Ionosphere-free Linear Combination Research Articles

Analysis on the Potential Performance of GPS and Galileo Precise Point Positioning using Simulated Real-Time Products

With the evolving Global Navigation Satellite System (GNSS) landscape, the International GNSS Service (IGS) has started the Multi-GNSS Experiment (MGEX) to produce precise products for new generation systems. Various analysis centres are working on the estimation of precise orbits, clocks and bias for Galileo, Beidou and Quasi-Zenith Satellite System (QZSS) satellites. However, at the moment these products can only be used for post-processing applications. Indeed, the IGS Real-Time service only broadcasts Global Positioning System (GPS) and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) corrections. In this research, a simulator of multi-GNSS observations and real-time precise products has been developed to analyse the performance of GPS-only, Galileo-only and GPS plus Galileo Precise Point Positioning (PPP). The error models in the simulated orbits and clocks were based on the difference between the GPS Real-Time and the Final products. Multiple scenarios were analysed, considering different signals combined in the Ionosphere Free linear combination. Results in a simulated open area environment show better performance of the Galileo-only case over the GPS-only case. Indeed, up 33% and 29% of improvement, respectively, in the accuracy level and convergence time can be observed when using the full Galileo constellation compared to GPS. The dual constellation case provides good improvements, in particular in the convergence time (47% faster than GPS). This paper will also consider the impact of different linear combinations of the Galileo signals, and the potential of the E5 Alternative Binary Offset Carrier (AltBOC) signal. Even though it is significantly more precise than E5a, the PPP performance obtained with the Galileo E1-E5a combination is either better or similar to the one with Galileo E1-E5. The reason for this inconsistency was found in the use of the ionosphere free combination with E1. Finally, alternative methods of ionosphere error mitigation are considered in order to ensure the best possible positioning performance from the Galileo E5 signal in multi-frequency PPP.

Temporal Stability of GPS Transmitter Group Delay Variations.

The code observable of global navigation satellite systems (GNSS) is influenced by group delay variations (GDV) of transmitter and receiver antennas. For the Global Positioning System (GPS), the variations can sum up to 1 m in the ionosphere-free linear combination and thus can significantly affect precise code applications. The contribution of the GPS transmitters can amount to 0.8 m peak-to-peak over the entire nadir angle range. To verify the assumption of their time-invariance, we determined daily individual satellite GDV for GPS transmitter antennas over a period of more than two years. Dual-frequency observations of globally distributed reference stations and their multipath combination form the basis for our analysis. The resulting GPS GDV are stable on the level of a few centimeters for C1, P2, and for the ionosphere-free linear combination. Our study reveals that the inconsistencies of the GDV of space vehicle number (SVN) 55 with respect to earlier studies are not caused by temporal instabilities, but are rather related to receiver properties.

Comparative study of using different ionosphere models in Thailand for single-frequency GNSS users

An ionosphere layer makes inaccurate global navigation satellite systems (GNSS) signal. The ionosphere layer contains free electrons delaying the speed of GNSS signals. A suitable selection of ionosphere model is very useful to eliminate this inaccurate GNSS signal. This article presents a comparative study by applying various ionosphere models in Thailand including: Klobuchar model, Global Ionosphere Maps, Ionosphere Model from Quasi-Zenith Satellite System and local ionosphere model. The local ionosphere model is generated from GNSS observations at with the use of locally available GNSS tracking stations by the Bernese GPS software 5.0. Coordinates derived from the above-mentioned models were compared and statistical tests in two observed scenarios; namely, single-frequency data and ionosphere-free linear combination from dual-frequency data. These experiment results proved that applying the local ionosphere model to the estimation produces the most accurate positioning results. They are similar to the results obtained from an ionosphere-free linear combination, but with significant differences.

Assessment of local GNSS baselines at co-location sites

As one of the major contributors to the realisation of the International Terrestrial Reference System (ITRS), the Global Navigation Satellite Systems (GNSS) are prone to suffer from irregularities and discontinuities in time series. While often associated with hardware/software changes and the influence of the local environment, these discrepancies constitute a major threat for ITRS realisations. Co-located GNSS at fundamental sites, with two or more available instruments, provide the opportunity to mitigate their influence while improving the accuracy of estimated positions by examining data breaks, local biases, deformations, time-dependent variations and the comparison of GNSS baselines with existing local tie measurements. With the use of co-located GNSS data from a subset sites of the International GNSS Service network, this paper discusses a global multi-year analysis with the aim of delivering homogeneous time series of coordinates to analyse system-specific error sources in the local baselines. Results based on the comparison of different GNSS-based solutions with the local survey ties show discrepancies of up to 10 mm despite GNSS coordinate repeatabilities at the sub-mm level. The discrepancies are especially large for the solutions using the ionosphere-free linear combination and estimating tropospheric zenith delays, thus corresponding to the processing strategy used for global solutions. Snow on the antennas causes further problems and seasonal variations of the station coordinates. These demonstrate the need for a permanent high-quality monitoring of the effects present in the short GNSS baselines at fundamental sites.

Utilization PPP method in aircraft positioning in post-processing mode

PurposeThe purpose of this paper is to study the implementation of GNSS technique in aviation for recovery of aircraft’s position using Precise Point Positioning (PPP) method.Design/methodology/approachThe aircraft’s coordinates in ellipsoidal frame were obtained based on GPS code and phase observations for PPP method. The numerical computations were executed in post-processing mode in the CSRS-PPP and magicPPP online services. The mathematical scheme of PPP method was development using indifference equations of Ionosphere-Free linear combination. In the experiment, airborne test using Cessna 172 aircraft on June 01, 2010 in the military airport in Deblin was realized. The aircraft’s position was determined using data from GNSS receiver (Topcon HiperPro with interval of 1 s).FindingsIn this paper, the accuracy of aircraft’s position is better than 0.07 m for CSRS-PPP service and better than 0.27 m for magicPPP service. In case of the Mean Radial Spherical Error parameter, the average value for CSRS-PPP service equals to 0.01 m, whereas for magicPPP, it is about 0.38 m. The values of vertical coordinate of Cessna 172 aircraft were also checked with results of Real Time Kinematic–On The Fly technique.Research limitations/implicationsIn this paper, the analysis of aircraft positioning is focused on the application of the PPP method in post-processing mode. In near real time, the PPP method still has limitations, especially in the area of ambiguity resolution and also instrumental biases (e.g. Narrow Lane Hardware Delays).Practical implicationsThe PPP method can be applied in aviation in post-processing mode for verification of true aircraft coordinates and elimination of blunder errors from adjustment processing of GNSS observations. The Zenith Wet Delay term as a product of troposphere delay and receiver clock bias as a product of precise time transfer can be obtained in the PPP method.Originality/valueThe paper presents that the PPP method is an alternative solution for the recovery of aircraft’s position in aviation, and this method can be also applied in the positioning of aircraft based on GLONASS or GPS/GLONASS data.

A theoretical and experimental comparison of the ionosphere‐free L1 pseudorange and the ionosphere‐free linear combination pseudorange by dual‐frequency SBAS users

This study verifies the performance of the ionosphere-free L1 pseudorange for dual-frequency space-based augmentation systems (SBAS) users by both of theoretical analysis and experiments with actual GPS data. Although the dual-frequency pseudorange from ionosphere-free linear combinations is commonly used as a standard method, the ionosphere-free L1 range based on the weighted Hatch filter has advantages in terms of the amplification factor caused by a dual-frequency combination and filter weights optimised by the least-squares method. For the experimental analysis, RINEX data were collected from five National Geographic Information Institute reference stations on the Korean peninsula and used to generate an SBAS correction message following international SBAS specifications. The experimental results show that using the proposed method results in a 29% improvement in the range domain compared with the use of a traditional ionosphere-free linear combination filter. In the position domain, the proposed method shows a horizontal accuracy improvement of 16% after the application of post-processed SBAS orbit/clock corrections w.r.t. the traditional filter. Finally, this study also demonstrates that the accuracy of dual-frequency users can surpass than that of single-frequency SBAS users only if corrections are estimated with ionospheric delay-free measurements in the master station as well.

Group delay variations of GPS transmitting and receiving antennas

GPS code pseudorange measurements exhibit group delay variations at the transmitting and the receiving antenna. We calibrated C1 and P2 delay variations with respect to dual-frequency carrier phase observations and obtained nadir-dependent corrections for 32 satellites of the GPS constellation in early 2015 as well as elevation-dependent corrections for 13 receiving antenna models. The combined delay variations reach up to 1.0 m (3.3 ns) in the ionosphere-free linear combination for specific pairs of satellite and receiving antennas. Applying these corrections to the code measurements improves code/carrier single-frequency precise point positioning, ambiguity fixing based on the Melbourne–Wübbena linear combination, and determination of ionospheric total electron content. It also affects fractional cycle biases and differential code biases.

Research Article. Improved Dual Frequency PPP Model Using GPS and BeiDou Observations

Abstract This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines GPS and BeiDou observations. Combining GPS and BeiDou observations in a PPP model offers more visible satellites to the user, which is expected to enhance the satellite geometry and the overall PPP solution in comparison with GPSonly PPP solution. However, combining different GNSS constellations introduces additional biases, which require rigorous modelling, including GNSS time offset and hardware delays. In this research, ionosphere-free linear combination PPP model is developed. The additional biases, which result from combining the GPS and BeiDou observables, are lumped into a new unknown parameter identified as the inter-system bias. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS/BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets at four IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the IGS-MGEX network are used to correct both of the GPS and BeiDou measurements. It is shown that a sub-decimeter positioning accuracy level and 25% reduction in the solution convergence time can be achieved with combining GPS and Bei-Dou observables in a PPP model, in comparison with the GPS-only PPP solution.

Triple-frequency GNSS models for PPP with float ambiguity estimation: performance comparison using GPS

This contribution proposes two new precise point positioning (PPP) models that use triple-frequency data, designed to accelerate convergence of carrier-phase float ambiguities. The first model uses a triple-frequency ionosphere-free linear combination that has minimum noise propagation and geometry-preserving properties. The second model uses a mixed code and carrier-phase linear combination with the same properties. A third model was also implemented, which uses individual uncombined triple-frequency measurements. The three models were validated using triple-frequency GPS data and their performance was compared to the traditional dual-frequency model in terms of the convergence time taken to achieve and maintain a uniform three-dimensional accuracy of 5 cm. Testing includes PPP processing of 1-h measurement blocks using 1–8 days of data from three locations in Australia. It was shown that all the three triple-frequency models had improved solution convergence time compared to the traditional PPP dual-frequency model although they gave almost similar accuracy and precision. The convergence time, when using the triple-frequency ionosphere-free model improved, by 10%, the improvement was 9% when using the mixed code-phase model, whereas the individual uncombined model resulted in 8% improvement.

A Phase-Altimetric Simulator: Studying the Sensitivity of Earth-Reflected GNSS Signals to Ocean Topography

This paper presents a simulation study on Global Navigation Satellite System (GNSS) reflections focusing on a phase altimetric method for ocean topography retrieval. It examines carrier phase residuals of Earth-reflected GNSS signals in preparation for the GNSS Reflectometry Radio Occultation and Scatterometry experiment aboard the International Space Station (GEROS-ISS). The residuals' sensitivity to ocean topography (maximum of 2-m amplitude variation of global sea level) is shown. A trigonometric approach to determine the specular reflection point is proposed. Reflection events are simulated assuming different low Earth orbit receivers and GNSS-type transmitters. Suitable events for phase altimetry are assumed between 5° and 30° elevation lasting between 10 and 15 min with ground tracks length of > 3000 km. Typical along-track footprints (1 s integration time) have a length of about 5 km. Within the assumed elevation range the coherent footprint ellipse has a major axis between 1 and 6 km. A Master-Slave sampling is proposed to approximate large-scale delay and Doppler variations of the reflected signal (Slave channel) relative to the direct signal (Master channel). Slave residuals of an example event are simulated to retrieve a small-scale phase delay for ocean topography inversion. The signal-to-noise ratio restricts the quality of the topography results. Height precision on sub-decimeter level for 30-dB SNR is degraded up to a meter level for 20-dB SNR. Ionosphere-free linear combination allows keeping the precision level. Troposphere refraction degrades precision particularly at the low elevation limit. Precision improves toward higher elevations. The tolerance to ocean roughness decreases in the same way.

Un-differenced precise point positioning model using triple GNSS constellations

AbstractThis paper introduces a dual-frequency precise point positioning (PPP) model, which combines the observations of three different global navigation satellite system (GNSS) constellations, namely GPS, Galileo, and BeiDou. A drawback of a single GNSS system such as GPS, however, is the availability of sufficient number of visible satellites in urban areas. Combining GNSS observations offers more visible satellites to users, which in turn is expected to enhance the satellite geometry and the overall positioning solution. However, combining several GNSS observables introduces additional biases, which require rigorous modeling, including the GNSS time offsets and hardware delays. In this paper, un-differenced ionosphere-free linear combination PPP model is developed. The additional biases of the GPS, Galileo, and BeiDou combination are accounted for through the introduction of a new unknown parameter, which is identified as the inter-system bias, in the PPP mathematical model. Natural Resources Canada’s...

Improving integer ambiguity resolution for GLONASS precise orbit determination

The frequency division multiple access adopted in present GLONASS introduces inter-frequency bias (IFB) at the receiver-end both in code and phase observables, which makes GLONASS ambiguity resolution rather difficult or even not available, especially for long baselines up to several thousand kilometers. This is one of the major reasons that GLONASS could hardly reach the orbit precision of GPS, both in terms of consistency among individual International GNSS Service (IGS) analysis centers and discontinuity at the overlapping day boundaries. Based on the fact that the GLONASS phase IFB is similar on L1 and L2 bands in unit of length and is a linear function of the frequency number, several approaches have been developed to estimate and calibrate the IFB for integer ambiguity resolution. However, they are only for short and medium baselines. In this study, a new ambiguity resolution approach is developed for GLONASS global networks. In the approach, the phase ambiguities in the ionosphere-free linear combination are directly transformed with a wavelength of about 5.3 cm, according to the special frequency relationship of GLONASS L1 and L2 signals. After such transformation, the phase IFB rate can be estimated and corrected precisely and then the corresponding double-differenced ambiguities can be directly fixed to integers even for baselines up to several thousand kilometers. To evaluate this approach, experimental validations using one-month data of a global network with 140 IGS stations was carried out for GLONASS precise orbit determination. The results show that the GLONASS double-difference ambiguity resolution for long baselines could be achieved with an average fixing-rate of 91.4 %. Applying the fixed ambiguities as constraints, the GLONASS orbit overlapping RMS at the day boundaries could be reduced by 37.2 % in ideal cases and with an averaged reduction of about 21.4 %, which is comparable with that by the GPS ambiguity resolution. The orbit improvement is also confirmed by the better agreement with the independent satellite laser ranging observations.

Evaluation of GPS Standard Point Positioning with Various Ionospheric Error Mitigation Techniques

AbstractThe present paper investigates accuracy of single and dual-frequency Global Positioning System (GPS) standard point positioning solutions employing different ionosphere error mitigation techniques. The total electron content (TEC) in the ionosphere is the prominent delay error source in GPS positioning, and its elimination is essential for obtaining a relatively precise positioning solution. The estimated delay error from different ionosphere models and maps, such as Klobuchar model, global ionosphere models, and vertical TEC maps are compared with the locally derived ionosphere error following the ion density and frequency dependence with delay error. Finally, the positional accuracy of the single and dual-frequency GPS point positioning solutions are probed through different ionospheric mitigation methods including exploitation of models, maps, and ionosphere-free linear combinations and removal of higher order ionospheric effects. The results suggest the superiority of global ionosphere maps for single-frequency solution, whereas for the dual-frequency measurement the ionosphere-free linear combination with prior removal of higher-order ionosphere effects from global ionosphere maps and geomagnetic reference fields resulted in improved positioning quality among the chosen mitigation techniques. Conspicuously, the susceptibility of height component to different ionospheric mitigation methods are demonstrated in this study which may assist the users in selecting appropriate technique for precise GPS positioning measurements.

Precise Point Positioning Model Using Triple GNSS Constellations: GPS, Galileo and BeiDou

AbstractThis paper introduces a comparison between dual-frequency precise point positioning (PPP) post-processing model, which combines the observations of three different GNSS constellations, namely GPS, Galileo, and BeiDou and real-time PPP model. A drawback of a single GNSS system such as GPS, however, is the availability of sufficient number of visible satellites in urban areas. Combining GNSS observations offers more visible satellites to users, which in turn is expected to enhance the satellite geometry and the overall positioning solution. However, combining several GNSS observables introduces additional biases, which require rigorous modelling, including the GNSS time offsets and hardware delays. In this paper, a GNSS post-processing PPPP model is developed using ionosphere-free linear combination. The additional biases of the GPS, Galileo, and BeiDou combination are accounted for through the introduction of a new unknown parameter, which is identified as the inter-system bias, in the PPP mathematical model. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS / Galileo / BeiDou PPP solution and to handle the newly inter-system bias. A total of four data sets at four IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the IGS-MGEX network are used to correct of the GPS, Galileo and BeiDou measurements. For the real-time PPP model the corrections of the satellites orbit and clock are obtained through the international GNSS service (IGS) real-time service (RTS). GPS and Galileo Observations are used for the GNSS RTS-IGS PPP model as the RTS-IGS satellite products are not available for BeiDou satellites. This paper provides the GNSS RTS-IGS PPP model using different satellite clock corrections namely: IGS01, IGC01, IGS01, and IGS03. All PPP models results of convergence time and positioning precision are compared to the traditional GPS-only PPP model. It is shown that combining GPS, Galileo, and BeiDou observations in a PPP model reduces the convergence time by 25 % compared with the GPS-only PPP model.

Advective diffusion of volcanic plume captured by dense GNSS network around Sakurajima volcano: a case study of the vulcanian eruption on July 24, 2012

Data from a dense GNSS network were used to investigate the temporal and spatial development of a volcanic plume during the eruptive event at Sakurajima volcano in Japan on July 24, 2012. We extracted the post-fit phase residuals (PPR) of ionosphere-free linear combinations for each satellite based on the precise point positioning (PPP) approach. Temporal and spatial PPR anomalies clearly detected the movement of the volcanic plume. The maximum height of the crossing points of anomalous PPR paths was determined to be approximately 4000 m. We also compared the estimated wet zenith tropospheric delay with the estimated PPR anomalies, which suggested that we might successfully extract the PPR anomalies caused by the eruptive event. We then compared the PPR with the signal-to-noise ratio (SNR) anomalies. Only the path passing just above the crater showed significant change in the SNR value, suggesting that the volcanic ash and the water vapor within the volcanic plume became separated after reaching a high altitude because of ash fall during the plume’s lateral movement. Each of the two observables might reflect different characteristics of the water vapor and volcanic ash.

Single-frequency precise point positioning: an analytical approach

An analytical approach to single-frequency precise point positioning (PPP) is discussed in this paper. To obtain highest precision results, all biases must be eliminated or modelled to centimetre level. The use of the GRAPHIC ionosphere-free linear combination that is based on single-frequency phase and code observations eliminates the ionosphere bias; however, the rank deficient Gauss–Markov model is obtained. We explicitly determine rank deficiency of a Gauss–Markov model as a number of all ambiguity clusters, each of them defined as a set of all ambiguities overlapping in time. On the basis of S-transformation we prove that the single-frequency PPP represents an unbiased estimator for station coordinates and troposphere parameters, while it presents a biased estimator for ambiguities and receiver-clock error parameters. Additionally we describe the estimable parameters in each ambiguity cluster as the differences between ambiguity parameters and the sum of receiver-clock parameters with one of the ambiguities. We also show that any other particular solution on the basis of S-transformation is obtained only when the common least-squares estimation in single step is applied. The recursive least-squares estimation with parameter pre-elimination only determines the vector of unknowns as possible to transform through S-transformation, whereas the same does not hold for the cofactor matrix of unknowns. For a case study, we present our method on GPS data from 19 permanent stations (14 IGS and 5 EPN) in Europe, for 89 consecutive days in the beginning of 2013. The static case study revealed the precision of daily coordinates as 7.6, 11.7 and 19.6 mm for \(N\), \(E\) and \(U\), respectively. The accuracies of the \(N\), \(E\) and \(U\) components were determined as 6.9, 13.5 and 31.4 mm, respectively, and were calculated using the Helmert transformation of weighted-mean daily single-frequency PPP and IGb08 coordinates. The estimated convergence times were relatively diverse, expanding from 1.75 h (CAGL) to 5.25 h (GRAZ) for the horizontal position with the 10-cm precision threshold, and from 1.00 h (GRAS) to 3.25 h (BZRG) for the height component with a 20-cm precision threshold. The convergence times were shown to be strongly correlated to the remaining unmodelled biases in the GRAPHIC linear combination, primarily with multipath, where the correlation coefficient for the horizontal position was determined as \(\rho _P\) \(=\) 0.68 and for height as \(\rho _U\) \(=\) 0.85. The comparison to the model where raw observations are used (\(C\), \(L\)) and where the ionosphere bias is mitigated with global ionosphere models (GIM) revealed the supremacy of the proposed single-frequency PPP method based on the GRAPHIC linear combination in both the static and the semi-kinematic case study. In the static case study, the proposed single-frequency PPP model was superior both in terms of precision and accuracy. In the semi-kinematic case study, the usage of raw observations with GIM would improve results only when multipath and noise of code observations would prevail over the remaining ionosphere bias, i.e. after applying GIM.

Integration of GPS precise point positioning and MEMS-based INS using unscented particle filter.

Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) integrated system involves nonlinear motion state and measurement models. However, the extended Kalman filter (EKF) is commonly used as the estimation filter, which might lead to solution divergence. This is usually encountered during GPS outages, when low-cost micro-electro-mechanical sensors (MEMS) inertial sensors are used. To enhance the navigation system performance, alternatives to the standard EKF should be considered. Particle filtering (PF) is commonly considered as a nonlinear estimation technique to accommodate severe MEMS inertial sensor biases and noise behavior. However, the computation burden of PF limits its use. In this study, an improved version of PF, the unscented particle filter (UPF), is utilized, which combines the unscented Kalman filter (UKF) and PF for the integration of GPS precise point positioning and MEMS-based inertial systems. The proposed filter is examined and compared with traditional estimation filters, namely EKF, UKF and PF. Tightly coupled mechanization is adopted, which is developed in the raw GPS and INS measurement domain. Un-differenced ionosphere-free linear combinations of pseudorange and carrier-phase measurements are used for PPP. The performance of the UPF is analyzed using a real test scenario in downtown Kingston, Ontario. It is shown that the use of UPF reduces the number of samples needed to produce an accurate solution, in comparison with the traditional PF, which in turn reduces the processing time. In addition, UPF enhances the positioning accuracy by up to 15% during GPS outages, in comparison with EKF. However, all filters produce comparable results when the GPS measurement updates are available.

GNSS triple-frequency geometry-free and ionosphere-free track-to-track ambiguities

During the last few years, more and more GNSS satellites have become available sending signals on three or even more frequencies. Examples are the GPS Block IIF and the Galileo In-Orbit-Validation (IOV) satellites. Various investigations have been performed to make use of the increasing number of frequencies to find a compromise between eliminating different error sources and minimizing the noise level, including the investigations in the triple-frequency geometry-free (GF) and ionosphere-free (IF) linear combinations, which eliminate all the geometry-related errors and the first-order term of the ionospheric delays.In contrast to the double-difference GF and IF ambiguity resolution, the resolution of the so-called track-to-track GF and IF ambiguities between two tracks of a satellite observed by the same station only requires one receiver and one satellite. Most of the remaining errors like receiver and satellite delays (electronics, cables, etc.) are eliminated, if they are not changing rapidly in time, and the noise level is reduced theoretically by a factor of square root of two compared to double-differences. This paper presents first results concerning track-to-track ambiguity resolution using triple-frequency GF and IF linear combinations based on data from the Multi-GNSS Experiment (MGEX) from April 29 to May 9, 2012 and from December 23 to December 29, 2012. This includes triple-frequency phase and code observations with different combinations of receiver tracking modes. The results show that it is possible to resolve the combined track-to-track ambiguities of the best two triple-frequency GF and IF linear combinations for the Galileo frequency triplet E1, E5b and E5a with more than 99.6% of the fractional ambiguities for the best linear combination being located within ±0.03 cycles and more than 98.8% of the fractional ambiguities for the second best linear combination within ±0.2 cycles, while the fractional parts of the ambiguities for the GPS frequency triplet L1, L2 and L5 are more disturbed by errors as e.g. the uncalibrated Phase Center Offsets (PCOs) and Phase Center Variations (PCVs), that have not been considered. The best two GF and IF linear combinations between tracks are helpful to detect problems in data and receivers. Furthermore, resolving the track-to-track ambiguities is helpful to connect the single-receiver ambiguities on the normal equation level and to improve ambiguity resolution.

Performance Analysis of GPS / GALILEO PPP Model for Static and Kinematic Applications

In this paper, the contribution of Galileo observations to GPS precise point positioning (PPP) is assessed for both static and kinematic applications. As well, the performance of Galileo-only PPP is investigated in static mode using the existing four operational Galileo satellites. Un-differenced ionosphere-free linear combinations of pseudorange and carrier phase measurements are considered herein. Rigorous models are used to account for tropospheric delay, satellite clock error, ocean loading, Earth tide, carrier phase windup, relativity, and satellite antenna phase-center variations. The accuracy of combined GPS/ Galileo PPP solution is assessed in static mode using data from a number of GNSS stations within the multi-GNSS experiment (MGEX). To assess the accuracy of kinematic GPS/Galileo PPP, we use data from a real test scenario in downtown Kingston, Ontario. The results indicate that Galileo-only PPP achieves decimetre to metre-level positioning accuracy. However, the solution convergence time exceeds the one-hour level due to the presence of code biases. The addition of Galileo observations slightly enhances the PPP accuracy and convergence time in comparison with the GPS-only PPP solution.

Integration of Multi-Constellation GNSS Precise Point Positioning and MEMS-Based Inertial Systems Using Tightly Coupled Mechanization

We develop a new integrated navigation system, which integrates multi-constellations GNSS precise point positioning (PPP), including GPS, GLONASS and Galileo, with low-cost micro-electro-mechanical sensor (MEMS) inertial system, for precise positioning applications. To integrate GNSS and the MEMS-based inertial system, the process and measurement models are developed. Tightly coupled mechanism is adopted, which is carried out in the GNSS raw measurements domain. Both un-differenced and between-satellite single-difference (BSSD) ionosphere-free linear combinations of pseudorange and carrier phase GNSS measurements are processed. Rigorous models are employed to correct GNSS errors and biases. The GNSS inter-system biases are considered as additional unknowns in the integrated error state vector. The developed stochastic model for inertial sensors errors and biases are defined based on first order Gaussian Markov process. Extended Kalman filter is developed to integrate GNSS and inertial measurements and estimate inertial measurements biases and errors. Two field experiments are executed, which represent different real-world scenarios in land-based navigation. The data are processed by using our developed Ryerson PPP GNSS/MEMS software. The results indicate that the proposed integrated system achieves decimeter to centimeter level positioning accuracy when the measurement updates from GNSS are available. During complete GNSS outages the developed integrated system continues to achieve decimeter level accuracy for up to 30 seconds while it achieves meter-level accuracy when a 60-second outage is introduced.