BDS/GPS Multi-frequency Real-time Kinematic Positioning Theory And Algorithms

The regional constellation of Bei Dou Navigation Satellite System(BDS)has been officially in operation since December 27,2012 and about 20 satellites of BDS and GPS are visible in China and its surrounding areas.Consequently,the combined BDS and GPS positioning will significantly improve the availability and reliability of GPS point positioning and also advance the performance of high precise real-time and near real-time surveying.Research on the theory and algorithms of BDS/GPS multi-frequency real-time precise positioning will be of significant to real-time high precise positioning services under multi-system condition and also generalizing the industrialization of BDS high precise surveying.In this contribution,the theory and algorithms of real-time precise positioning by BDS/GPS multi-frequency observations are studied in detail.Main effort is made on triple-frequency linear combination theory,cycle-slip detection and correction,triple-frequency geometry-free ambiguity resolution(AR),the multi-system multi-frequency un-combined geometry-based AR model as well as its optimized computation.Besides,the performance of BDS/GPS multi-frequency Real-Time Kinematic(RTK)positioning over short and medium-long baselines is also evaluated with a lot of real BDS/GPS multi-frequency datasets.Furthermore,a multi-system multi-frequency RTK algorithm with good adaptability and compatibility is designed and the corresponding embedded RTK software is developed and has applied to the BDS/GPS multi-frequency RTK surveying system.The main contributions of this dissertation include:1.An analytical method for solving optimal integer linear coefficients with minimal noise amplification factor is presented,when the wavelength and ionospheric scale factor of the combinations are given.Then,three especial useful combinations in cycle-slip detection and AR process are derived,which are the Geometry-Free combination that the Sum of its linear coefficients equal to 0(GFS0),the Ionosphere-Free combination that the Sum of its linear coefficients equal to 0(IFS0)and the Geometry-Free and Ionosphere-Free(GFIF)combination.Their specific linear coefficients for GPS and BDS are also given,namely,GPS: GFS0=(5,-39,34),IFS0=(77,-468,391)and GFIF=(18095,-125892,107134);BDS: GFS0=(30,-173,143),IFS0=(2289,-10726,8437)and GFIF=(83930,-439766,353587).The relationship between the sum of linear coefficients of a combination and its wavelength and ionospheric scale factor is also examined.2.The relationship between the carrier-phase linear combinations expressed in units of length and their counterparts expressed in units of cycle are given.It is shown that the ambiguity of all real coefficients carrier-phase linear combinations expressed in units of length still reserve integer characteristic when their coefficients are rational number.3.The precision of BDS pseudorange and carrier-phase observations is evaluated by analyzing the residual error of zero baselines and very short baselines.It is shown that the precision of B1 I and B2 I pseudorange is about 33 cm and that of B1 and B2 carrier-phase measurement is about 2 mm.4.The total optimal search criterion and its orthogonal decomposition expression are derived from the object function of the mixed integer least-square estimation,which confirm that the least-square ambiguity search criterion is equivalent to the total optimal search criterion.Further,the search criterion in real parameter domain for solving the mixed integer least-square problem is also derived.5.The geometry-free carrier-phase linear combinations for cycle-slip detection are selected based on the carrier-phase linear combination expressed in units of cycle and the analytical expression of their insensitive cycle-slip groups is also given.It is shown that when the between-epoch ionospheric delay error is ignorable,the optimal geometry-free phase combinations for GPS are(10,-9,-4)and(5,7,-14),and for BDS,they are(20,-17,-8)and(10,21,-35).The success rate of ionosphere-weighted geometry-free cycle-slip estimation in triple-frequency case is analyzed.It is shown that all cycle-slip can be corrected reliably in real-time when the priori constraint of the between-epoch ionospheric delay variation is smaller than 0.02 m.This is also confirmed by the real BDS triple-frequency data test.6.The single-epoch AR performance of the geometry-free triple-frequency AR approach is demonstrated by the real BDS triple-frequency datasets over short baselines.The formula of narrow-lane ambiguity estimator of triple-frequency geometry-free and ionosphere-free AR scheme is redefined in a straightforward form,which proves that the narrow-lane ambiguity estimators are identical in various existing triple-frequency geometry-free and ionosphere-free AR schemes.7.The multi-system multi-frequency un-combined RTK model is constructed based on double-differenced multi-frequency original observations.The model is adaptable to multi-system single-,dual-and multi-frequency scenarios or multi-system mixed single-,dual-and multi-frequency scenarios,as well as compatible to short and long baselines positioning model.Therefore,it is very feasible for developing the RTK software in multi-system multi-frequency scenario.8.In order to improve the computation efficiency of the float solution estimation in multi-system multi-frequency case,the sequential measurement update and the multiplication of sparse matrixes strategies are presented.A multi-carrier fast partial ambiguity resolution strategy is also developed with the property that the Extra-Wide-Lane(EWL)and Wide-Lane(WL)ambiguities in the multi-frequency case can be resolved reliably in advance.The strategy is demonstrated with real BDS/GPS dual-and triple-frequency observations.Experimentally,the new method is about 2.5 times as fast as the batch AR in the dual-frequency case,3 times in the mixed dual-and triple case and 3.5 times in the triple-frequency case.9.The performance of BDS/GPS multi-frequency RTK positioning over short baseline is evaluated by a lot of real BDS/GPS multi-frequency datasets.The following conclusions can be drawn:(a)The single-epoch AR success rate of single-frequency BDS/GPS RTK positioning is comparable to that of the dual-frequency GPS.Therefore,the initialization of the single-frequency BDS/GPS RTK positioning can be achieved instantaneously or conservatively within only several seconds.Furthermore,the accuracy of single-frequency BDS/GPS RTK positioning is superior to that of the dual-frequency GPS and the dual-or triple-frequency BDS.(b)The single-epoch AR success rate of the dual-frequency BDS RTK positioning is also comparable to that of the dual-frequency GPS.It means that the dual-frequency Bei Dou-only RTK is already feasible,but its accuracy is worse to that of GPS since the serious multipath error of BDS GEO satellites.(c)The dual-frequency BDS/GPS RTK positioning can significantly enhance the reliability of single-epoch AR compared to the dual-frequency GPS alone.More importantly,the reliable AR in case of high cut-off elevations is still achievable.Therefore,the availability and reliability of the current GPS-only RTK positioning under some challenging conditions can be improved,which will extend the application field of the RTK positioning.10.The performance of BDS/GPS multi-frequency RTK positioning over medium-long baselines is evaluated preliminarily by four real BDS/GPS datasets.The results shown that:(a)The fast convergence of three coordinates and a troposphere parameters(geometry parameter)is mainly depend on the changing receiver-satellite geometry.The receiver-satellite geometry of BDS positioning changes slowly since BDS constellation mostly consists of GEO and IGSO satellites.As a result,the float solution of BDS RTK positioning converges slowly so that the Time To First Fix of BDS RTK positioning is very long and even its ambiguities cannot been fixed correctly.(b)The combined BDS/GPS RTK positioning can reduce the initialization time of the GPS RTK positioning over medium-long baselines.For the 15.6 km test,the averaged initialization time reduce from 3 minutes 23 seconds to 21 seconds,and the longest initialization time is smaller than 2 minutes;for the 52.6 km test,reduce from 13 minutes 30 seconds to 6 minutes 33 seconds,and the longest one is 15 minutes 26 seconds;for the 56.6 km test,reduce from 6 minutes to 1 minutes 54 seconds,and the longest one is 7 minutes 10 seconds;for the 98.8 km test,reduce from 4 minutes 39 seconds to 3 minutes 41 seconds,and the longest one is 11 minutes 40 seconds.