Research On Relative Positioning Algorithm Based On Differential Inter System Bias

The relative positioning technique uses the pseudo range and carrier phase observations of two receivers and uses the broadcast ephemeris or precise ephemeris to obtain high-precision relative coordinates.According to the number of base stations and working distance,relative positioning technology can be divided into short baseline positioning technology,medium and long baseline positioning technology and network RTK technology;Relative positioning technology can be divided into tightly-combined relative positioning technology and loose combination relative positioning technology according to differences in observation value difference methods.Loose combination relative positioning is a traditional relative positioning method which best satellite is selected in the-intra-system,and its differential method is intra-system.The tightly combined relative positioning selects only one best satellite,and the differential method includes intra-system differential and inter-system differential.Compared with loosely combined positioning,selecting a tightly combined relative positioning technique under a complex environment is expected to increase its ambiguity fixing rate and positioning accuracy.In this paper,based on the derivation of the mathematic model of the tightly combined relative positioning algorithm,a relative short-baseline and medium-long baseline relative positioning algorithm based on GPS/BDS/GALILEO three systems is implemented.The main content of this article includes:(1)It elaborates the development status of tightly combined relative positioning technology at home and abroad,introduces the coordinate system and time system thatwill be used in GNSS data processing,and explains in detail the influence of different types of GNSS errors on relative positioning data processing,and gives some error correction methods in relative positioning data processing.(2)The stochastic model and function model of tight combination positioning technology positioning technology and loose combination positioning technology are deduced in detail,and the treatment methods of the troposphere and ionosphere in the middle and long baselines are given.Through formula derivation,it proves that the tight combination algorithm with the same frequency of observations is a special case of the tight combination algorithm with different frequency of observations.The tightly combined relative positioning algorithm with the same observation frequency and the tightly combined relative positioning algorithm with different frequency of observations are unified.(3)The pseudo range DISB is related to the pseudo range hardware delay between the receivers,the phase DISB of the same frequency is related to the phase hardware delay between the receivers,and the phase DISB of the different frequencies is related to the phase hardware delay and initial phase deviation between the receivers.The effects of receiver type and differential observation frequency on the stability of DISB between receivers are analyzed in detail.The experimental results show that when the receiver type and differential frequency at the two ends of the baseline are the same,the phase of the DISB between the receivers is zero;The receivers at the two ends of the baseline are of the same type,but when the differential frequencies are not the same,the phase DISB between the receivers is not zero,but the phase DISB is very stable;when the receiver type and differential frequency at both ends of the receiver are not the same,the receiver The size of the phase DISB is not zero,and the stability of the phase DISB changes slightly with time.The DISB estimation method between GPS,BDS and GALILEO satellite systems is given based on whether the receiver type and differential frequency are the same at both ends of the baseline.(4)The tight combination algorithm based on the estimated DISB implements the GPS+BDS dual system and the GPS+BDS+GALILEO triple system short-baseline and mid-long baseline localization algorithms,and compares it with the loose combination relative positioning algorithm.The measured data shows that:when the satellite cut-off height When the angle is low,that is,when the number of satellites is sufficient,the positioning performance of the tightly combined positioning and the loose combination is equivalent;in the case of the high elevation angle,the tightly combined positioning can increase the success rate of the fixed ambiguity through the short baseline.Under the 40-degree cut-off elevation angle verification,it was found that the fixed success ratio of the ambiguities of the tightly combined positioning is about 10%higher than the fixed success rate of the ambiguities of the loose combined positioning.By comparing the short-baseline and long-baseline localization results of tightly combined and loosely combined,it is found that the accuracy of the fixed solution with tightly combined and loosely combined positioning is equivalent;compared with the dual-system positioning,the three-system positioning can increase the success rate of fixed ambiguity.At the 40-degree cut-off elevation angle,the success ratio of the three-system short baseline loose composite ambiguity and that of the double-system loose composite ambiguity increase by about 9%.