An improved GNSS ambiguity best integer equivariant estimation method with Laplacian distribution for urban low-cost RTK positioning

The integer least squares(ILS)estimation is commonly used for carrier phase ambiguity resolution(AR).More recently,the best integer equivariant(BIE)estimation has also attracted an attention for complex application scenarios,which exhibits higher reliability by a weighted fusion of integer candidates.However,traditional BIE estimation with Gaussian distribution(GBIE)faces challenges in fully utilizing the advantages of BIE for urban low-cost positioning,mainly due to the presence of outliers and unmodeled errors.To this end,an improved BIE estimation method with Laplacian distribution(LBIE)is proposed,and several key issues are discussed,including the weight function of LBIE,determination of the candidates included based on the OIA test,and derivation of the variance of LBIE solutions for reliability evaluation.The results show that the proposed LBIE method has the positioning accuracy similar to the BIE using multivariate t-distribution(TBIE),and significantly outperforms the ILS-PAR and GBIE methods.In an urban expressway test with a Huawei Mate40 smartphone,the LBIE method has positioning errors of less than 0.5 m in three directions and obtains over 50%improvements compared to the ILS-PAR and GBIE methods.In an urban canyon test with a low-cost receiver STA8100 produced by STMicroelectronics,the positioning accuracy of LBIE in three directions is 0.112 m,0.107 m,and 0.252 m,respectively,with improvements of 17.6%,27.2%,and 26.1%compared to GBIE,and 23.3%,28.2%,and 30.6%compared to ILS-PAR.Moreover,its computational time increases by 30–40%compared to ILS-PAR and is approximately half of that using TBIE.

Investigating GNSS PPP-RTK with external ionospheric constraints

Real-Time Kinematic Precise Point Positioning(PPP–RTK)is inextricably linked to external ionospheric information.The PPP-RTK performances vary much with the accuracy of ionospheric information,which is derived from diferent network scales,given diferent prior variances,and obtained under diferent disturbed ionospheric conditions.This study investigates the relationships between the PPP–RTK performances,in terms of precision and convergence time,and the accuracy of external ionospheric information.The statistical results show that The Time to First Fix(TTFF)for the PPP-RTK constrained by Global Ionosphere Map(PPP-RTK-GIM)is about 8–10 min,improved by 20%–50%as compared with that for PPP Ambiguity Resolution(PPP-AR)whose TTFF is about 13–16 min.Additionally,the TTFF of PPP-RTK is 4.4 min,5.2 min,and 6.8 min,respectively,when constrained by the external ionospheric information derived from diferent network scales,e.g.small-,medium-,and large-scale networks,respectively.To analyze the infuences of the optimal prior variances of external ionospheric delay on the PPP–RTK results,the errors of 0.5 Total Electron Content Unit(TECU),1 TECU,3 TECU,and 5 TECU are added to the initial ionospheric delays,respectively.The corresponding convergence time of PPP–RTK is less than 1 min,about 3,5,and 6 min,respectively.After adding the errors,the ionospheric information with a small variance leads to a long convergence time and that with a larger variance leads to the same convergence time as that of PPP-AR.Only when an optimal prior variance is determined for the ionospheric delay in PPP-RTK model,the convergence time for PPP-RTK can be shorten greatly.The impact of Travelling Ionospheric Disturbance(TID)on the PPP-RTK performances is further studied with simulation.It is found that the TIDs increase the errors of ionospheric corrections,thus afecting the convergence time,positioning accuracy,and reliability of PPP-RTK.

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.