Principle And Mathematical Model Research For GPS Network RTK

GPS network RTK positioning is a kind of high precise GPS positioning technique which hasdeveloped in recent years. It forms a GPS network from multiple reference stations and theneliminates or mitigates the influence of GPS observation errors on roving receiver, based on thebasic principle and techniques of WADGPS and LADGPS with multiple reference stations so as toincrease the distance between reference stations and roving receivers and enhance the accuracy ofGPS real time kinematic positioning. Compared with conventional RTK, this technique has manyadvantages like wider action area, more accurate, more reliable positioning etc. It can also provideRTK positioning in centimeter accuracy for users. In this thesis, the concept and principle of GPSnetwork are described and three methods ---interpolation method, linear combination method andvirtual reference station method in GPS network RTK are discussed systematically. The main tasksand contributions of this research can therefore be summarized as follows:The principle and mathematical model of interpolation method in GPS network RTKBy using the condition of the known coordinates of reference stations, the residual error termsincluding orbit errors, ionospheric delay, tropopheric delay and multipath and obervation noise arecalculated comprehensively in the double-differenced mathematical model for carrier phaseobservations and then by using the calculated result of the mixed errors on the reference station, theobservation errors on the roving receiver are estimated based on the interpolation method.According to the principle mentioned above, establishing GPS network RTK interpolationmathematical model has the characteristics of simple formula, good positioning and high precision.Through practical calculation and theoretical evidence, the orbit errors and ionospheric delay can beeliminated, and in addition, the tropospheric delay, multipath and observation noise can besignificantly reduced by the interpolation method so as to increase the distance between referencestations and roving receivers and enhance the accuracy of GPS real time kinematic positioning. Thisthesis develops the interpolation mathematical formula based on the basic principle of GPS networkRTK and lists specific procedures of how to position GPS network RTK by using interpolationmethod.The principle and mathematical model of linear combination method in the network RTKIf that the influence of the residual error terms mentioned above is linear is assumed, thismethod will be based on a linear combination model, formed from the single-differenced functionalequation for baselines from the roving receiver to three or more reference receivers to eliminate ormitigate the influence of the roving receiver on these errors by using the condition of the knowncoordinates of base stations. Deriving from the combination model, combined observation candirectly eliminate or mitigate the influence of roving receivers on these errors. This thesisintroduces the mathematical formula based on the principle of linear combination method and liststhe specific operations of GPS network positioning using interpolation method.The principle and mathematical model of virtual reference station methodIf a roving receiver is far away from a reference station, the correlation of the errors betweenthe two stations will be decreased and the errors of residual orbit bias, ionospheric delay,tropopheric delay and multipath will increase the influence of relative positioning so as to degradepositioning precision of conventional RTK. In order to solve the problem, new reference stationsshould be established so that the users can use the information provided by the reference stationsand adopt some algorithm to eliminate or mitigate the influence the errors. The principle of virtualreference station method is intended to establish a virtual reference station near a roving receiverand calculate the virtual observation at the virtual reference station according to the raw observationaround reference stations. Because a virtual reference station is very close to a roving receiver, onlyseveral meters or 10 meters apart, roving users only need to use conventional RTK technique andcan do real time relative positioning with virtual reference stations to get more accurate positioningresult. The purpose of establishing a virtual reference station near a roving receiver is to enhancethe error correlation between a roving receiver and a reference station so as to improve the result ofconventional RTK positioning. So the method aims at how to find out virtual observations. Thisthesis, based on the basic principle of virtual reference station method, starting from themathematical model of interpolation and linear combination methods, preliminarily establishes themathematical model of finding out virtual reference station observations and lists the specificoperations of GPS network RTK positioning using virtual reference stations.The relationship between interpolation, linear combination and virtual reference stationmethodsIn recent GPS research field, when studying network RTK positioning theory, interpolationmethod, linear combination method and virtual reference station method are usually discussedseparately. Therefore, the relationship between them is ignored. In this thesis, it discusses theirrelationship and reaches some conclusions: (1) The linear combination method and the interpolationcan be transformed each other and therefore linear combination can be regarded as a specialexample of the interpolation. (2) The virtual observation formula of the virtual reference station canbe derived from the formula of interpolation and linear combination methods. (3) The orbit errorsand ionospheric delay can be eliminated, and in addition, the tropospheric delay, multipath andobservation noise can be significantly reduced by the mentioned three methods above so as toincrease the distance between reference stations and roving receivers and enhance the accuracy ofGPS real time kinematic positioning. (4) There is, in nature, no difference among the three networkRTK positioning methods. In this way, the theoretical precision of the positioning result should beabout the same. (5) Using the three methods to do network RTK positioning, for example, by usingprecise ephemeris to do post-positioning and using broadcast ephemeris to do real time kinematicpositioning, in theory, the precision of both positioning results should be the same.The influence of the parameter in network RTK mathematical model and the precision ininitial positions of roving stations on the positioning resultsThe precision of network RTK positioning result is influenced not only by the systematicerrors like conventional orbit errors, ionospheric delay, tropopheric delay and multipath, but also bythe mathematical model parameter and the initial positioning precision at roving stations. Thisthesis discusses this problem in details and concludes: (1) Roving stations should be located in thearea of reference stations. So the simulated error information will be acceptable and good result willbe achieved. (2) In general, network RTK data processing centers use point positioning resultsdisseminated from roving stations to calculate the interpolation error correction which can meet therequirements of centimeter accurate positioning and not to calculate the point positioning results atroving stations repeatedly.Testing the theory in this thesisThe correctness of the mathematical model established in this thesis is to be tested throughexperimental calculations. On the basis of the accurate coordination of the 4 GPS control pointsobtained from some region, according to the experimental design with the network RTK positioningprinciple, setting interpolation mathematical model as an example, this thesis calculates GPSpositioning data of 60 epochs altogether. The result shows that the difference between bothpositioning results is only ±4mm, which proves that the interpolation mathematical modelestablished in this thesis can simulate the observation errors between roving receivers and referencestations very well.The thesis is divided into eight chapters:The first chapter is an introduction. It briefly introduces conventional RTK technique and thendescribes the basic principle of GPS network RTK, the systematic form, the research backgroundsat home and abroad and the significance of studying network RTK. Finally, it listes the mainresearch contents in this thesis and the main research results obtained.The second chapter discusses the basic principle and formulae involved in GPS network dataprocessing, mainly including satellite positioning principle, observable linear combination and thelocation calculation of broadcast ephemeris satellites. The contents of this chapter, in theory, hasbeen well prepared for studying the establishment of network RTK positioning mathematicalmodel.The third chapter analyzes some common errors in network RTK positioning, for example,ionospheric delay, tropopheric delay, orbit error and etc. in details and also discusses how toeliminate or mitigate them.The fourth chapter is about network RTK interpolation mathematical model, which is the mostimportant part in this thesis. In this chapter, it first introduces the basic principle in GPS networkRTK, and then it derives interpolation mathematical formula from the basic principle ofinterpolation and lists some specific operations of network RTK positioning using interpolationmethod. Finally, it analyzes the standard deviation of double-differenced mathematical model forcarrier phase observations, the influence of roving receivers at reference stations on interpolationmodel parameters and the influence of initial locations at roving receivers on precision ofinterpolation correctness.The fifth chapter is about mathematical model of linear combination method for network RTK.This chapter first establishes a virtual observable equation of linear combination at roving receivers,based on single-differenced observations of reference stations and roving receivers. Next itdiscusses how to eliminate residual ephemeris errors, ionospheric delay and so on in that equation.Then it derives the mathematical formula based on the principle of linear combination method.Finally, it describes the relationship between linear combination and interpolation methods.The sixth chapter talks about the mathematical model of network RTK virtual reference stationmethod. It introduces the basic concept on virtual reference stations and then starting from themathematical model of interpolation and linear combination methods, it preliminarily establishesthe mathematical model of virtual reference stations. After that, it lists specific procedures of how todo network RTK positioning using virtual reference stations.The seventh chapter introduces ambiguity resolution techniques for network RTK. It states thebasic concept about the ambiguity search and the classic method of current ambiguity resolutionOTF and then introduces the method of integer ambiguity search using single epoch for networkRTK roving stations.The eighth chapter is mainly about experimenting data and analysis. In order to test thecorrectness of the mathematical model and its theory in this thesis, on the basis of practical situation,according to the simulated experimental design, setting interpolation mathematical model as anexample, using post-data processing method, it calculates GPS positioning data of 60 epochsaltogether and meanwhile it analyzes the simulated calculating results.