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.     

Real-time cycle slip detection in triple-frequency GNSS

The modernization of the global positioning system and the advent of the European project Galileo will lead to a multifrequency global navigation satellite system (GNSS). The presence of new frequencies introduces more degrees of freedom in the GNSS data combination. We define linear combinations of GNSS observations with the aim to detect and correct cycle slips in real time. In particular, the detection is based on five geometry-free linear combinations used in three cascading steps. Most of the jumps are detected in the first step using three minimum-noise combinations of phase and code observations. The remaining jumps with very small amplitude are detected in the other two steps by means of two-tailored linear combinations of phase observations. Once the epoch of the slip has been detected, its amplitude is estimated using other linear combinations of phase observations. These combinations are defined with the aim of discriminating between the possible combinations of jump amplitudes in the three carriers. The method has been tested on simulated data and 1-second triple-frequency undifferenced GPS data coming from a friendly multipath environment. Results show that the proposed method is able to detect and repair all combinations of cycle slips in the three carriers.     

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%。     

A cycle slip fixing method with GPS + GLONASS observations in real-time kinematic PPP

A key limitation of precise point positioning (PPP) is the long convergence time, which requires about 30 min under normal conditions. Frequent cycle slips or data gaps in real-time operation force repeated re-convergence. Repairing cycle slips with GPS data alone in severely blocked environments is difficult. Adding GLONASS data can supply redundant observations, but adds the difficulty of having to deal with differing wavelengths. We propose a single-difference between epoch (SDBE) method to integrate GPS and GLONASS for cycle slip fixing. The inter-system bias can be eliminated by SDBE, thus only one receiver clock parameter is needed for both systems. The inter-frequency bias of GLONASS satellites also cancels in the SDBE, so cycle slips are preserved as integers, and the LAMBDA method is adopted to search for cycle slips. Data from 7 days of 20 globally distributed IGS sites were selected to test the proposed cycle slip fixing procedure with artificial blocking of the signal; cycle slips were introduced for all un-blocked satellites at each epoch. For a 30-s sampling interval, the average success rate of fixing can be improved from 73 to 98 % by adding GLONASS. Even for a 180-s sampling interval, GPS + GLONASS can achieve a success rate of 81 %. A real-time kinematic PPP experiment was also performed, and the results show that using GPS + GLONASS can achieve continuous high-accuracy real-time PPP without re-convergence.     

Instantaneous re-initialization in real-time kinematic PPP with cycle slip fixing

The network-based real-time kinematic (RTK) positioning has been widely used for high-accuracy applications. However, the precise point positioning (PPP) technique can also achieve centimeter to decimeter kinematic positioning accuracy without restriction of inter-station distances but is not as popular as network RTK for real-time engineering applications. Typically, PPP requires a long initialization time and continuous satellite signals to maintain the high accuracy. In case of phase breaks or loss of signals, re-initialization is usually required. An approach of instantaneous cycle slips fixing using undifferenced carrier phase measurements is proposed, which leads to instantaneous re-initialization for real-time PPP. In the proposed approach, various errors such as real-time orbit and clock errors, atmosphere delay and wind-up effects are first refined and isolated from integer cycle slips. The integer values of cycle slips can then be estimated and fixed with the LAMBDA technique by applying a cascade cycle slip resolution strategy. Numerical experiments with different user dynamics are carried out to allow a comprehensive evaluation of efficiency and robustness of the cycle slip fixing algorithm. The results show that the cycle slips can be fixed correctly in all cases considered and that data gaps of up to 300?s can be connected with high confidence. As a result, instantaneous re-initialization is achieved in the real-time PPP processing.     

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.     

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。     

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。      

一种改进的基于 BDS 三频非差观测的周跳实时探测与修复模型

BDS三频观测条件下可以组合得到具有优良特性的虚拟载波观测量,有利于改善非差观测数据的周跳实时探测与修复。文中提出一种基于BDS三频非差数据的周跳实时探测与修复模型:首先,采用消电离层无几何HMW组合观测量探测和修复EWL周跳;然后,将经过修复的EWL观测量与WL组合消除几何相关项,忽略电离层延迟残差进而确定WL周跳;最后采用经过修复的WL观测量与NL组合形成无几何观测量,并通过优化载波相位组合确定电离层延迟的变化量以探测和计算NL周跳,并通过简单变换得到原始载波观测量的周跳值。通过实测BDS三频数据对模型可行性进行验证分析,结果表明,即使在30s的采样率以及电离层活动活跃条件下,该模型都可有效实时探测和修复各类周跳。     

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。     

一种GPS周跳探测与修复的组合算法

周跳是影响GPS定位精度的一个重要因素,对周跳的探测与修复一直是个重要问题。首先研究了电离层残差法、宽巷相位减窄巷伪距法两种经典方法的优缺点,提出了一种探测周跳的组合算法。根据周跳的整数特性,利用搜索整数解的思想确定周跳的大小进而修复周跳。经实测数据检验,该算法有效可行,有很强的实用性。     

The Bayesian detection of discontinuities in a polynomial regression and its application to the cycle-slip problem

This paper deals with the problem of detecting and correcting cycle-slips in Global Navigation Satellite System (GNSS) phase data by exploiting the Bayesian theory. The method is here applied to undifferenced observations, because repairing cycle-slips already at this stage could be a useful pre-processing tool, especially for a network of permanent GNSS stations. If a dual frequency receiver is available, the cycle-slips can be easily detected by combining two phase observations or phase and range observations from a single satellite to a single receiver. These combinations, expressed in a distance unit form, are completely free from the geometry and depend only on the ionospheric effect, on the electronic biases and on the initial integer ambiguities; since these terms are expected to be smooth in time, at least in a short period, a cycle-slip in one or both the two carriers can be modelled as a discontinuity in a polynomial regression. The proposed method consists in applying the Bayesian theory to compute the marginal posterior distribution of the discontinuity epoch and to detect it as a maximum a posteriori (MAP) in a very accurate way. Concerning the cycle-slip correction, a couple of simultaneous integer slips in the two carriers is chosen by maximazing the conditional posterior distribution of the discontinuity amplitude given the detected epoch. Numerical experiments on simulated and real data show that the discontinuities with an amplitude 2 or 3 times larger than the noise standard deviation are successfully identified. This means that the Bayesian approach is able to detect and correct cycle-slips using undifferenced GNSS observations even if the slip occurs by one cycle. A comparison with the scientific software BERNESE 5.0 confirms the good performance of the proposed method, especially when data sampled at high frequency (e.g. every 1 s or every 5 s) are available.     

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。     

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.     

GPS周跳探测及修复的小波变换法

利用小波分析方法对常用的GPS周跳检测量进行了周跳探测，获得了小波方法所能探测到的最小周跳值，并与高次差法进行了时比，提出了利用小波变换探测出周跳后如何直接进行周跳修复的方法。计算结果表明，该方法是可行的。     

基于几何模型的惯性辅助PPP周跳修复与快速重新收敛

在复杂观测环境下,GNSS信号容易发生周跳和失锁现象,导致精密单点定位技术（PPP）模糊度重新初始化,影响定位精度及可靠性。本文基于PPP／SINS紧组合,提出了利用短时间内惯导递推的高精度位置信息辅助PPP周跳修复的几何模型。该模型采用原始观测值建立历元间差分方程,将周跳作为参数进行估计,而惯导提供的高精度位置作为带权的虚拟观测值参与平差解算,在固定周跳整数值后修复相位观测值,从而保持高精度的连续定位。以车载和机载两组数据分析了该方法的有效性,结果表明,引入惯性辅助能够显著加快PPP定位的重新收敛,实现周跳的准确修复。      

GPS三频非差观测数据周跳的自动探测与改正研究

在GPS三频非差观测数据的处理中,由于伪距噪声的影响,利用原始的伪距和载波相位观测数据估计的模糊度误差比较大,不能用于探测和改正周跳。对原始观测数据进行平滑或适当的组合处理,可降低观测噪声的影响。因此,本文选择合适的经过平滑或组合处理后的观测数据作为探测周跳的检验量,探测并改正单个频点上的周跳。在分析了一般周跳的特点并在研究双频周跳自动探测与改正方法基础上,提出了选取检验量的四条基本原则。最后,依此原则选取了三个观测值组合作为周跳检验量,利用该组检验量实现三频非差观测数据周跳的自动探测与改正。     

GPS／GLONASS组合定位中模糊度的处理

在对GPS／GLONASS组合定位的周跳探测和修复方法进行深入研究的基础上，论述了适合于两种数据联合解算的GPS／GLONASS模糊度迭代处理方法及相应的基于FARA方法的整周模糊度固定方法。在现有BERNESE Ver4.0GSP数据处理软件的基础上，增加及改进了其中的若干模块，从而研制出组合定位系统高精度数据处理软件，并进行了试验计算。结果表明，所开发的组合定位系统数据处理软件内、外符合精度均达到mm级，证明了这种高精度相对定位理论、方法、软件的正确性和可行性。     

GPS周跳探测的两种方法研究

在GPS定位中,有时需要测站的高精度坐标,为此模糊度的解算和周跳的探测与修复成为关键问题,在周跳探测中,特别是小周跳的探测成为当今的热点问题。本文中利用接收机的双频观测值进行周跳的探测研究,通过实例分析,证明这两种方法可行。