Precise Point Positioning Model Research Articles

Evaluating the single-frequency static precise point positioning accuracies from multi-constellation GNSS observations at an Indian low-latitude station

Abstract Multiple constellations and their combinations in the global navigation satellite systems (GNSS) provide a great opportunity for single-station precise point positioning (PPP) models. The PPP models are of more importance for GNSS users as they are cost-effective with reasonable accuracy. There are abundant models in the market that use different data processing techniques based on the location and constellations used. In this study, we used the precise point positioning (PPP) software Net_Diff to verify the positioning accuracy at a low latitude Indian location using individual global satellite constellations (GPS, GLONASS, Galileo, BeiDou) and their combinations with GPS fixed. The ionospheric correction models such as GIM and Klobuchar are applied in the post-processing to determine the positioning accuracy. The Kalman filter method is applied to model the input data along with including the noise to derive the position solution. The results revealed that the GPS showed constant residual error for both quiet and disturbed days. In terms of single constellation Galileo produced less residuals in WGS 84 and ECEF coordinate systems whereas in the multi-constellation combination GPS, Galileo and GLONASS resulted in residuals of lesser magnitudes compared to the other combinations considered in this study. The RMS and STD of the residuals confirmed the high precision for Galileo and low precision for BeiDou constellations at the location.

BDS-3 six-frequency precise point positioning: effects of receiver-dependent inter-frequency clock bias and multi-frequency contributions

We find that there is time-varying bias at the receiver in BDS-3 multi-frequency phase observations, which will lead to receiver-dependent inter-frequency clock bias (RIFCB) and damage the rigor of BDS-3 multi-frequency precise point positioning (PPP) model. A unified RIFCB correction method compatible with uncombined and ionospheric-free combined PPP models using any BDS-3 frequencies is proposed. The contributions of multi-frequency integration to BDS-3 static and kinematic PPP performance are evaluated. The results indicate that the RIFCB amplitude can reach 1 dm. If the RIFCB correction is ignored, the phase observation residuals present a systematic bias. RIFCB has potential effects on precise time transfer, ionospheric monitoring, and fractional cycle bias estimation. Experimental results show that the long-term frequency stability of time transfer can be improved by correcting RIFCB. The joint use of all BDS-3 six-frequency signals can significantly shorten the convergence time, and the positioning accuracy can also be slightly improved.

The analysis on time transfer of GPS/Galileo /BDS PPP with integer ambiguity resolution

GPS precise point positioning (PPP) approach has been considered for achieving time transfer for a long time. By virtue of GPS/Galileo/BDS FCB products, PPP model has the possibilities for changing phase ambiguities from ‘float’ value to ‘integer’ value. In this study, PPP time/frequency transfer model has been presented and performance of seven links equipped with Hydrogen Masers (H-Masers) and cesium atomic clocks are compared in static and kinematic modes. With partial ambiguity resolution (PAR) enabled, in contrast to GPS, results show that multi-GNSS’s fixing rate is much higher and TTFF(Time To First Fixing) is much shorter. It is verified that the fixing rate and TTFF has nothing to do with the atomic clock type but has strong correlation with the quality of observation. We find that frequency stability of time link is seriously dependent on the type of atomic clock. As far as H-Masers, it has reached the order of 1E-16/1E-15 at the averaging time of 122880 s, respectively. As far as Cesium clock, it has reached the order of 1E-15/1E-14 at the averaging time of 122880 s, respectively. For H-Maser, the long-term frequency stabilities of integer PPP (IPPP) have been improved by roughly 3% at the static mode and 4% at the kinematic mode on average, respectively. For positioning, compared to PPP solutions, the stabilities of the IPPP coordinates are improved after an averaging time of 7680 s in static or kinematic mode.

An Interstation Undifferenced Real-Time Time Transfer Method with Refined Modeling of Receiver Clock

Due to their advantages of high measurement accuracy and wide coverage, global navigation satellite systems (GNSSs) can carry out long-distance time transfers, among which the precise point positioning (PPP) method is widely used. However, the accuracy and stability of PPP real-time time transfer are restricted by the real-time satellite clock offset products. In addition, the receiver clock offset is usually estimated using the white noise model, which ignores the correlation of the clock offsets between adjacent epochs and the stability of the atomic clock itself. In order to obtain higher performance time transfer results, we propose an interstation undifferenced time transfer method with refined modeling of the receiver clock. This method takes the satellite clock offset as the parameter to be estimated, which can avoid the influence of external satellite clock offset products. In addition, the refined modeling of the receiver clock can improve the strength of the model and the accuracy of time transfer. Based on the ultrarapid satellite orbit products provided by the International GNSS Service (IGS), time transfer experiments are carried out using data from IGS observatories and self-collected data. The results show that sub-nanosecond accuracy can be achieved in real-time time transfer using this method. Compared with the traditional PPP model, the accuracies of the four time links are increased by 88.4%, 92.9%, 88.6%, and 74.5%, respectively, and the stability is increased by approximately 66.4% on average. Moreover, after applying the clock offset constraint model, frequency stability is further improved, in which the short-term stability is improved significantly, with a maximum of 86.9% and an average improvement of approximately 66.8%.

Evaluation of Triple-Frequency GPS/Galileo/Beidou Kinematic Precise Point Positioning Using Real-Time CNES Products for Maritime Applications

Abstract Our research aims to evaluate the triple-frequency GPS/Galileo/BeiDou kinematic precise point positioning (PPP) accuracy for the international maritime organization (IMO) positioning accuracy and integrity requirements. The real-time Centre National d’Etudes Spatiales (CNES) satellite orbit and clock products are used to simulate real-time scenarios. GPS/Galileo/BeiDou observations are collected from a moving vessel. Both dual-frequency and triple-frequency ionosphere-free PPP models are developed. Different satellite system combinations are used, including GPS-only, GPS/Galileo, GPS/BeiDou, and GPS/Galileo/BeiDou. The GPS-only differential solution is used as a reference. It is found that both dual- and triple-frequency kinematic PPP solutions achieve the IMO accuracy requirements at 95% confidence level for ocean, coastal, port approach, port, inland waterways, and track control navigation applications, except the automatic docking application. Moreover, the PPP solutions fulfilled the IMO integrity requirements for all navigation phase applications, but the GPS and GPS/BeiDou PPP solutions did not fulfill the automatic docking integrity requirement.

The Implementation of Precise Point Positioning (PPP): A Comprehensive Review.

High-precision positioning from Global Navigation Satellite Systems (GNSS) has garnered increased interest due to growing demand in various applications, like autonomous car navigation and precision agriculture. Precise Point Positioning (PPP) offers a distinct advantage over differential techniques by enabling precise position determination of a GNSS rover receiver through the use of external corrections sourced from either the Internet or dedicated correction satellites. However, PPP's implementation has been challenging due to the need to mitigate numerous GNSS error sources, many of which are eliminated in differential techniques such as Real-Time Kinematics (RTK) or overlooked in Standard Point Positioning (SPP). This paper extensively reviews PPP's error sources, such as ionospheric delays, tropospheric delays, satellite orbit and clock errors, phase and code biases, and site displacement effects. Additionally, this article examines various PPP models and correction sources that can be employed to address these errors. A detailed discussion is provided on implementing the standard dual-frequency (DF)-PPP to achieve centimeter- or millimeter-level positioning accuracy. This paper includes experimental examples of PPP implementation results using static data from the International GNSS Service (IGS) station network and a kinematic road test based on the actual trajectory to showcase DF-PPP development for practical applications. By providing a fusion of theoretical insights with practical demonstrations, this comprehensive review offers readers a pragmatic perspective on the evolving field of Precise Point Positioning.

A Simple Approach to Determine Single-Receiver Differential Code Bias Using Precise Point Positioning.

In this study, a precise single-receiver differential code bias (DCB) estimation method using the precise point positioning (PPP) model is presented. The first step is to extract the high-precision ionospheric observations, including DCBs, based on the PPP model. Then, the satellite DCBs are corrected using International GNSS Service (IGS) products. Lastly, the algorithm for the minimization of the standard deviation of vertical total electron content (VTECmstd) is employed to determine the value of receiver DCB. To check the method, GNSS data from more than 200 IGS stations around the globe on four days with various geomagnetic and solar activity circumstances are processed. The receiver DCBs are compared to those obtained using previous carried-to-code level (CCL) models. The experimental results show that, compared to the CCL model, the values of VTECmstd for most stations are significantly reduced, the mean number of stations with negative ionospheric measurements is reduced by 40% after correcting the receiver DCBs, and the mean error of estimated receiver DCBs is reduced by approximately 0.6 ns using the PPP model. These results suggest that this method can provide more high-precision receiver DCB estimation.

Single-Epoch Decimeter-Level Precise Point Positioning with a Galileo Five-Frequency Ionosphere-Reduced Combination

Currently, there are two main methods for single-epoch decimeter-level precise point positioning (PPP); one is a model based on ambiguity-fixed ionosphere-free (AFIF) observations, and the other is based on uncombined (UC) PPP. The implementation of these two models requires both extra-wide-lane (EWL) and wide-lane (WL) ambiguity fixing. Different from the existing methods, this paper proposes a multi-frequency ionosphere-reduced (IR) PPP model suitable for single-epoch decimeter-level positioning. Based on Galileo five-frequency data, the optimal selection strategy of IR combinations is first studied with ionosphere, noise level and wavelength factors considered. Then, based on the selected IR combination, two IR PPP models, namely IR(EST) and IR(IGN), are established according to whether ionosphere parameters are estimated or ignored. Finally, the proposed models are verified with real tracked data from globally distributed stations, and further compared with the existing AFIF/UC models in terms of positioning performance and time consumption. The relationship between the ionosphere equivalent ranging error and satellite elevation in the IR models is analyzed. The lower the elevation is, the larger the residual ranging error is, and its impact on positioning is weakened by downweighting its observations and adjusting the cut-off elevation during the partial ambiguity fixing (PAF) process. The results show that the performance of the two IR models is basically the same, and both can achieve horizontal and vertical accuracies better than 20 cm and 40 cm, respectively. Compared with the existing AFIF/UC models, the proposed IR models can achieve similar decimeter-level accuracy with only one step of EWL ambiguity fixing, and at the same time, the IR models have varying degrees of improvement in time consumption: 38% shorter than the AFIF model and 97% shorter than the UC model.

TECX-TCN: Prediction of ionospheric total electron content at different latitudes in China based on XGBoost algorithm and temporal convolution network

The correction of ionospheric delay error through the estimation of ionospheric total electron content (TEC) parameters is very important for the accuracy and rapid convergence of precise point positioning (PPP), especially for single frequency PPP position and double frequency undifferenced and uncombined PPP models. This paper studies the prediction method of ionospheric TEC by analyzing various influencing factors. Firstly, considering the influence of latitude, the TEC values of different observation stations in China at middle and low latitudes are used for research. Secondly, due to the influence of solar storms, the years with and without solar storms are selected for comparative study. At the same time, the moving average value of TEC and the lag value of each solar and geomagnetic index are also added. Because the influence of each feature on ionospheric TEC is not clear, the importance score of each feature is obtained according to the EXtreme Gradient Boosting (XGBoost) algorithm to establish a reasonable feature combination. Then, the temporal convolution network (TCN) is used to train according to data of the collected solar cycle and predict data for the next year. Through experiments, the prediction model with feature selection can obtain higher prediction accuracy, the error reaches ∼2TECU at middle latitude region and ∼3 TECU at low latitude region. Finally, compared with other algorithms, our ionospheric TEC prediction algorithm based on XGBoost and TCN (TECX-TCN) significantly has better performance. When the solar activity is low, its RMSE can reach ∼2.5TECU, the correlation coefficient can reach ∼0.9, and even in the low latitude area with high solar activity, its RMSE can reach ∼5TECU, the correlation coefficient can reach ∼0.85.

The mathematical weighting of GNSS observations based on different types of receivers/antennas and environmental conditions

Stochastic models play an important role in achieving high accuracy in positioning, the ideal estimator in the least-squares (LS) can be obtained only by using the suitable stochastic model. This study investigates the role of variance component estimation (VCE) in the LS method for Precise Point Positioning (PPP). This estimation is performed by considering the ionospheric-free (IF) functional model for code and the phase observation of Global Positioning System (GPS). The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes: a) antenna type, b) receiver type, c) the tropospheric effect, and d) the ionosphere effect. The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model. This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions. Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE. The position error difference for the east-west, north-south, and height components was 1.5 cm, 4 mm, and 1.8 cm, respectively. Therefore, weight estimation with LS-VCE can provide more appropriate results. Eventually, the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight. According to the results, the LS-VCE has a higher convergence rate than the nominal weight. The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11, 13, 12, and 9 min, respectively.

Role of Multi-Constellation GNSS in the Mitigation of the Observation Errors and the Enhancement of the Positioning Accuracy

Using Precise point positioning (PPP) technique can help to reach decimeters accuracy for positioning by using one receiver only. Since it set to track Global Navigation Satellite System (GNSS). Recently BeiDou and Galileo systems have been devolved periodically and increasing the number of working satellites. Addition to those all-global Navigation systems is able to receive triple frequency signals. The effect of using Multi constellation of GNSS and combination of different systems with each other’s need to be investigated. In this paper, four Multi GNSS EXPERIMENT (MGEX) stations with 24 hours observation files and 30 second interval time during a 1 week of averaged data of January 2020 (2134 GPS week) are used to investigate the accuracy of using combined solution of GNSS with 12 cases of study. Data were processed by PPPH program. To investigate the effect of using the different GNSS combinations while using the PPP method, contrast experiments have been tested by mixing dual frequency ionospheric-free PPP models in static mode with G only, GLO only, G + GLO, G+ B, GLO+B, G+GAL, GLO+GAL, GLO+B+GAL, GNSS, G +GAL+B, G+GLO+B and G+GLO+GAL combination cases, where G refers to GPS, GLO refers to GLONASS, GAL refers to Galileo and B refers to BeiDou. The results show that the combined GPS and Galileo observation in PPP solution improves the convergence time and gives the shortest convergence time of the 12 study cases with average value 53 minute and with minimum value 35 minute. By comparing the root mean square error (RMS) values, the combination of G+GL+B had the minimum RMS error in North and East direction with minimum value 1.2 cm, maximum value 1.8 cm and average value1.45 cm. And the combination of GLO+GAL+B had the minimum RMS errors in up directions with average value 2.775 cm and minimum 2.775 cm and maximum 4.5 cm. In conclusion, the results indicate that the combination of different GNSS can give more accurate solution of the PPP. The combined PPP has shown an improvement in the convergence time in the case of using combined of G and GAL observation, while the positioning accuracy after convergence has no shown significant improvement. The result of G+GAL+B give the minimum RMS error in North and East direction and the combination of GLO+GAL+B give the minimum RMS errors in up directions.

Analysis of Characteristics for Inter-System Bias on Multi-GNSS Undifferenced and Uncombined Precise Point Positioning

Multi Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP) has become the mainstream of PPP technology. Due to the differences in the coordinates and time references of each GNSS, multi-GNSS PPP must include additional Inter-System Bias (ISB) parameters to ensure compatibility between different GNSSs. Therefore, research on the characteristics of ISB is also essential. To analyze the short- and long-term time characteristics of multi-GNSS ISBs, as well as their relationship with receiver type and receiver antenna type, the Undifferenced and Uncombined (UDUC) PPP model of Global Positioning System (GPS), BeiDou navigation satellite system (BDS), and Galileo satellite navigation system (Galileo) was rigorously derived, and the physical of ISBs was elaborated in depth. ISB parameters were estimated and analyzed using 31 days of data from the 31 Multi-GNSS Experimental stations (MGEX). The results indicate that: (1) the ISB value is dependent on the station receiver type, receiver antenna type, analysis center product utilized, and GNSS system. (2) The short-term time characteristics of ISB-COM, ISB-WUM, and ISB-GBM are similar for the same station but not for the long term. In addition, ISBs are more stable in the short term. (3) There is little correlation between the ISB time characteristics, the receiver type, and the receiver antenna type, and the day-boundary discontinuity(DBD) on the ISB can be ignored for the concussive days’ process.

Monitoring Structural Displacements on a Wall with Five-Constellation Precise Point Positioning: A Position-Constrained Method and the Performance Analyses

The global navigation satellite system (GNSS) precise point positioning (PPP) technique has been commonly applied to structural displacement monitoring. Considering the sheltering effect, GNSS receivers are regularly mounted on the top of a structure, but the structure is often not a rigid body; therefore, the receiver should also be mounted on the wall of the structure. Combining five constellations, GNSS can effectively reduce the sheltering effect. Therefore, this study attempts to apply the five-constellation PPP technique to monitor structural long-term displacements on the wall (SLDW) and structural vibrational displacements on the wall (SVDW) and then analyze their performance. Two novel methods are proposed in monitoring SVDW. Firstly, semi-generated measurements are designed to generate pseudo-environments with vibrations for the receiver. Therefore, additional instruments are not necessary to generate vibrations. Secondly, to further reduce the sheltering effect, a position-constrained PPP (PCPPP) model is developed. Formal performance analyses are presented in this study, and the results show that using the five-constellation PPP to monitor SLDW and SVDW in the horizontal direction is possible as long as the sheltering effect over the half sky of the receiver is not severe. In monitoring SVDW, the PCPPP model can perform better than the classical PPP model and be successful in the horizontal direction when the condition of elevation cutoff is given as high as 50°. For Asia-Pacific mid-low-latitude regions, the global positioning system (GPS) and BeiDou system (BDS) are important to maintain the availability of monitoring SVDW.

Performance Analysis of Real-Time GPS/Galileo Precise Point Positioning Integrated with Inertial Navigation System

The integration of global navigation satellite system (GNSS) precise point positioning (PPP) and inertial navigation system (INS) is widely used in navigation for its robustness and resilience, especially in case of GNSS signal blockage. With GNSS modernization, a variety of PPP models have been developed and studied, which has also led to various PPP/INS integration methods. In this study, we investigated the performance of a real-time GPS/Galileo zero-difference ionosphere-free (IF) PPP/INS integration with the application of uncombined bias products. This uncombined bias correction was independent of PPP modeling on the user side and also enabled carrier phase ambiguity resolution (AR). CNES (Centre National d'Etudes Spatiales) real-time orbit, clock, and uncombined bias products were used. Six positioning modes were evaluated, including PPP, PPP/INS loosely coupled integration (LCI), PPP/INS tightly coupled integration (TCI), and three of these with uncombined bias correction through a train positioning test in an open sky environment and two van positioning tests at a complex road and city center. All of the tests used a tactical-grade inertial measurement unit (IMU). In the train test, we found that ambiguity-float PPP had almost identical performance with LCI and TCI, which reached an accuracy of 8.5, 5.7, and 4.9 cm in the north (N), east (E) and up (U) direction, respectively. After AR, significant improvements on the east error component were achieved, which were 47%, 40%, and 38% for PPP-AR, PPP-AR/INS LCI, and PPP-AR/INS TCI, respectively. In the van tests, frequent signal interruptions due to bridges, vegetation, and city canyons make the IF AR difficult. TCI achieved the highest accuracies, which were 32, 29, and 41 cm for the N/E/U component, respectively, and also effectively eliminated the solution re-convergence in PPP.

BDS pseudorange biases handling: Simultaneous estimation, daily magnitude and analytical comparison of the BDS PPP models

With the completed establishment of the Beidou global navigation satellite system (BDS-3), the BDS constellation is qualified for the global positioning, navigation and timing (PNT) services. The simultaneous observed B1I/B3I signals of the BDS-2 and BDS-3 satellites facilitate the BDS-2/BDS-3 joint precise point positioning (PPP) solution. For reasons related to the modulation modes, signal property, receiver front end design, precise satellite clock products arising from the different analysis centers and so on, BDS pseudorange biases are absorbed by the pseudorange measurements, including the pseudorange bias variation, signal distortion bias (SDB) and time delay bias (TDB). The large magnitude of the BDS pseudorange biases will degrade the BDS PPP performance. Herein, the simultaneous estimation of the BDS pseudorange biases are applied in BDS PPP and totally six pseudorange biases processing strategies are presented. The magnitudes of the existed BDS SDB and TDB are analyzed. The statistics showed that the BDS PPP performance in term of the convergence time and positioning accuracy can be remarkably improved by considering the BDS pseudorange biases. By comparing the BDS PPP performance in different scenarios, we recommend three processing schemes that are reducing weight of the BDS-2 pseudorange observations, estimating the BDS TDB as constant and neglecting the SDB, and estimating the BDS SDB as the constant per satellite. The analytical results can facilitate the optimal BDS PPP performance.

An Improved Strategy for Real-Time Troposphere Estimation and Its Application in the Severe Weather Event Monitoring

The water vapor content in the atmosphere is highly correlated with rainfall events, which can be used as a data source for rainfall prediction or drought monitoring. The GNSS PPP (Precise Point Positioning) technique can be used to estimate the troposphere ZWD (Zenith Wet Delay) parameter which can be converted into precipitable water vapor (PWV). In this study, we first investigate the impacts of the weighting strategies, observation noise settings, and gradient estimation on the accuracy of ZWD and positions. A refined strategy is proposed for the troposphere estimation with uncombined raw PPP model, down-weighting of Galileo/GLONASS/BDS code observation by a factor of 3, using a sine2-type elevation-dependent weighting function and estimating the horizontal gradients. Based on the strategy, the correlation of the estimated tropospheric parameters with the rainfall is analyzed based on the data from the “7.20” rainstorm in Henan Province, China. The PWV is first calculated based on the hourly global pressure and temperature (HGPT) model and compared with the results from ERA5 products. Results show their good consistency during the rainfall period or the normal period with a standard deviation of 3 mm. Then, the high correlation between the PWV and the heavy rain rainfall event is validated. Results show that the accumulated PWV maintains a high level before the rainstorm if a sustainable water supply is available, while it decreased rapidly after the rainfall. In comparison, the horizontal gradients and the satellite residuals are less correlated with the water vapor content. However, the gradients can be used to indicate the horizontal asymmetry of the water vapor in the atmosphere.

On the potential of undifferenced and uncombined GNSS time and frequency transfer with integer ambiguity resolution and satellite clocks estimated

The use of global navigation satellite systems (GNSS) has been a competitive way to provide high-precision and low-cost time and frequency transfer results. However, the traditional GNSS method, the precise point positioning (PPP), is usually based on the ionosphere-free (IF) combination, which is not flexible when applying multi-frequency scenarios. In addition, PPP relies on precise satellite clock products with an accuracy of tens of picoseconds, limiting the time and frequency transfer performance. More importantly, achieving integer ambiguity resolution (IAR) is challenging, which makes high-precision phase observations underutilized. To achieve a better time transfer performance, we must consider all those factors from the GNSS end. In this contribution, a new GNSS time and frequency model at the undifferenced and uncombined (UDUC) level is first derived. In the UDUC model, the satellite clocks are estimated together with other parameters, and the integer ambiguities are resolved in the double-differenced (DD) form for their reliable estimation. Our numerical tests suggest three major findings. First, with integer ambiguities resolved, the UDUC model with satellite clocks fixed showed a 20% to 50% improvement compared with the UDUC PPP model. Second, with IAR and satellite clocks estimated, the proposed UDUC model shows a 10%–40% improvement over the model with satellite clocks fixed. Third, with integer ambiguities resolved and satellite clocks estimated, GPS, Galileo, and BDS-3 all have the potential to achieve frequency transfer in the low-mid 10^{ - 17} range for averaging times within one day.

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.

The Initial Performance Evaluation of Mixed Multi-Frequency Undifferenced and Uncombined BDS-2/3 Precise Point Positioning under Urban Environmental Conditions

With the full operation of the global BeiDou navigation satellite system (BDS-3), positioning performance can be further enhanced by BDS-3 combined with the regional BeiDou navigation satellite system (BDS-2). However, due to satellite signals being out of lock and the limited visibility of satellites, the traditional multi-frequency BDS-2/3 precise point positioning (PPP) model is unable to maintain great positioning performance under urban environmental conditions. In this study, a mixed multi-frequency undifferenced and uncombined (UDUC) BDS-2/3 PPP model is presented to improve the positioning performance under urban environmental conditions by making full use of B1I, B1C, B2I, B2a, and B3I signals from all visible BDS satellites. In this model, BDS satellites with single-, dual-, triple- and quad-frequency observations all can participate in PPP. The static and kinematic experiments were carried out using the mixed multi-frequency UDUC BDS-2/3 PPP model to fully assess the positioning performance under urban environmental conditions with comparisons to the multi-frequency model. The static experiments indicated that the mixed multi-frequency UDUC BDS-2/3 PPP could continuously achieve decimeter-level positioning accuracy at a cut-off elevation angle of 40°, but part of the BDS-3 PPP would lose resolution due to limited visible satellites. Furthermore, the initial kinematic vehicle experiment showed that mixed multi-frequency UDUC BDS-2/3 PPP had better satellite geometry and more observation redundancy than the traditional multi-frequency model. Compared with the traditional multi-frequency BDS-2/3 model, the positioning accuracy of the mixed multi-frequency model was improved by 51.6, 35.5, and 39.1%, respectively, in east, north, and up directions. The convergence time was shortened by 40%.

Modelling and Assessment of a New Triple-Frequency IF1213 PPP with BDS/GPS

The currently available triple-frequency signals give rise to new prospects for precise point positioning (PPP). However, they also bring new bias, such as time-varying parts of the phase bias in the hardware of receivers and satellites due to the fact that dual-frequency precise clock products cannot be directly applied to triple-frequency observation. These parameters generate phase-based inter-frequency clock bias (PIFCB), which impacts the PPP. However, the PIFCBs of satellites are not present in all GNSSs. In this paper, various IF1213 PPP models are constructed for these parts, namely, the triple-frequency PIFCB (TF-C) model with PIFCB estimation, the TF inter-frequency bias (IFB) (TF-F) model ignoring the PIFCB, and the TF-PIFCB-IFB (TF-CF) model with one system PIFCB estimation. Additionally, this study compares these IF1213 PPP models with the dual-frequency ionosphere-free (DF) model. We conducted single system static PPP, dual-system static and kinematic PPP experiments based on BDS/GPS observation data. The GPS static PPP experiment demonstrates the reliability of the TF-C model, as well as the non-negligibility of the GPS PIFCB. The BDS static PPP experiment demonstrates the reliability of the TF-F and TF-CF models, and that the influence of the BDS-2 PIFCB can be neglected in BDS. The BDS/GPS PPP experimental results show that the third frequency does not significantly improve the positioning accuracy but shortens the convergence time. The positioning accuracy of TF-C and TF-CF for static PPP is better than 1.0 cm, while that for kinematic PPP is better than 2.0 cm and 4.0 cm in the horizontal and vertical components, respectively. Compared with the DF model, the convergence time of the TF-C and TF-CF models for static PPP is improved by approximately 23.5%/18.1%, 13.6%/9.7%, and 19.8%/12.1%, while that for kinematic PPP is improved by approximately 46.2%/49.6%, 33.5%/32.4%, and 35.1%/36.1% in the E, N and U directions, respectively. For dual-system PPP based on BDS/GPS observations, the TF-C model is recommended.