A double-differenced cycle slip detection and repair method for GNSS CORS network

The difficulty to detect and repair cycle slip of carrier phase measurements is a key limit for continuously high accuracy of GNSS positioning and navigation services. We propose an automated cycle slip detection and repair method for data preprocessing of a CORS network. The method jointly uses double-differenced (DD) geometry-free (GF) combination and ionospheric-free observation corrected for the computed geometrical distance (IF-OMC) to estimate the cycle slips in dual-frequency observations. The DD GF combination, which is only affected by the ionospheric residual, can be used to detect cycle slips with high reliability except for special pairs such as (77, 60) on GPS L1/L2 frequencies. The detection principle of the IF-OMC observable is such that there is a large discontinuity related to the previous epoch when cycle slips occur at the present epoch. The disadvantages of these two combinations can be overcome employing the proposed detection method. The cycle slip pair (77, 60) has no effect on the GF combination, while a change of 14.65 m is derived from GPS L1/L2 observations using the IF-OMC algorithm. Using pre-determined station coordinates as precise values, we found that the accuracy of the DD IF-OMC combination was 18 mm for a 200-km CORS baseline. Therefore, cycle slips in dual-frequency observations can be correctly and uniquely determined using DD GF and IF-OMC equations. The proposed method was verified by adding simulated cycle slips in observations collected from the CORS network under a quiet ionosphere and shown to be effective. Moreover, the method was assessed with observations made during intense ionospheric activity, which generated extensive cycle slips. The results show that the algorithm can detect and repair all cycle slips apart from two exceptions relating to long data gaps.     

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.     

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。     

基于数据质量分析的TECR周跳处理算法

针对电离层活跃期或磁暴发生时,现有周跳探测算法未能正确探测并修复周跳的问题,提出了基于数据质量分析的电离层总电子含量变化率（以下简称电离层速率,TECR）拟合残差算法。通过对电离层拟合残差进行数据质量分析,可自适应确定最优拟合历元数,利用此历元数拟合得到的TECR拟合值可有效削弱电离层延迟影响。为保证周跳修复的准确性,采用搜索再判定与TECR补充检测方法对周跳修复值进行验证与确认。通过高电离层延迟条件下的实测数据对本文算法进行验证分析,实验结果表明该方法能够消除电离层延迟影响,实现电离层活跃期时的周跳探测与修复。     

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。     

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。     

一种历元间差分单站单频周跳探测与修复方法

提出了一种基于历元间单差观测值的单站单频周跳探测与修复方法。通过假定前一历元为基准站,当前历元为流动站,采用相对定位处理模式获取当前历元观测值的验后单位权中误差,并基于抗差最小二乘获取每颗卫星的观测值残差,对单站单频数据进行周跳探测与修复。通过对实测数据的验证分析表明,按照本文方法可以100%探测周跳发生的历元。并且,当至少4颗卫星未发生周跳时,如发生异常卫星数小于可视卫星数的30%,则在95%以上的情况下可以有效确定异常卫星;当异常卫星过多时,本文方法确定异常卫星的成功率会有所下降。但是,对于探测出发生周跳的异常卫星,本文方法均可100%对其周跳进行修复。     

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。     

利用历元间差分观测值进行参考站周跳探测与修复

载波观测量是高精度卫星导航定位及其相关应用的基础，其整周模糊度的正确解算是实现厘米级导航定位和纳米级授时的关键。周跳探测与修复直接影响整周模糊度解算的性能，尤其对于连续运行参考站网等高精度位置服务的核心基础设施，保证连续可靠的模糊度解算是实现高精度位置服务的重要保障。参考站接收机具有观测值精度高、静止等特点，且采样频率较高（一般为1 Hz），在较短的时间间隔内，电离层延迟、对流层延迟、硬件延迟等误差相关性较强。基于以上特点，本文将历元间差分法应用于参考站周跳探测与修复，结合参考站静止的特性，提出了一种适用于参考站的周跳探测与修复的方法。该方法无需进行观测值组合，同时避免了伪距噪声的影响，探测精度高，且单站各个频率可以单独探测，在周跳修复的过程中，考虑非整周粗差并进行剔除。试验表明，该方法可以准确地探测和修复1周的整周周跳，可以探测小数偏差大于0.1周的非整周粗差。     

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。      

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/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%。     

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。     

BDS/GPS单历元短基线动对动定位性能分析

针对在城市峡谷环境下观测卫星较少、观测质量差和周跳频繁,导致动对动定位过程中双差模糊度不连续的问题,提出了一种GPS/BDS组合系统的单历元模糊度解算方法。通过GPS/BDS组合定位提高了卫星的可用数量,利用单历元模糊度固定减弱了周跳频繁带来的影响。实验采用GPS/BDS组合的7组数据,分析了在不同高度角下动对动定位单历元解的模糊度固定率、解算失败率、粗差率和定位精度。结果表明,GPS/BDS组合动对动定位单历元模糊度解算方法,在高遮挡的城市峡谷环境仍然可以取得较好的定位结果。     

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。     

A new triple-frequency cycle slip detecting algorithm validated with BDS data

Triple-frequency global navigation satellite systems allow the introduction of additional linear observation combinations. We define two geometry-free phase combinations and one geometry-free pseudorange minus phase linear combination to detect and correct cycle slip in real time. At first, the optimal BDS (BeiDou System) triple-frequency geometry-free phase combinations are selected for cycle slip detection. Then, a detailed analysis of the cycle slip detection is performed by examining whether some special cycle slip groups cannot be discovered by the selected combinations. Since there still remain some cycle slip groups undetectable by the two geometry-free phase combinations, we add a pseudorange minus phase linear combination which is linearly independent with these two phase combinations, to be sure that all the cycle slips can be detected. After that, an effective decorrelation search based on LAMBDA and least squares minimum principle is applied to calculate and determine the cycle slips. The method has been tested on triple-frequency undifferenced BDS data coming from a benign observation environment. Results show that the proposed method is able to detect and repair all the small cycle slips in the three carriers.     

Benefits of the third frequency signal on cycle slip correction

Cycle slip detection and correction are important issues when carrier phase observations are used in high-precision GNSS data processing and have, therefore, been intensively investigated. Along with the GNSS modernization, the cycle slip correction (CSC) problem has been raised to deal with more signals from multi-frequencies. We extend the geometry-based approach by integrating time-differenced pseudorange and carrier phase observations to estimate the integer number of triple-frequency cycle slips together with the receiver clock offset, ionospheric delay variations and receiver displacements. The Least-squares AMBiguity Decorrelation Adjustment method can be employed. The benefit of the third frequency observation on the cycle slip estimate is first investigated with simulation tests. The results show that adding the third frequency observation can significantly improve the model strength and that a reliable triple-frequency CSC with a theoretical success rate of higher than 99.9 % can still be achieved, even under the condition that the range or ionosphere delay variation is poorly defined. The performance of triple-frequency CSC is validated with real triple-frequency BDS data since all BDS satellites in orbit are transmitting triple-frequency signals. The results show that the fixing rate of CSC can reach 99.1 % in static precise point positioning (PPP) and 98.8 % in the kinematic case. PPP solutions with cycle slip-uncorrected and cycle slip-corrected data sets are compared to validate the correctness of triple-frequency CSC. The standard deviations of the PPP solution in east, north and vertical component, respectively, can be improved by 31.1, 30.7 and 37.6 % for static, and by 42.0, 53.8 and 39.7 % for kinematic after cycle slips are corrected. The performance of dual- and triple-frequency CSC is also compared. Results show that the performance of dual-frequency CSC is slightly worse than that of triple-frequency CSC. These results demonstrate that the performance of CSC can be significantly improved with triple-frequency observations.     

星载双频GPS二次周跳探测方法研究

在利用W-M宽巷组合进行周跳初步探测的基础上,加入了新方法进行二次周跳探测。该方法通过利用来自同颗GPS卫星的无电离层影响L3组合相位观测值在相邻历元间的变化量与dm级精度的先验轨道坐标,计算得出星载GPS接收机历元间的钟差变化值。对于存在周跳的载波相位观测值,其计算结果会与同历元其他无周跳观测值解算的钟差变化量存在较大差异。实验结果表明,二次探测可以发现新的周跳并对初步探测结果进行检核。     

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.     

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.