A new automated cycle slip detection and repair method for a single dual-frequency GPS receiver

This paper develops a new automated cycle slip detection and repair method that is based on only one single dual-frequency GPS receiver. This method jointly uses the ionospheric total electron contents (TEC) rate (TECR) and Melbourne–Wübbena wide lane (MWWL) linear combination to uniquely determine the cycle slip on both L1 and L2 frequencies. The cycle slips are inferred from the information of ionospheric physical TECR and MWWL ambiguity at the current epoch and that at the previous epoch. The principle of this method is that when there are cycle slips, the MWWL ambiguity will change and the ionospheric TECR will usually be significantly amplified, the part of artificial TECR (caused by cycle slips) being significantly larger than the normal physical TECR. The TECR is calculated based on the dual-frequency carrier phase measurements, and it is highly accurate. We calculate the ionospheric change information (including TECR and TEC acceleration) using the previous epochs (30 epochs in this study) and use the previous data to predict the TECR for the epoch needing cycle slip detection. If the discrepancy is larger than our defined threshold 0.15 TECU/s, cycle slips are regarded to exist at that epoch. The key rational of method is that during a short period (1.0 s in this study) the TECR of physical ionospheric phenomenon will not exceed the threshold. This new algorithm is tested with eight different datasets (including one spaceborne GPS dataset), and the results show that the method can detect and correctly repair almost any cycle slips even under very high level of ionospheric activities (with an average Kp index 7.6 on 31 March 2001). The only exception of a few detected but incorrectly repaired cycle slip is due to a sudden increased pseudorange error on a single satellite (PRN7) under very active ionosphere on 31 March 2001. This method requires dual-frequency carrier phase and pseudorange data from only one single GPS receiver. The other requirement is that the GPS data rate ideally is 1 Hz or higher in order to detect small cycle slips. It is suitable for many applications where one single receiver is used, e.g. real-time kinematic rover station and precise point positioning. An important feature of this method is that it performs cycle slip detection and repair on a satellite-by-satellite basis; thus, the cycle slip detection and repair for each satellite are completely independent and not affected by the data of other satellites.     

GPS双频非差周跳探测修复SET法

分析了TurboEdit方法中MW组合和GF组合的缺陷,提出了GPS双频非差周跳探测修复SET（satellite elevation TurboEdit）法。设计了自适应滑动窗口模型对MW组合进行改进,避免了在低高度角时引入多径误差和噪声误差对后续处理精度的影响,增强了对小周跳的探测与修复能力。对GF（geometry-free）组合中引入的伪距误差采用历元间求差法进行替换,同时在卫星低高度角时,对其探测阈值引入高度角加权系数,有效剔除虚假周跳,提高周跳探测成功率与可靠性。在探测出周跳后,联合两种方法组合进行周跳修复。实验结果表明,SET法能够有效地抑制低高度角时的多径效应和观测噪声,降低周跳误探率,并对周跳进行有效修复。     

Cycle slip detection and repair for undifferenced GPS observations under high ionospheric activity

We develop a new approach for cycle slip detection and repair under high ionospheric activity using undifferenced dual-frequency GPS carrier phase observations. A forward and backward moving window averaging (FBMWA) algorithm and a second-order, time-difference phase ionospheric residual (STPIR) algorithm are integrated to jointly detect and repair cycle slips. The FBMWA algorithm is proposed to detect cycle slips from the widelane ambiguity of Melbourne–Wübbena linear combination observable. The FBMWA algorithm has the advantage of reducing the noise level of widelane ambiguities, even if the GPS data are observed under rapid ionospheric variations. Thus, the detection of slips of one cycle becomes possible. The STPIR algorithm can better remove the trend component of ionospheric variations compared to the normally used first-order, time-difference phase ionospheric residual method. The combination of STPIR and FBMWA algorithms can uniquely determine the cycle slips at both GPS L ₁ and L ₂ frequencies. The proposed approach has been tested using data collected under different levels of ionospheric activities with simulated cycle slips. The results indicate that this approach is effective even under active ionospheric conditions.     

一种顾及电离层约束的非差周跳的实时探测与修复方法

提出了一种顾及电离层约束的非差周跳实时探测与修复方法。通过构造3个线性无关的组合观测量,按逐级模糊度确定的思路,分别对超宽巷、宽巷和窄巷进行探测与修复;然后联合三步的探测结果,将周跳恢复到原始载波值上。在宽巷组合上进行了改进,将宽巷波长放大了5.34倍(GPS为3.4倍),由于窄巷波长较短需考虑电离层的影响,对不敏感周跳组合引入电离层残差法辅助窄巷的探测与修复。实验结果表明,该方法能够有效地进行周跳的实时探测和修复。     

CORS基准站周跳探测与修复方法研究

在高精度GNSS测量中,周跳的存在直接影响到整周模糊度的解算及最终定位精度。针对目前各省市连续运行基准站网多系统观测数据的获取导致周跳探测工作量增加,该文基于甘肃省卫星定位连续运行基准站网(GSCORS)双频观测值提出了一种满足普遍条件的多系统周跳探测方法。采用相位减伪距结合电离层残差法分别对GPS和BDS原始观测值进行周跳探测与修复,通过对相应载波的模拟周跳探测发现,BDS较大的卫星钟差和伪距噪声影响了数据质量,其周跳检测量时间序列波动大于GPS,对7周以上周跳探测的精度较GPS会有1周的偏差,但电离层残差法能对BDS相位减伪距法探测残留的1周小周跳进行二次探测并修复。实验最终证实该方法能够有效探测并且正确分离GPS和BDS每个频率1周以上的周跳。     

Cycle slip detection and repair of undifferenced single-frequency GPS carrier phase observations

Cycle slip detection and repair is an important issue in the GPS data processing. Different methods have been developed to detect and repair cycle slips on undifferenced , single- or double-differenced observations. The issue is still crucial for high-precision GPS positioning, especially for the undifferenced GPS observations. A method is proposed to fix cycle slips based on the generalized likelihood ratio (GLR) test. The method has a good performance on cycle slip fixing of undifferenced carrier phase observations on individual frequencies, either on L1 or on L2, without making a linear combination among the observables. The functional model is a piecewise cubic curve fitted to a number of consecutive data using the least squares cubic spline approximation (LS-CSA). For fixing the cycle slips, an integer estimation technique is employed to determine the integer values from the float solution. The performance of the proposed method is then compared with the existing two methods using simulated data. The results on a few GPS data sets with sampling rate of 1 Hz or higher confirm that this method can detect and correct all simulated cycle slips regardless of the size of the cycle slip or the satellite elevation angle. The efficacy of the method is then investigated on the GPS data sets with lower sampling rates of 5, 10, and 30 s. The results indicate that the proposed method always performs the best for the data sets considered. This is thus an appropriate method for cycle slip detection and repair of single-frequency GPS observations.     

惯导辅助的无电离层与宽巷组合周跳探测与修复方法

由于卫星信号被遮挡、低信噪比或接收机运动等原因,载波相位观测值较正常值会发生周跳。为解决这一问题,基于精密单点定位与惯导组合系统,提出了一种有效的惯导辅助周跳探测与修复方法。该方法基于无电离层（ionospheric free,IF）组合与宽巷（wide lane,WL）组合,利用惯导短时高精度信息代替伪距消除站星几何距离,结合历元间差、星间差等建立惯导辅助的IF组合模型和惯导辅助的WL组合模型。惯导辅助的IF组合模型不受电离层延迟影响,但无法探测特殊比例周跳,惯导辅助的WL组合模型波长较长,却无法探测双频等周周跳,两者的综合使用实现了优势互补。实验结果表明,该方法不仅能有效探测出各种大、小、双频等周和特殊比例周跳,而且在一定卫星信号中断时间内能实现周跳瞬时校正。     

GPS/INS紧组合的INS辅助周跳探测与修复

建立了GPS/INS紧组合定位模型,改正惯性器件误差及电离层折射误差,对不同组合观测量的误差影响进行了分析,构造不同观测值组合,提出了基于惯性信息辅助的GPS周跳自适应探测方法,分析了INS定位误差对周跳探测的影响,给出了周跳探测误报率及修复成功率评价指标,提出了一种周跳检测阈值自适应确定方法。利用实测组合导航试验数据验证本文的算法,文中模拟了不同的单历元多周跳及信号失锁条件,结果表明,在GPS信号完全失锁20 s内,该方法能准确检测和修复所有周跳,中断时间的延长降低了周跳修复的成功率;GPS信号部分失锁时,在模拟的90 s中断时段内仍能修复所有周跳;模拟了170历元的5 s间隔密集周跳,周跳探测成功率为100%,正确修复率为99.41%。     

北斗三频非差观测值的电离层周跳探测与修复

针对历元间隔较大或电离层延迟较大的情况,采用两个无几何相位组合与一个最优无几何无电离层组合形成3个线性无关的探测量,将历元间高次差法引用到无几何相位组合探测量中,通过选取合适的探测阈值,使无几何相位组合能够正确探测到较大电离层影响情况下的不敏感周跳。此外,文中采用了一种特殊的无几何无电离组合观测量进行辅助修复,通过两次取整保证了周跳修复的准确性,避免了传统三频周处理中的搜索算法造成错误修复的问题,试验表明,文中算法可以正确探测与修复较大电离层影响情况下不同北斗卫星星座类型的所有小周跳组合以及不敏感周跳组合。     

基于抗差Chebyshev多项式的相位伪距周跳探测与修复算法

相位伪距组合(1,-1)受多路径变化和电离层延迟的影响,周跳探测精度为2周,严重影响了传统相位伪距法的周跳探测性能。针对这一问题,利用基于抗差估计的Chebyshev多项式对各备选周跳的观测值进行拟合,依据残差和最小的原则,准确判别出原始相位的周跳值。实例验证该方法实用性强,可靠性高,相比传统相位伪距法具有更好的周跳探测与修复能力。     

GPS三频无几何相位组合周跳探测与修复

随着GPS现代化的实施和L5频率的开设,GPS进入了三频时代。相对于双频观测数据三频观测值线性组合可以形成更多长波长、弱电离层、低噪声的组合。本文分析了GPS三频无几何相位组合的特性,利用两个GPS三频无几何相位组合和一个三频伪距载波组合组成观测矩阵探测周跳,并采用搜索方法确保周跳修复的正确。最后利用模拟的L5观测数据进行验证,结果表明该算法可以有效地探测并修复周跳。     

GPS现代化后电离层折射误差高阶项的三频改正方法

研究了电离层对GPS观测信号的主要影响及电离层折射误差模型,总结了电离层双频改正模型。针对GPS现代化中增加的第三频率,系统推导了三个频率的电离层改正模型及相位观测值无电离层组合(LC组合)模型。该模型将电离层折射误差模型改正至二阶项,可进一步提高GPS定位精度,同时,为GPS定位中其他误差的改正及分离、周跳的探测等提供了有力的技术手段。     

多普勒积分辅助的动态单频周跳探测

相位伪距组合法常应用于动态单频周跳探测,但其探测周跳的效果受伪距噪声的影响较大。因此有必要结合其他的观测值,以降低伪距噪声的影响,从而提高单频周跳探测能力。提出了一种多普勒积分辅助的动态单频周跳探测方法,先采用多普勒观测值平滑伪距观测值,降低伪距的噪声,再进行历元间差分,显著提高了动态单频周跳探测的能力。实验分别采用不同采样率、高度角变化、连续周跳和含粗差的实时动态实测数据,分别在不同历元加入1周、3周、10周的模拟周跳,在相邻历元分别加入3周、4周和5周的连续周跳。结果表明,相较于相位伪距组合法与基于多项式拟合法的相位伪距组合法,该方法可以实时探测出所有的模拟周跳。多普勒积分辅助的动态单品周跳探测方法能够显著提升单频观测值的周跳探测能力。     

利用三频组合观测值的GPS周跳探测与修复

本文分析了GPS三频组合观测值在波长、电离层误差和偶然误差等方面的特性,并定义了衡量其特性的3种指标;结合传统的伪距/相位组合法,探讨了三频组合观测值探测与修复周跳的原理和方法。利用模拟的L5观测数据,进行了多种情况下周跳的探测与修复。结果表明:该方法能在单历元间准确探测出各个频率上发生的大、小不等的周跳。相对于原始观测值,长波长的三频组合观测值可以更有效地探测与修复周跳。     

Analysis of geometry-free residuals in case of traveling ionosphere disturbances and their impact cycle slip detection

GPS Solutions - We discuss the impact of a traveling ionospheric disturbance (TID) on cycle slip detection for the geometry-free (GF) combination. Based on the GF combination algorithm, we deduce...     

三种常用周跳探测与修复方法的性能分析

针对全球卫星导航系统（GNSS）数据处理中周跳探测与修复方法的合理选择问题,本文对三种常见的周跳探测与修复方法的性能进了评价分析.给出一种基于数理统计理论的周跳探测结果可靠性评价新方法,利用该新方法评价了多项式拟合法和TurboEdit法对同一组双频实测数据进行周跳探测所得结果的可靠性,以及多项式拟合法和三频无几何组合法对同一组三频实测数据进行周跳探测所得结果的可靠性.综合两组评价结果可知,对于双频实测数据而言,TurboEdit法的探测效果优于多项式拟合法；对三频实测数据而言,三频无几何组合法的探测效果优于多项式拟合法；但多项式拟合法对双频、三频观测数据均可进行周跳探测与修复,因此适用性更广.      

利用改进的TurboEdit算法与Chebyshev多项式探测与修复周跳

根据利用TurboEdit方法对GPS观测数据进行周跳探测的特点,设计了固定弧段长度的滑动窗口拟合模型,对其中的Geometry-Free组合法进行改进;在探测出周跳后,利用最小二乘Chebyshev多项式拟合来修复周跳。实验结果表明,改进后的TurboEdit算法可以探测出等周的1周小周跳、等周的大周跳和连续的小周跳、大周跳,同时,最小二乘Chebyshev多项式拟合可以精确修复以上周跳对。     

基于多普勒辅助的电离层残差探测与修复周跳改进方法

针对典型周跳探测与修复方法中的电离层残差法当同一历元多个频点发生周跳时,无法准确探测及修复周跳的问题,提出了一种用多普勒辅助电离层残差法的周跳探测与修复的改进方法。基于实测及仿真数据,证明了该方法能够有效解决电离层残差法存在的上述问题,即使某一历元多个频点同时发生周跳,也可以准确探测周跳发生的位置、频点及相应数值,精度达到1周,有效提高了电离层残差法探测与修复周跳的准确性与可靠性。     

一种改进的星载GPS周跳探测与修复方法

周跳探测与修复是星载GPS数据预处理的重要内容。首先使用SWARM卫星实测数据对TurboEdit算法的有效性进行了分析,针对算法在观测噪声较大情况下无法有效探测小周跳的问题,提出了一种改进算法。该算法利用载波相位观测值对伪距组合观测值进行平滑,降低了观测噪声对宽巷模糊度的影响,提高了周跳探测能力。实验结果表明,改进算法能够有效提高小周跳的探测能力。      

实时修复双频原始载波相位观测值周跳的虚拟值探测法

利用各频率观测值间物理上的相关性,采用数学变换得到一个含有双频原始载波观测信息的虚拟观测值,与双频数据按长波长特性进行多频组合来放大周跳。对探测出的周跳候选值利用Melbourne-Wubbena组合及多项式拟合作为两个判别条件来进行甄选,达到了实时修复双频原始载波相位观测值周跳的目的。