| The ionosphere is an upper atmosphere about 50 to 1000(or extended to 2000)kilometers above the ground.It is a plasma area formed by solar radiation and cosmic rays.It is such an important part of the solar-terrestrial space that is closely related to human activities.As a medium for electromagnetic waves,the ionosphere affects electromagnetic waves by reflection,refraction,scattering and absorption,and it has an important influence on radio communications,broadcasting,radar,and satellite positioning and navigation applications.With the rapid developments of technologies and people's exuberant demands for positioning and navigation,applications of the Global Navigation Satellite System(GNSS)have thrived over the decades in both military and civilian fields.Nowadays researchers are putting forward higher demands for GNSS positioning accuracy,and centimeter or even millimeter level precision has become common.From transmission in space to reception on the ground,GNSS signals are affected by various factors,resulting in a variety of errors are absorbed in the observables.Among all kinds of errors in GNSS measurements,the ionospheric error has always been vital-range error derived from ionospheric effect can vary from a few meters to tens of meter at the zenith.Based on dual-frequency GNSS measurements,the ionospheric-free combination has long been adopted to reduce the refractive error,which can eliminate most of the error derived from the first-order ionospheric term.The impact of the remaining higher-order ionospheric terms is relatively small,however,studies show that the effect of the second-order ionospheric term,which related to the total electron content(TEC)in ionosphere and the magnetic field of the earth,can still reach up to millimeter to centimeter level,and in some extreme cases,such as during the ionospheric storm,it becomes even higher.Thus,when high-accuracy geodetic applications being conducted,the effect of the higher-order ionospheric terms cannot be ignored and should get more attention.Estimating and correcting the effects of higher-order ionospheric terms on GPS(Global Positioning System),GLONASS(GLObal NAvigation Satellite System),Galileo(Galileo Satellite System)and BDS(Beidou Navigation Satellite System)is of great value and significance in the research and application of high precision GNSS and geodesy applications.Based on the data from globally distributed GNSS continuous running station,this article focuses on the effects of the high-order ionospheric terms(mainly the second-order term)on GNSS positioning and the estimation of differential code biases(DCB).The main work and achievements of this article are:(1)Based on the data from 35 globally distributed multi-GNSS stations,the effects of the second-order ionospheric terms on GPS,GLONASS,Galileo and BDS positioning have been modeled and estimated respectively.Results show that the effects of the second-order ionospheric term on positioning for the multi-GNSS systems are generally on submillimeter to millimeter level.Ignoring the differences between stations,the average impacts on positioning derived from the second-order ionospheric term on these four systems are 0.736,0.789,1.222,and 0.680 mm in the horizontal direction,respectively;and 0.512,0.441,0.870,and 0.322 mm in the vertical direction,respectively.Whether in the horizontal or vertical direction,Galileo suffers the most from the second-order ionospheric term—1.66 times of GPS horizontally and 2.70 times of BDS vertically.For different navigation systems,the impact of the second-order ionospheric term on coordinates solutions show almost the same trend—an overall northward shift in the northern hemisphere,and vice versa,with an overall southward shift in the southern hemisphere;in the vertical direction,most stations show a tendency to shift upwards.In addition,the effect of the second-order ionospheric term on GNSS positioning shows a strong positive correlation with the vertical total electron content(VTEC),and have a period of approximately one day,which is due to the periodic changes of VTEC.(2)Focused on the impacts of the second-order ionospheric term on GPS positioning in Antarctic in the whole year of 2012,data from 12 IGS(International GNSS Service)stations,7 POLENET(The Polar Earth Observing Network)stations and 2 stations maintained by CACSM(Chinese Antarctic Center of Surveying and Mapping,Wuhan University)have been adopted,then the impact has been estimated and analyzed.Results show that for these 21 stations,the second-order ionospheric term has similar characteristics on GPS positioning for each station in the time domain:larger in the Antarctic summer and smaller in winter.Neglecting the differences between stations,the average annual effects of the second-order ionospheric term on GPS positioning in the east,north,and vertical directions were 0.175,-0.866,and 1.390 mm,respectively;neglecting the differences between directions,and let January and July represents Antarctic summer and winter,respectively,then the impact of the summer was 5.3 times that of the winter.If only the first-order ionospheric term was considered in the positioning process and the second-order term was neglected,the final positioning results will show a mainly southward and upward shift.In addition,the effect of the second-order ionospheric term on GPS positioning is positively correlated to the change of the total electron content over the Antarctic continent.(3)A new method of adding the second-order ionospheric term in the GPS DCB estimation was proposed.The DCB of 3 GPS receivers and 32 GPS satellites in the experimental area in March 2012 was estimated.The results show that the impact of the second-order ionospheric term on GPS DCB estimation is in the order of 10-3 to 10'2 ns,ignoring the differences between GPS satellites and receivers.The average of the impact is 0.0044 ns with a standard deviation of 0.0082 ns,which multiplies by the signal propagation velocity(where the speed of light is taken as a reference)is 1.32 ? 2.46 mm.In the process of estimating GPS DCB parameters,the ionospheric model parameters of the experimental area were also obtained.It was found that the impact on VTEC modeling derived by the second-order ionospheric term in the region is at the level of 10-2 TECU.At the same time,the impact of the second-order ionospheric terms on DCB estimates also shows an obvious change with the local VTEC. |
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