Multi-frequency Precise Point Positioning Research Articles

Dual-frequency to five-frequency real-time precise point positioning using new BDS-3 PPP-B2b service

BeiDou global navigation satellite system (BDS-3), a developed GNSS by China, has the ability to support five different signals, including B1I, B3I, B1C, B2a, and B2b. Meanwhile, BDS-3 has officially provided the satellite-based precise point positioning (PPP) service through the B2b signal (PPP-B2b) since 2021. It’s necessary to conduct a comprehensive analysis on multi-frequency PPP with PPP-B2b corrections. In this study, a multi-frequency undifferenced and uncombined PPP model (UDUC) using PPP-B2b corrections was employed to investigate dual-frequency to five-frequency real-time PPP performance. The results show that compared with the conventional dual-frequency solutions, multi-frequency solutions can improve both the convergence performances and positioning accuracy of PPP-B2b service, especially during the convergence stage. The quad-frequency and five-frequency solutions can achieve the best positioning performance. The static solutions of multi-frequency PPP models reach the centimeter-level accuracy after convergence. In kinematic mode, the convergence time of the five-frequency PPP results is reduced by 23.5% compared with the dual-frequency results. The root mean square (RMS) errors of the five-frequency PPP in the E, N, and U components are 7.1 cm, 4.8 cm, and 12.4 cm, which are improved by 6.8%, 11.5%, and 5.5%, respectively.Graphical

Uncalibrated phase delay estimation and ambiguity resolution for BDS-3 six-frequency uncombined PPP with legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals

Multi-frequency integration can accelerate the ambiguity resolution (AR) and shorten the convergence time of precise point positioning (PPP). BDS-3 satellites can broadcast legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals, which facilitates the multi-frequency PPP. An uncalibrated phase delay (UPD) estimation method and a fast AR method are extended for BDS-3 six-frequency uncombined PPP. The characteristics of UPD estimates are analyzed in terms of stability, ambiguity residuals, and usage rate. The data sets on seven consecutive days from 224 globally distributed stations are selected for UPD estimation, and those from 21 stations are employed for PPP AR. The results indicate that the static convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions (with a threshold of 10 cm) can reach 8.2, 4.0, and 13.4 min in the east, north, and up directions, respectively, and the three-dimensional (3D) convergence time is shortened by 21.1 % and 26.5 % compared with the six-frequency ambiguity-float solutions and the dual-frequency ambiguity-fixed solutions, respectively. The corresponding kinematic convergence time can reach 13.0, 7.0, and 33.2 min in three directions, respectively, and the corresponding improvement rates are 21.0 % and 33.7 %, respectively. In addition, the convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions can be slightly shortened even compared with the five-frequency case. The static and kinematic positioning accuracy of BDS-3 six-frequency PPP ambiguity-fixed solutions can reach 4, 3, and 9 mm, and 18, 14, and 38 mm in three directions, respectively, which is slightly better than other cases.

Influence of Stochastic Modeling for Inter-Frequency Clock Biases on Multi-Frequency Precise Point Positioning

Influence of Stochastic Modeling for Inter-Frequency Clock Biases on Multi-Frequency Precise Point Positioning

Multi-Frequency BDS-3 Real-Time Positioning Performance Assessment Using New PPP-B2b Augmentation Service

A new precise point positioning (PPP)-B2b augmentation service broadcast by the BeiDou Navigation Satellite System (BDS-3) geosynchronous Earth orbit (GEO) satellite can provide real-time and high-precision orbit and clock offset corrections for global navigation satellite system (GNSS) users in China and its surrounding areas. It has great significance and research value for real-time and high-precision positioning applications. First, orbit, clock offset, and differential code bias (DCB) of PPP-B2b products are evaluated. Second, the influence of PPP-B2b service on the enhanced positioning of single-frequency (SF), dual-frequency (DF), and Multi-Frequency (MF) real-time PPP using 30 days of BDS-3 observations is verified. The result shows that the standard deviation (STD) of clock offset and the root mean square (rms) of orbit in the 3-D direction for medium Earth orbit (MEO) satellites are 0.118 ns and 0.286 m, respectively, which is 75.9% and 18.3% higher than that of broadcast ephemeris. The statistical results show that the median positioning accuracy of static SF PPP, DF PPP, and MF PPP is better than 0.20/0.09/0.08 m, and the convergence time is better than 51/10/8 min. The median positioning accuracy of kinematic SF PPP, DF PPP, and MF PPP is better than 0.40/0.12/0.12 m, and the convergence time is better than 145/16/12 min. Using the PPP-B2b products, the positioning accuracy of DF PPP and MF PPP is comparable and close to that of DF PPP using the precise products, while the convergence time of MF PPP is improved by 24.8% and 27.7% over DF PPP in static and kinematic solutions, respectively.

Analysis of Galileo five-frequency precise satellite clock estimation models and its effect on multi-frequency PPP

The Global Navigation Satellite System (GNSS) multi-frequency observations are widely used in positioning applications, while precise orbit determination and precise clock estimation (PCE) techniques typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global networks. To fully utilize the multi-frequency GNSS observations for generating satellite products at the server-end, we develop some new five-frequency PCE models based on Galileo data, which are five-frequency uncombined FFUC model, FFIF0 model combining the E1/E5a, E1/E5b, E1/E5 and E1/E6 IF observables, FFIF1 model combining E1/E5a and E1/E5a/E5b/E5/E6 IF observables, respectively. The traditional dual-frequency UD IF and triple-frequency PCE models are also introduced for comparison. The new multi-frequency PCE models can not only make full use of the modern GNSS multi-frequency observations, but also obtain satellite clock offsets and inter-frequency clock bias (IFCB) at the same time, which can better support multi-frequency precise point positioning (PPP) applications. The multi-frequency models can improve the stability of GNSS satellite clock estimation, the precision of satellite clock offsets can be improved by 8–12% for triple-frequency models, and 19–27% for five-frequency PCE models compared with the traditional dual-frequency IF model. The PPP positioning accuracy using only multi-frequency satellite clock offsets can be improved by 7–18% for dual-frequency PPP, 8–15% for triple-frequency PPP, 4–16% for five-frequency PPP. The positioning accuracy can be further improved by 11–28% for triple-frequency PPP and 7–20% for five-frequency PPP. Therefore, the new multi-frequency PCE models are demonstrated to support PPP applications with better performance.

A mixed multi-frequency precise point positioning strategy based on the combination of BDS-3 and GNSS multi-frequency observations

Due to the traditional fixed model used in precise point positioning (PPP) solutions, multi-frequency and multi-Global Satellite Navigation System (GNSS) observations have not been fully introduced into positioning services. In consideration of the BDS-3 multi-frequency signals and the new development of other GNSS systems, a new multi-frequency and multi-GNSS PPP solution strategy should be proposed to flexibly model and use all observations. In this study, a preliminary mixed multi-frequency PPP solution strategy is analyzed and tested based on a combination of BDS-3 and GNSS observations. First, the multi-frequency observations are combined and their coefficients are rapidly estimated by least squares; then, the inter-system bias parameter and the stochastic model are introduced into the function model; and finally, the mixed PPP solution and its software are developed and verified by three groups of experiments. According to the experimental results of 96 stations and ten-day multi-GNSS experiment observations, it is indicated that the root-mean-square error of positioning and the convergence time are significantly optimized with the aid of additional frequencies, where the accuracy improvements of multi-frequency and multi-GNSS scheme in the east (E), north (N) and up (U) directions can respectively reach up to 23.2%, 13.3% and 23.8% compared with the traditional BDS-3 dual-frequency ionosphere-free (IF) PPP model; and the corresponding convergence time is reduced from 18.54 min to 13.18 min. Meanwhile, from the results of multi-frequency BDS-3 PPP experiments based on 53 stations, it is suggested that a better performance of positioning and convergence can be obtained by the mixed PPP solution, where the position RMS of the E, N and U directions are reduced by 38.2%, 23.9% and 26.3%, and the convergence time is decreased from 23.86 min to 12.43 min for the combined BDS-3 of all observations, compared with the BDS-3-only solution. Furthermore, in the vehicle experiment of multi-frequency kinematics PPP, a convergence process can be found for different scenarios of BDS-3 combination with other observations. Moreover, the residual series are different for each solution, in which reductions of 71.1%, 33.3% and 77.1% in the E, N and U directions, respectively, can be obtained compared with the traditional BDS-3 dual-frequency IF model in kinematics experiments based on multi-GNSS and multi-frequency scenarios. Therefore, it is meaningful to recommend the mixed PPP solution in the GNSS community to fully use multi-frequency and multi-GNSS observations by the adaptive combination of different observations.

Multi-GNSS products and services at iGMAS Wuhan Innovation Application Center: strategy and evaluation

Over the past years the International Global Navigation Satellite System (GNSS) Monitoring and Assessment System (iGMAS) Wuhan Innovation Application Center (IAC) dedicated to exploring the potential of multi-GNSS signals and providing a set of products and services. This contribution summarizes the strategies, achievements, and innovations of multi-GNSS orbit/clock/bias determination in iGMAS Wuhan IAC. Both the precise products and Real-Time Services (RTS) are evaluated and discussed. The precise orbit and clock products have comparable accuracy with the precise products of the International GNSS Service (IGS) and iGMAS. The multi-frequency code and phase bias products for Global Positioning System (GPS), BeiDou Navigation Satellite System (BDS), Galileo navigation satellite system (Galileo), and GLObal NAvigation Satellite System (GLONASS) are provided to support multi-GNSS and multi-frequency Precise Point Positioning (PPP) Ambiguity Resolution (AR). Compared with dual-frequency PPP AR, the time to first fix of triple-frequency solution is improved by 30%. For RTS, the proposed orbit prediction strategy improves the three dimensional accuracy of predicted orbit by 1 cm. The multi-thread strategy and high-performance matrix library are employed to accelerate the real-time orbit and clock determination. The results with respect to the IGS precise products show the high accuracy of RTS orbits and clocks, 4–9 cm and 0.1–0.2 ns, respectively. Using real-time satellite corrections, real-time PPP solutions achieve satisfactory performance with horizontal and vertical positioning errors within 2 and 4 cm, respectively, and convergence time of 16.97 min.

Toward BDS/Galileo/GPS/QZSS triple-frequency PPP instantaneous integer ambiguity resolutions without atmosphere corrections

Multi-frequency precise point positioning (PPP) has drawn attention along with the modernization of the Global Navigation Satellite Systems. There are now nearly 90 satellites providing multi-frequency signals. This contribution aims to achieve fast convergence of a few seconds for BDS/Galileo/GPS/QZSS integrated triple-frequency PPP with integer ambiguity resolution (IAR) without atmosphere corrections. A unified model of an uncombined and undifferenced manner for PPP-IAR with dual- and triple-frequency observations is presented. The uncalibrated phase delays (UPD) of extra wide-lane (EWL), wide-lane (WL), and N1 ambiguities for triple-frequency PPP are estimated with standard deviations of 0.02, 0.05, and 0.10 cycles achieved, respectively. The PPP-IAR validation based on 20 stations evenly distributed in China is conducted using UPD products generated from a regional network covering a large part of China. The EWL, WL, and N1 ambiguities are sequentially fixed utilizing the least-squares ambiguity decorrelation adjustment (LAMBDA) technique. In terms of convergence time, PPP instantaneous IAR is achievable without using atmosphere corrections, thanks to the contribution of the multi-frequency and multi-constellation observations. This has been proved by performing PPP-IAR restart every 10-min over 2520 times in our case study. For PPP-IAR solutions produced with BDS/Galileo/GPS/QZSS triple-frequency observations with an interval of 1 s, the convergence is fulfilled within 1 s for the horizontal components with an accuracy of better than 5 cm, while 2 s for the vertical component with better than 10 cm accuracy, and both are at 95% confidence level.

Modeling and performance assessment of precise point positioning with multi-frequency GNSS signals

The development of global navigation satellite system (GNSS), especially BeiDou-3 Navigation Satellite System (BDS-3) and Galileo system, promotes the progress of the precise point positioning (PPP) technology. Considering deep integration and full utilization of GNSS signals, this study dedicates to developing three triple-frequency PPP models apply to multi-constellation including BDS-3. Besides, some biases such as differential code bias (DCB), inter-frequency bias (IFB) and inter-system bias (ISB) are also addressed. Through the ten-day datasets collected from 160 stations, the multi-frequency PPP models for single- and multi-constellation solutions are analyzed and compared from static positioning performance, Zenith Tropospheric Delay (ZTD) estimates, ISB estimates, and IFB estimates. The results indicate that the triple-frequency PPP models, especially two dual-frequency ionosphere-free (IF) model namely TIF with triple-constellation which can provide the positioning accuracy of 4.89, 7.31, 12.1 mm after the convergence time of 10.75 min in east, north and up directions, perform better than the dual-frequency model, apart from the a single IF model with GPS. Interestingly, the positioning performance is not effectively improved with the addition of GLONASS constellation. But the performance of GAL/BDS combined constellation is comparable to GPS single constellation in TIF model.

Galileo Time Transfer with Five-Frequency Uncombined PPP: A Posteriori Weighting, Inter-Frequency Bias, Precise Products and Multi-Frequency Contribution

Galileo satellites can broadcast signals on five frequencies, namely E1, E5A, E5B, E5 (A+B), and E6. The multi-frequency integration has become an emerging trend in Global Navigation Satellite System (GNSS) data processing. This study focused on the precise time transfer based on Galileo five-frequency uncombined precise point positioning (PPP), including the performance comparison of PPP time transfer with a priori and a posteriori weighting strategies, with different inter-frequency bias (IFB) dynamic models, and with the precise satellite products from different analysis centers, as well as the contribution of multi-frequency observations for time transfer. Compared with the a priori weighting strategy, the short-term frequency stability of time transfer adopting the Helmert variance component estimation method can be improved by 28.9–37.6% when the average time is shorter than 100 s. The effect of IFB dynamic models on Galileo five-frequency PPP time transfer is not obvious. When employing the post-processed precise satellite products from seven analysis centers, the accuracy of time transfer can be better than 0.1 ns, while an accuracy of 0.253 ns can be obtained in the real-time mode. At an average time of approximately 10,000 s, the post-processed time transfer with Galileo five-frequency PPP can provide a frequency stability of 3.283 × 10−14 to 3.459 × 10−14, while that in real-time mode can be 3.541 × 10−14. Compared with dual-frequency PPP results, the contribution of multi-frequency combination to the accuracy and frequency stability of time transfer is not significant, but multi-frequency PPP can achieve more reliable time transfer results when the signal quality is poor.

Modeling and assessment of five-frequency BDS precise point positioning

Since its full operation in 2020, BeiDou Satellite Navigation System (BDS) has provided global services with highly precise Positioning, Navigation, and Timing (PNT) as well as unique short-message communication. More and more academics focus on multi-frequency Precise Point Positioning (PPP) models, but few on BDS five-frequency PPP models. Therefore, this study using the uncombined and Ionospheric-Free (IF) observations develops five BDS five-frequency PPP models and compares them with the traditional dual-frequency model, known as Dual-frequency IF (DF) model. Some biases such as Inter-Frequency Biases (IFB) and Differential Code Bias (DCB) are also addressed. With the data collected from 20 stations, the BDS dual- and five-frequency PPP models are comprehensively evaluated in terms of the static and simulated kinematic positioning performances. Besides, the study also analyzes some by-product estimated parameters in five-frequency PPP models such as Zenith Troposphere Delay (ZTD). The results of experiment show that five-frequency PPP models have different levels of improvement compared with the DF model. In the static mode, the one single Five-Frequency IF combination (FF5) model has the best positioning consequent, especially in the up direction, and in the simulated kinematic mode, the Three Dual-frequency IF combinations (FF3) model has the largest improvement in convergence time.

Performance Analysis of Zero-Difference GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 Point Positioning Using CNES Uncombined Bias Products

The modernization of Global Navigation Satellite System (GNSS) including the transmission of signals on multiple frequencies has greatly promoted the development of the popular PPP (Precise Point Positioning) technique. A key issue of multi-frequency PPP is the handling of the observable-specific signal biases in order to allow for carrier-phase ambiguity resolution (AR). As a result, PPP modeling at a user side in the multi-frequency case varies depending on the definition of the applied phase bias products. In this study, we investigate the positioning performance of GPS L1/L2/L5 and Galileo E1/E5a/E5b/E6 undifferenced ionosphere-float model in the conventional PPP mode and the single-epoch mode using the uncombined code and phase bias products generated at the French CNES (Centre National D’Etudes Spatiales). A series of widelane ambiguities are configured in our multi-frequency PPP functional model instead of forming the classical Melbourne–Wübbena (MW) combination. The best integer equivariant (BIE) estimator is used for the ambiguity resolution in a conventional cascading scheme according to the wavelength of the combined ambiguities for each constellation. Real data collected at IGS stations with a 30-s sampling interval is applied to evaluate the above models. For the conventional kinematic PPP configuration, a significant accuracy improvement of 63% on the east component of the fixed solution is obtained with respect to the ambiguity-float solution. The PPP convergence is accelerated by 17% after the AR. Regarding the single-epoch positioning, an accuracy of 32 and 31 cm for north and east components can be achieved, respectively, (68th percentile) with the instantaneous widelane-ambiguity resolution, which is improved by 13% and 16% compared to multi-frequency code-based or float solution.

Multi-GNSS Fast Precise Point Positioning with Multi-Frequency Uncombined Model and Cascading Ambiguity Resolution

Conventional ambiguity resolution (AR) strategy of directly fixing all raw frequency ambiguities for uncombined precise point positioning (PPP) generally requires a long initial time to ensure fixing reliability. The rich signals from multi-frequency GNSS can provide new opportunities for rapid PPP AR. In this paper, based on a unified multi-frequency uncombined PPP model, the raw frequency ambiguities are linearly transformed to the between-satellite-single-differenced extra-wide-lane (EWL), wide-lane (WL), and narrow-lane (NL) ambiguities, and a cascading ambiguity resolution (CAR) method of fixing EWL/WL/NL ambiguities sequentially is proposed. Meanwhile, a partial ambiguity fixing (PAF) strategy with ambiguity subset adaptively selected based on the successively increased elevations is also adopted in each step to improve the fixing rate. Further, experiments with globally distributed stations are carried out to verify the algorithm. With the constraints of EWL/WL AR, the precision of NL ambiguity and its variance-covariance matrix can be effectively optimized, so the time to first fix (TTFF) is significantly shortened, and the ratio value is also improved to varying degrees. As for BDS-only solution, the average TTFF is shortened from 23.7 min to 10.9 min, with an improvement over 50%; for GPS/BDS, GPS/Galileo, and GPS/Galileo/BDS combined solutions, the TTFF is shortened from 14.3 min, 9.4 min, and 6.7 min to 8.1 min, 2.6 min, and 1.8 min, which are, respectively, shortened by 43.4%, 72.3%, and 73.1%. In general, the proposed CAR strategy can shorten the TTFF of multi-GNSS multi-frequency PPP to about 2 min. The performance of EWL/WL/NL ambiguity-fixed solutions is also analyzed. The NL solution is generally at centimeter-level accuracy over the entire period; however, limited by the atmosphere errors during the convergence stage, the EWL/WL solutions can only obtain decimeter-level accuracy, and the difference between them and NL solution gradually decreases with the continuous improvement of atmosphere accuracy.

Analytical performance and validations of the Galileo five-frequency precise point positioning models

Galileo navigation satellite system provides global services with five-frequency signals. The contribution of this study is to develop four Galileo five-frequency precise point positioning (PPP) models with the ionospheric-free (IF) and uncombined observables, namely FF1, FF2, FF3 and FF4 models, respectively. Galileo dual- and triple-frequency IF models, known as DF and TF models, are also investigated for comparisons. The Galileo dual- and multi-frequency PPP models are comprehensively evaluated with thirty consecutive days period observations collected from 26 multi-GNSS experiment (MGEX) network stations, together with a dynamic experiment dataset, in terms of the static and kinematic performance. The by-product estimated parameters in five-frequency PPP models including the receiver clock, tropospheric delay, receiver inter-frequency biases (IFBs) and differential code bias (DCB) are also analyzed. The experimental results show that the FF1, FF2, and FF3 models perform basic consistent and the FF4 model exhibits inconsistency due to the external ionospheric constraint. The Galileo kinematic PPP performance is significantly improved with the multi-frequency observations under the limited observed satellites circumstance. The significance and potency of the Galileo five-frequency PPP is demonstrated for future Galileo applications.

BDS multi-frequency PPP ambiguity resolution with new B2a/B2b/B2a + b signals and legacy B1I/B3I signals

As of December 2019, the core constellation of BeiDou Navigation Satellite System with global coverage (BDS-3) has been fully deployed with 24 MEO, 3 IGSO and 1 GEO satellites. In addition to the legacy B1I and B3I signals, BDS-3 satellites are capable of transmitting several new navigation signals, including B1C, B2a, B2b and B2a + b. The multi-frequency signals of BDS-3 bring new opportunities for fast ambiguity resolution (AR) of BDS precise point positioning (PPP). In this contribution, the BDS five-frequency PPP AR method was developed and the benefits of BDS-3 multi-frequency signals for precise positioning were investigated. The multi-frequency uncalibrated phase delay (UPD) products were estimated firstly using observations from 222 Multi-GNSS Experiment stations. The extra-wide-lane, wide-lane and narrow-lane UPDs of BDS-3 exhibit high stability with standard deviations less than 0.1 cycle. With the derived UPD products, five-frequency PPP AR was conducted at 12 static stations and a moving vehicle. The time to first fix of BDS PPP AR was shortened to 25.5 min with multi-frequency observations, showing improvement of 25.4% when compared to dual-frequency PPP AR. Moreover, instantaneous PPP wide-lane ambiguity resolution (WAR) can be achieved with success rate of over 90%. A fast decimeter-level accuracy can be achieved for BDS five-frequency PPP WAR with positioning accuracy improved by 68%-82% compared to PPP float solutions. The vehicle-borne experiment further demonstrates that BDS PPP WAR is potential to maintain decimeter-level positioning accuracy even in a complex environment.

Assessment of multi-frequency global navigation satellite system precise point positioning models using GPS, BeiDou, GLONASS, Galileo and QZSS

The development of a global navigation satellite system (GNSS) brings the benefit of positioning, navigation and timing (PNT) services with three or even more available frequency signals. This paper developed five-system multi-frequency precise point positioning (PPP) models based on mathematical and stochastic models. Static positioning performances were evaluated and analyzed with multi-GNSS experiment (MGEX) network datasets and a vehicle-borne kinematic experiment was conducted to verify the kinematic PPP performances. In addition, the receiver clock, zenith tropospheric delay (ZTD), inter-frequency bias (IFB) and differential code bias (DCB) estimates were discussed. Results show that the triple-frequency PPP performances perform slightly better than the dual-frequency solutions, apart from the GPS-related PPP models based on a single ionosphere-free (IF) combined measurement. By introducing the external ionospheric products, the mean convergence time is reduced. For instance, the mean convergence time of ionosphere-constrained (IC) multi-frequency PPP is reduced by 7.4% from 35.7 to 33.1 min and by 19.0% from 7.8 to 6.3 min, for Galileo-only and five-constellation solutions, respectively, compared with dual-frequency IF PPP models. Similarly, the kinematic PPP can also achieve improved performances with more frequency signals and multi-GNSS observations.

Galileo PPP rapid ambiguity resolution with five-frequency observations

Galileo, transmitting signals on the five frequencies E1, E5a, E5b, E5 and E6, has completed the fundamental constellation with 26 satellites and now can provide the global positioning service independently. Multi-frequency (triple-frequency or above) signals allow a variety of combinations on different frequencies, which has the potential to improve the performance of the precise point positioning (PPP) ambiguity resolution (AR). We developed a multi-frequency PPP AR method to make use of the Galileo five-frequency observations. The stable multi-frequency uncalibrated phase delay (UPD) products of Galileo were estimated first. It is interesting to find that the extra-wide-lane (EWL) UPDs on the E5a/E5b, E5a/E5 and E5/E5b combined frequencies are very close to zero. With the obtained UPD products, the Galileo triple-, quad- and five-frequency PPP AR was conducted. Triple-frequency PPP AR with different frequency combinations can improve the positioning accuracy of 30 min by 36.6–86.8% compared with float solutions, and 2.3–62.5% compared with dual-frequency PPP AR. Among the five types of frequency combinations, the triple-frequency PPP AR on E1/E5/E6 frequencies shows the best positioning performance with the averaged convergence time shortened to 16.9 min. Furthermore, the averaged convergence time is 15.3 min and 15.0 min for quad- and five-frequency PPP AR, respectively. Compared with the time to first fix (TTFF) of 19.9 min for narrow-lane ambiguity resolution with dual-frequency observations, the TTFF is only shortened by about 1 min with multi-frequency observations. It is beneficial that the EWL and wide-lane (WL) ambiguities can be fixed to integers instantaneously, and the decimeter-level positioning accuracy can be achieved within 0.5 min by utilizing triple-/quad-/five-frequency PPP wide-lane AR (WAR). Moreover, the positioning accuracy of the first epoch derived from Galileo five-frequency PPP WAR is (0.112, 0.144, 0.641) m in the east, north and up components, which has an improvement of 2.1–42.0% compared to triple-/quad-frequency PPP WAR.

Improved PPP Ambiguity Resolution with the Assistance of Multiple LEO Constellations and Signals

The fusion of low earth orbit (LEO) constellation and Global Navigation Satellite Systems (GNSS) can increase the number of visible satellites and optimize spatial geometry, which is expected to improve the performance of precise point positioning (PPP) ambiguity resolution (AR). In addition, the multi-frequency signals of LEO satellites can bring a variety of observation combinations, which is potential to further improve the efficiency of PPP AR. In this contribution, multi-frequency PPP AR was achieved with the augmentation of different LEO constellations. Three types of LEO constellations were designed with 60, 192, and 288 satellites. Moreover, the corresponding observation data were simulated with the GNSS observations over the ground stations. The LEO constellations were designed to transmit navigation signals on three frequencies: L1, L2, and L5 at 1575.42, 1227.6, and 1176.45 MHz, respectively, which are consistent with the GPS signals. For PPP AR, the uncalibrated phase delay (UPD) products of GNSS and LEO were estimated first. Furthermore, the quality of UPD products was also analyzed. The research findings show that the performance of estimated LEO UPD is comparable to that of GNSS UPD. Based on the UPD products, LEO-augmented multi-GNSS PPP AR can be achieved. Numerous results show that the performance of single-system and multi-GNSS PPP AR can be significantly improved by introducing the LEO constellations. The augmentation performance is more remarkable in the case of increasing LEO satellites. The time to first fix (TTFF) of the GREC fixed solution can be shortened from 7.1 to 4.8, 1.1, and 0.7 min, by introducing observations of 60-, 192-, and 288-LEO constellations, respectively. The positioning accuracy of multi-GNSS fixed solutions is also improved by about 60%, 80%, and 90% with the augmentation of 60-, 192-, and 288-LEO constellations, respectively. Compared to the dual-frequency solutions, the triple-frequency LEO-augmented PPP fixed solution presents a better performance. The TTFF of GREC fixed solutions is shortened to 33 s with the augmentation of 288-LEO constellation under the triple-frequency environment. It is worth indicating that the 288-satellite LEO-only PPP AR was conducted in dual-frequency and triple-frequency modes, respectively. The averaged TTFFs of both modes are 71.8 s and 55.2 s, respectively. It indicates that LEO constellation with 288 satellites is capable of achieving high-precision positioning independently and shows an even better performance than GNSS-only solutions.

Improving GNSS PPP Convergence: The Case of Atmospheric-Constrained, Multi-GNSS PPP-AR.

GNSS positioning performance has been shown to improve with the ingestion of data from Global Ionospheric Maps (GIMs) and tropospheric zenith path delays, which are produced by, e.g., the International GNSS Service (IGS). For both dual- and triple-frequency Precise Point Positioning (PPP) processing, the significance of GIM and tropospheric products in processing is not obvious in the quality of the solution after a few hours. However, constraining the atmosphere improves PPP initialization and solution convergence in the first few minutes of processing. The general research question to be answered is whether there is any significant benefit in constraining the atmosphere in multi-frequency PPP? A key related question is: regarding time and position accuracy, how close are we to RTK performance in the age of multi-GNSS PPP-AR? To address these questions, this paper provides insight into the conceptual analyses of atmospheric GNSS PPP constraints. Dual- and triple-frequency scenarios were investigated. Over 60% improvement in convergence time was observed when atmospheric constraints are applied to a dual-frequency multi-GNSS PPP-AR solution. Future work would involve employing the constraints to improve low-cost PPP solutions.

A Unified Model for Multi-Frequency PPP Ambiguity Resolution and Test Results with Galileo and BeiDou Triple-Frequency Observations

With the modernization of Global Navigation Satellite System (GNSS), triple- or multi-frequency signals have become available from more and more GNSS satellites. The additional signals are expected to enhance the performance of precise point positioning (PPP) with ambiguity resolution (AR). To deal with the additional signals, we propose a unified modeling strategy for multi-frequency PPP AR based on raw uncombined observations. Based on the unified model, the fractional cycle biases (FCBs) generated from multi-frequency observations can be flexibly used, such as for dual- or triple- frequency PPP AR. Its efficiency is verified with Galileo and BeiDou triple-frequency observations collected from globally distributed MGEX stations. The estimated FCB are assessed with respect to residual distributions and standard deviations. The obtained results indicate good consistency between the input float ambiguities and the generated FCBs. To assess the performance of the triple-frequency PPP AR, 11 days of MGEX data are processed in three-hour sessions. The positional biases in the ambiguity-fixed solutions are significantly reduced compared with the float solutions. The improvements are 49.2%, 38.3%, and 29.6%, respectively, in east/north/up components for positioning with BDS, while the corresponding improvements are 60.0%, 29.0%, and 21.1% for positioning with Galileo. These results confirm the efficiency of the proposed approach, and that the triple-frequency PPP AR can bring an obvious benefit to the ambiguity-float PPP solution.