Modeling and Prediction of Inter-System Bias for GPS/BDS-2/BDS-3 Combined Precision Point Positioning

The combination of Precision Point Positioning(PPP)with Multi-Global Navigation Satellite System(MultiGNSS),called MGPPP,can improve the positioning precision and shorten the convergence time more effectively than the combination of PPP with only the BeiDou Navigation Satellite System(BDS).However,the Inter-System Bias(ISB)measurement of Multi-GNSS,including the time system offset,the coordinate system difference,and the inter-system hardware delay bias,must be considered for Multi-GNSS data fusion processing.The detected ISB can be well modeled and predicted by using a quadratic model(QM),an autoregressive integrated moving average model(ARIMA),as well as the sliding window strategy(SW).In this study,the experimental results indicate that there is no apparent difference in the ISB between BDS-2 and BDS-3 observations if B1I/B3I signals are used.However,an obvious difference in ISB can be found between BDS-2 and BDS-3 observations if B1I/B3I and B1C/B2a signals are used.Meanwhile,the precision of the Predicted ISB(PISB)on the next day of all stations is about 0.1−0.6 ns.Besides,to effectively utilize the PISB,a new strategy for predicting the PISB for MGPPP is proposed.In the proposed strategy,the PISB is used by adding two virtual observation equations,and an adaptive factor is adopted to balance the contribution of the Observed ISB(OISB)and the PISB to the final estimations of ISB.To validate the effectiveness of the proposed method,some experimental schemes are designed and tested under different satellite availability conditions.The results indicate that in open sky environment,the selective utilization of the PISB achieves almost the same positioning precision of MGPPP as the direct utilization of the PISB,but the convergence time of MGPPP is reduced by 7.1%at most in the north(N),east(E),and up(U)components.In the blocked sky environment,the selective utilization of the PISB contributes to more significant improvement of the positioning precision and convergence time than that in the open sky environment.Compared with the direct utilization of the PISB,the selective utilization of the PISB improves the positioning precision and convergence time by 6.7%and 12.7%at most in the N,E,and U components,respectively.

Performance analysis of the tight combination of GPS, BDS, GALILEO, and QzsS mixed frequencies signals

With the gradual development and modernization of satellite navigation systems,using observation information from multi-GNss has become one of the hot-spot issues in recent years.Multi-system loose combinations form double-difference observation equations within their respective systems,and the positioning effect is improved.However,the interchangeability and compatible interoperability between global navigation satellite systems(GNSS)cannot be truly realized.At the same time,when the number of visible satellites decreases abruptly,the positioning performance deteriorates sharply.This paper focuses on the GNsS multi-system tight combination relative positioning technique,gives a mathe-matical model of multi-system tight combination relative positioning considering differential inter-system bias(DISB),and analyzes the time-varying characteristics of DISB at overlapping and non-overlapping frequencies among GPS/Galileo,GPS/BDS,and GPS/QZSS in terms of receiver brand,tem-perature,and receiver restart.The GNsS tight combination relative positioning performance is verified by static data from Curtin University and dynamic data measured at Taiyuan University of Technology.The results show that compared with loose combination,the ambiguity-fixed rate increases from 62.18%to 97.60%for static data and from 74.97%to 99.53%for dynamic data when the elevation mask angle is 50°,resulting in a significant improvement in positioning performance.

Estimation of the inter-frequency clock bias for the satellites of PRN25 and PRN01

We present two efficient approaches,namely the epoch-differenced(ED) and satellite-and epoch-differenced(SDED) approaches,for the estimation of IFCBs of the two Block IIF satellites.For the analysis,data from 18 stations from the IGS network spanning 96 d is processed.Results show that the IFCBs of PRN25 and PRN01 exhibit periodical signal of one orbit revolution with a magnitude up to 18 cm.The periodical variation of the IFCBs is modeled by a sinusoidal function of the included angle between the sun,earth and the satellite.The presented model enables a consistent use of L1/L2 clock products in L1/L5-based positioning.The algorithm is incorporated into the MGPSS software at SHAO(Shanghai Astronomical Observatory,Chinese Academy of Sciences) and is used to monitor the IFCB variation in near real-time.

Impact of receiver inter-frequency bias residual uncertainty on dual-frequency GBAS integrity

Dual-Frequency Ground-Based Augmentation Systems(GBAS)can be affected by receiver Inter-Frequency Bias(IFB)when Ionosphere-Free(Ifree)smoothing is applied.In the framework of the proposed GBAS Approach Service Type F(GAST-F),the IFB in the Ifree smoothed pseudorange can be corrected.However,IFB residual uncertainty still exists,which may threaten the integrity of the system.This paper presents an improved algorithm for the airborne protection level considering the residual uncertainty of IFBs to protect the integrity of dual-frequency GBAS.The IFB residual uncertainty multiplied by a frequency factor is included in the Ifree protection level together with the uncertainty of other error sources.To verify the proposed protection level algorithm,we calculate the IFB residual uncertainties of ground reference receivers and user receiver based on BDS B1I and B3I dual-frequency observation data and carry out a test at the Dongying Airport GBAS station.The results show that the proposed Ifree protection level with IFB residual uncertainty is 1.48 times the current protection level on average.The probability of Misleading Information(MI)during the test is reduced from 3.2×10^(-4)to the required value.It is proven that the proposed protection level can significantly reduce the integrity risk brought by IFB residual uncertainty and protect the integrity of dual-frequency GBAS.

A new inter‑system double‑difference RTK model applicable to both overlapping and non‑overlapping signal frequencies

Aiming at the problem that the traditional inter-system double-difference model is not suitable for non-overlapping signal frequencies,we propose a new inter-system double-difference model with single difference ambiguity estimation,which can be applied for both overlapping and non-overlapping signal frequencies.The single difference ambiguities of all satellites and Differential Inter-System Biases(DISB)are first estimated,and the intra-system double difference ambiguities,which have integer characteristics,are then fixed.After the ambiguities are successfully fixed,high-precision coordinates and DISB can be obtained with a constructed transformation matrix.The model effectively avoids the DISB parameter filtering discontinuity caused by the reference satellite transformation and the low precision of the reference satellite single difference ambiguity calculated with the code.A zero-baseline using multiple types of receivers is selected to verify the stability of the estimated DISB.Three baselines with different lengths are selected to assess the positioning performance of the model.The ionospheric-fixed and ionospheric-float models are used for short and medium-long baselines,respectively.The results show that the Differential Inter-System Code Biases(DISCB)and Differential Inter-System Phase Biases(DISPB)have good stability regardless of the receivers type and the signal frequency used and can be calibrated to enhance the strength of the positioning model.The positioning results with three baselines of different lengths show that the proposed inter-system double-difference model can improve the positioning accuracy by 6–22%compared with the intra-system double-difference model which selects the reference satellite independently for each system.The Time to First Fix(TTFF)of the two medium-long baselines is reduced by 30%and 29%,respectively.

Extraction of line-of-sight ionospheric observables from GPS data using precise point positioning

Here we propose a method for extracting line-of-sight ionospheric observables from GPS data using precise point positioning(PPP).The PPP-derived ionospheric observables(PIOs) have identical form with their counterparts obtained from leveling the geometry-free GPS carrier-phase to code(leveling ionospheric observables,LIOs),and are affected by the satellite and receiver inter-frequency biases(IFBs).Based on the co-location experiments,the effects of extracting error arising from the observational noise and multipath on the PIOs and the LIOs are comparatively assessed,and the considerably reduced effects ranging from 70% to 75% on the PIOs with respect to the LIOs can be verified in our case.In addition,based on 26 consecutive days' GPS observations from two international GNSS service(IGS) sites(COCO,DAEJ) during disturbed ionosphere period,the extracted PIOs and LIOs are respectively used as the input of single-layer ionospheric model to retrieve daily satellite IFBs station-by-station.The minor extracting errors underlying the PIOs in contrast to the LIOs can also be proven by reducing day-to-day scatter and improving between-receiver consistency in the retrieved satellite IFBs values.

Single-epoch RTK performance assessment of tightly combined BDS-2 and newly complete BDS-3

The BeiDou global navigation satellite system(BDS-3)constellation deployment has been completed on June 23,2020,with a full constellation comprising 30 satellites.In this study,we present the performance assessment of single-epoch Real-Time Kinematic(RTK)positioning with tightly combined BeiDou regional navigation satellite system(BDS-2)and BDS-3.We first investigate whether code and phase Differential Inter-System Biases(DISBs)exist between the legacy B1I/B3I signals of BDS-3/BDS-2.It is discovered that the DISBs are in fact about zero for the baselines with the same or different receiver types at their endpoints.These results imply that BDS-3 and BDS-2 are fully interoperable and can be regarded as one constellation without additional DISBs when the legacy B1I/B3I signals are used for precise relative positioning.Then we preliminarily evaluate the single-epoch short baseline RTK performance of tightly combined BDS-2 and the newly completed BDS-3.The performance is evaluated through ambiguity resolution success rate,ambiguity dilution of precision,as well as positioning accuracy in kinematic and static modes using the datasets collected in Wuhan.Experimental results demonstrate that the current BDS-3 only solutions can deliver comparable ambiguity resolution performance and much better positioning accuracy with respect to BDS-2 only solutions.Moreover,the RTK performance is much improved with tightly combined BDS-3/BDS-2,particularly in challenging or harsh conditions.The single-frequency single-epoch tightly combined BDS-3/BDS-2 solution could deliver an ambiguity resolution success rate of 96.9%even with an elevation cut-off angle of 40°,indicating that the tightly combined BDS-3/BDS-2 could achieve superior RTK positioning performance in the Asia-Pacific region.Meanwhile,the three-dimensional(East/North/Up)positioning accuracy of BDS-3 only solution(0.52 cm/0.39 cm/2.14 cm)in the kinematic test is significantly better than that of the BDS-2 only solution(0.85 cm/1.02 cm/3.01 cm)due to the better geometry of the current BDS-3 constellation.The tightly combined BDS-3/BDS-2 solution can provide the positioning accuracy of 0.52 cm,0.22 cm,and 1.80 cm,respectively.