Denghui Wang

Improving Ambiguity Resolution for Medium Baselines Using Combined GPS and BDS Dual/Triple-Frequency Observations

The regional constellation of the BeiDou navigation satellite system (BDS) has been providing continuous positioning, navigation and timing services since 27 December 2012, covering China and the surrounding area. Real-time kinematic (RTK) positioning with combined BDS and GPS observations is feasible. Besides, all satellites of BDS can transmit triple-frequency signals. Using the advantages of multi-pseudorange and carrier observations from multi-systems and multi-frequencies is expected to be of much benefit for ambiguity resolution (AR). We propose an integrated AR strategy for medium baselines by using the combined GPS and BDS dual/triple-frequency observations. In the method, firstly the extra-wide-lane (EWL) ambiguities of triple-frequency system, i.e., BDS, are determined first. Then the dual-frequency WL ambiguities of BDS and GPS were resolved with the geometry-based model by using the BDS ambiguity-fixed EWL observations. After that, basic (i.e., L1/L2 or B1/B2) ambiguities of BDS and GPS are estimated together with the so-called ionosphere-constrained model, where the ambiguity-fixed WL observations are added to enhance the model strength. During both of the WL and basic AR, a partial ambiguity fixing (PAF) strategy is adopted to weaken the negative influence of new-rising or low-elevation satellites. Experiments were conducted and presented, in which the GPS/BDS dual/triple-frequency data were collected in Nanjing and Zhengzhou of China, with the baseline distance varying from about 28.6 to 51.9 km. The results indicate that, compared to the single triple-frequency BDS system, the combined system can significantly enhance the AR model strength, and thus improve AR performance for medium baselines with a 75.7% reduction of initialization time on average. Besides, more accurate and stable positioning results can also be derived by using the combined GPS/BDS system.

The Analysis of Ill Posedness in GNSS High-Precision Differential Positioning

GNSS high-precision differential positioning generally requires the high-precision float solution and the reasonable covariance matrix for ambiguity integers in short observational time spans. But station-star geometric changes little in short observational time spans, which causes the design matrix to be ill-conditioned seriously during adjustment calculation and leads to the solving of parameters is unstable. With the development of Compass Navigation Satellite System, the GNSS high-precision positioning is now entering the multi-system combined ages. GPS, GLONASS and Compass have different orbits and operating features so that there is some difference from each other in adjustment calculation. The paper combining with the analysis theory on ill-conditioned system, analyses the ill posedness of GPS, GLONASS and Compass comparatively through a method called spectrum analysis of eigenvalue. The paper reveals the characteristics of the ill condition in several different positioning forms. The conclusion that the faster the satellites runs, the weaker the ill posedness of the parameters solving system will be is presented.

Combined GPS and BDS for single-frequency continuous RTK positioning through real-time estimation of differential inter-system biases

Double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can be fixed to integers if the associated differential inter-system biases (DISBs) are well known. In this case, only one common pivot satellite is sufficient for inter-system ambiguity resolution. This will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning especially when only a few satellites are observed. However, for GPS and current operational BDS-2, there are no overlapping frequencies. Due to the influence of different frequencies, the inter-system DD ambiguities still cannot be fixed to integers even if the DISBs are precisely known. In this contribution, we present an inter-system differencing model for combined GPS and BDS single-frequency RTK positioning through real-time estimation of DISBs. The stability of GPS L1 and BDS B1 DISBs is analyzed with different receiver types. Along with parameterization and using the short-term stability of DISBs, the DD ambiguities between GPS and BDS pivot satellites and the between-receiver single-difference ambiguity of the GPS pivot satellite can be estimable jointly with the differential phase DISB term from epoch to epoch. Then the inter-system differencing model can benefit from the near time-constant DISB parameters and thus has better multi-epoch positioning performance than the classical intra-system differencing model. The combined GPS and BDS single-frequency RTK positioning performance is evaluated with various simulated satellite visibilities. It will be shown that compared with the classical intra-system differencing model, the proposed model can effectively improve the positioning accuracy and reliability, especially for severely obstructed situations with only a few satellites observed.

High-Precision Oceanic Real-Time Positioning Application Based on Regional Continuous Operation Reference Stations

ABSTRACT Gao, C.; Gao, W.; Pan, S.; Chen, W.; Shi, X., and Wang, D., 2015. High-precision oceanic real-time positioning application based on regional continuous operation reference stations. With the rapid development of land-based Global Navigation Satellite System (GNSS) positioning technology, the high-precision oceanic GNSS positioning demands are more extensive. A real-time precise point positioning (PPP) method based on regional Continuous Operation Reference Stations (CORS) for ocean application is proposed in the paper. Starting fromthe requirement of real-time satellite orbit and clock products for the real-time PPP, the accuracy of IGU (International GNSS service Ultra-rapid) orbit product and its correlation with prediction time were analyzed. Also, a new easy and effective real-time estimation method of satellite clock based on regional CORS network was proposed, and the estimated clock was compared with the IGS final clock products. Then based on predicted IGU orbit and estimated real-time clock products, real-time PPP experiments in long-distance away areas were carried out to simulate ocean application. Experimental results show that the average RMS of estimated clock is less than 0.1ns compared with the IGS final clock. In the real-time PPP experiments, the average convergence time of the two selected long-distance areas are 16.5 minutes and 15.6 minutes respectively. The positioning errors in the three directions (North/East/Up) are within 6 cm after 1-hour filtering. The contents researched in the paper verify the feasibility of real-time PPP based on regional CORS for oceanic application and provide a new possible strategy for oceanic positioning application.

Characteristics and modelling of BDS satellite inter-frequency clock bias for triple-frequency PPP

Aiming at the problem of the inter-frequency clock bias (IFCB) in Beidou Navigation Satellite System (BDS) triple-frequency observations, the variation characteristics with time are analysed in detail. The IFCB models for all the three kinds of satellites, i.e. GEO, IGSO and MEO, are proposed. Then the attenuation and long-term forecasting performance of the models are evaluated. Finally, the validity and benefit of the model are verified by triple-frequency Precise Point Positioning (PPP) experiments. The IFCB results from consecutive two-month BDS triple-frequency observation data of 44 globally distributed Multi-GNSS Experiment (MGEX) stations show that the IFCBs of GEO satellites have prominent periodic variation in general. The correlation coefficient and the determination coefficient of predicted IFCB by the model for GEO satellites are up to 0.957 and 0.915 respectively, which shows the model has a high stability and is suitable for long-term prediction. The IFCBs of IGSO satellites have the same periodicity as those of GEO satellites. Although the model is not as good as that of GEO satellites, it still performs well overall and can be applied to long-term prediction in most instances. The model of MEO satellites performs worse than GEO and IGSO due to the numerical instability and less obvious periodicity of IFCBs. Moreover, the effect of the IFCB models is better than the substitution method of using the IFCB at the corresponding moment in the previous period as the IFCB forecast value of the current period. In the triple-frequency Precise Point Positioning (PPP) experiments, the modelled IFCB correction can improve the positioning accuracy by 21.1%, 9.0% and 9.9% in the north, east and up directions and also shorten the convergence time in these three directions by 26.8%, 10.4% and 24.4% respectively compared with the observation model without IFCB correction.

A Multi-Redundancies Network RTK Atmospheric Errors Interpolation Method Based on Delaunay Triangulated Network

Routine Network Real-time Kinematic (NRTK) techniques always use triangle as the interpolation unit to solve the users’ ambiguity and atmospheric effects. Because of the limitation of the calculating unit, the correction information based on virtual reference station (VRS) technique cannot fully use the information from all the reference stations, so that the users’ RTK initialization speed and positioning accuracy would be seriously affected. In order to avoid the loss of observation information, two interpolation methods, MLIM for ionosphere and RELIM for troposphere, were proposed in the paper. Relying on the existing Delaunay Triangulated Network (DTN) structure, the optimal and suboptimal units were selected to increase the interpolation baselines number. Using the data from the Earth Scope Plate Boundary, our methods obtained more accurate interpolation accuracy by 3 times and 6 to 30 times higher for ionosphere and troposphere, respectively, compared with the traditional models. Besides, these two models can get more stable performance regardless the change of satellites elevation and the altitude differences among reference stations. In addition, we developed an alternative integrity monitoring method for rover station, with the interpolating monitoring precision of centimeter level. The proposed method is feasible to evaluate the actual integrity index and monitor the actual accuracy in the users’ position.

A Robust Strategy for Ambiguity Resolution Using Un-Differenced and Un-Combined GNSS Models in Network RTK

An increasing number of reference stations have been established, leading to a sharp increase in the workload of Double-Difference (DD) baseline solutions, which are not appropriate for the integrated processing of denser networks. Correlations among the ambiguities in DD models are complex, and it is difficult to get precise solutions. This paper improves the DD ambiguity resolution performance over a long baseline, using a modified strategy based on an Un-Differenced (UD) and Un-Combined (UC) model. The satellite clocks are estimated as parameters, which are properly constrained by real-time satellite clock products for improving the smoothness of ambiguities. We use data from the Earth Scope Plate Boundary Observatory to examine the presented method in Global Positioning System (GPS) networks. Our method obtained more obviously centralised distributions. The successful fixed rate was 96·4% for the DD baseline solution, and 98·4% for the UD method. The proposed strategy is appropriate for the distributed architecture of extensive systems and avoids a heavy computational burden.

A Baseline Ambiguity Resolution Using Un-combined and Un-differenced Model with Equality Constraint

With the development of GNSS technology, the higher demand for calculation is put forward in the field of the whole network baseline solution. The conventional baseline solution is a three-step method, which is complex and relies on the success rate of ambiguity solution at each step. A modified strategy for baseline ambiguity resolution is proposed in the paper, using un-combined and un-differenced model. The equality constraint is also used to recover the integer property of ambiguities. By the constraint of the fixed ambiguities, the baseline solution could be obtained. The data sets from various lengths of baselines are conducted to investigate the performance of the UD strategy. Depending on the empirical fixed success rate and convergence time, the modified strategy has a better AR performance on the rising satellites and weakens the unknown coefficient of correlation between ambiguities.

Reliable RTK Positioning Method Based on Partial Wide-Lane Ambiguity Resolution from GPS/GLONASS/BDS Combination

Integration of multi-constellation GNSS creates a significant increase in the number of visible satellites, thus bring new opportunities for improving the accuracy and reliability of Real Time Kinematic (RTK) positioning. This paper proposes a reliable RTK positioning method based on partial wide-lane ambiguity resolution (AR) from GPS/GLONASS/BDS (G/R/C) combination. It takes advantage that wide-lane observation has much longer wavelength, and the multi-constellation combined wide-lane ambiguity-fixed observations are directly used to positioning calculation. In the paper, the G/R/C geometry-based wide-lane ambiguity resolution models are unified and combined. Then a partial ambiguity resolution (PAR) method is introduced to avoid the influence of extreme errors from low-elevation satellites. A set real G/R/C baseline data is used as typical example to reflect the benefits of the proposed method. Experiment results show that the multi-constellation combination can significantly improve the wide-lane AR effects, including the AR success rate, ratio and initialization speed. And the proposed PAR method can effectively avoid the negative influence of new-rising satellites. The positioning accuracy using the proposed method can still reach centimetre level.

Extraction and Application of Un-differenced Atmospheric Delays with Un-combined Precise Point Positioning Technique

A new method for the extraction and application of un-differenced atmospheric delays with un-combined precise point positioning technique, is proposed based on the regional continuous operational reference system (CORS) network. The estimable state vector, which lets in the receiver clock offset, the ionospheric slant delay and zenith tropospheric wet delay (ZWD), is estimated epoch by epoch at every reference station. In addition, the least squares and the ionospheric regional polynomial model is also used to separate the DCB and the ionospheric delay. For improving the convergence time of the PPP, a new PPP algorithm, which was suited for single-frequency and dual-frequency receivers, was put forward. The algorithm took full use of the interpolation of regional atmospheric delay value as the quasi-observable, and the un-combined satellite-different observations were used to obtain the precise positioning results. Nevertheless, the method mentioned above is investigated and examined on the IGS tracking stations. The results show that all the satellites’ DCB are solved and compared with the products published by CODE, the disparity between them is mostly not greater than 0.2 ns. Furthermore, with the aim of the real-time fast precise point positioning based on the sparse regional CORS, results from American CORS data set is introduced and discussed. The positioning accuracy can reach 10 cm in the plane within 30 min for the single-frequency PPP user and the plane position result in 1–2 cm also can be accomplished after the convergence of the filter. For dual-frequency receiver, it takes approximately 10 min to get positions with accuracy better than 10 cm at the three directions for the dual-frequency PPP user. On the other hands, due to its epoch-by-epoch nature, the method proposed above is also suited for dynamic precise point positioning.