5 mm for transverse components, which need to be considered for the high-precision terrestrial reference frame. The combined deformation caused by thermoelastic and mass-loading can explain the seasonal GPS observations better than the mass-loading alone, in particular for the transverse displacements.