Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS

Considering the contribution of the hardware biases to the estimated clock errors, an improved method for estimating the satellite inter-frequency clock bias (IFCB) is presented, i.e., the difference in the satellite clock error as computed from ionospheric-free pseudorange and carrier phase observations using L1/L2 and P1/P2 versus L1/L5 and P1/P5. The IFCB is composed of a constant and a variable part. The constant part is the inter-frequency hardware bias (IFHB). It contains the satellite and receiver hardware delays and can be expressed as a function of the DCBs [DCB (P1 ? P2) and DCB (P1 ? P5)]. When a reference satellite is selected, the satellite IFHB can be computed but is biased by a reference satellite IFHB. This bias will not affect the utilization of IFCB in positioning since it can be absorbed by the receiver clock error. Triple-frequency observations of 30 IGS stations between June 1, 2013, and May 31, 2014, were processed to show the variations of the IFHB. The IFHB values show a long-term variation with time. When a linear and a fourth-order harmonic function are used to model the estimated IFCB, which contains contributions of the hardware delays and clock errors, the results show that 89 % of the IFCB can be corrected given the current five triple-frequency GPS satellites with the averaged fitting RMS of 1.35 cm. Five days of data are processed to test the estimated satellite clock errors using the strategy presented. The residuals of P1/P5 and L1/L5 have a STD of <0.27 m and 0.97 cm, respectively. In addition, most predicted satellite IFCBs reach an accuracy of centimeter level and its mean accuracy of 5 days is better than 7 cm.     

Impact of GPS differential code bias in dual- and triple-frequency positioning and satellite clock estimation

The features and differences of various GPS differential code bias (DCB)s are discussed. The application of these biases in dual- and triple-frequency satellite clock estimation is introduced based on this discussion. A method for estimating the satellite clock error from triple-frequency uncombined observations is presented to meet the need of the triple-frequency uncombined precise point positioning (PPP). In order to evaluate the estimated satellite clock error, the performance of these biases in dual- and triple-frequency positioning is studied. Analysis of the inter-frequency clock bias (IFCB), which is a result of constant and time-varying frequency-dependent hardware delays, in ionospheric-free code-based (P1/P5) single point positioning indicates that its influence on the up direction is more pronounced than on the north and east directions. When the IFCB is corrected, the mean improvements are about 29, 35 and 52% for north, east and up directions, respectively. Considering the contribution of code observations to PPP convergence time, the performance of DCB(P1–P2), DCB(P1–P5) and IFCB in GPS triple-frequency PPP convergence is investigated. The results indicate that the DCB correction can accelerate PPP convergence by means of improving the accuracy of the code observation. The performance of these biases in positioning further verifies the correctness of the estimated dual- and triple-frequency satellite clock error.     

考虑随机模型精化的精密GPS动态定位新方法

GPS动态定位要求建立函数模型和随机模型。函数模型描述的是观测值和待估参数之间的物理和几何关系，随机模型描述了GPS观测值的统计特征，并通过观测值的方差协方差给定了每个观测值对最后的定位结果的贡献。正确给定函数模型和随机模型对于GPS定位结果的估计和观测值的粗差探测均至关重要。由于有各种误差存在于伪距和载波相位观测值中，一般GPS动态定位模型均采用双差观测值来构建函数模型。有时候，仔细地使用单差观测值，较之双差观测值有更多的优点，给出了选用单差观测值的理由。但是单差观测值给函数模型带来了接收机钟差，如果直接使用单差观测方程，设计矩阵是奇异的。为了解决这个问题，将伪距观测值中接收机钟差项和接收机延迟项合并为一个新的未知参数。至于载波相位观测值，首先选定一个参考卫星，然后在观测方程的右端同时增加一正一负的参考卫星单差整周模糊度，将正项与接收机钟差项和接收机延迟项合并为一个新的未知参数，将负项和原观测方程中的单差整周模糊度项合并为双差整周模糊度，而参考卫星观测方程的模糊度项则为零，这样无须组建双差观测值，软件实现较容易，也可以直接使用LAMBDA法求整周模糊度，最终也解决了观测方程奇异的问题。准确理解观测值的统计特征是建立GPS随机模型的基础，长期以来GPS商业软件均采用简化模型。关于GPS随机模型的研究远没有函数模型那样受到广泛关注，静态GPS定位可以采用方差协方差分量估计等严密的方法，而动态定位无法承担方差协方差分量估计的计算负担。GPS观测值的信噪比(SNR)是GPS接收机观测过程中的副产品，影响SNR值的因素，如大气层、多路径、接收机内部电路等，也正好是GPS观测值的误差源，因此GPS观测值的方差与SNR存在一定的对应关系。利用这个对应关系来精化GPS随机模型。为了验证本文采用的函数模型的正确性和随机模型的有效性，我们对1999年的一次实测数据(包括零基线和短基线)进行了试算。与零基线的真值和GPSurvey 2．35处理的短基线静态结果比较，表明使用的函数模型是正确的。简化随机模型和精化随机模型处理的结果比较说明精化模型提高了基线处理的精度，同时说明了研究GPS随机模型精化的必要性。     

Improving vertical GPS precision with a GPS-over-fiber architecture and real-time relative delay calibration

A limitation of GPS positioning is that the vertical component is generally two to three times less precise than the horizontal components. In a previous work by R. Santerre of Laval University and G. Beutler of University of Bern, it was shown in simulations that it is possible to improve the GPS vertical positioning precision by using a multi-antenna GPS receiver and a precise calibration technique of the relative hardware delay between the antennas and the receiver. However, no actual implementation of the system was done to prove the concept until now. A new multi-antenna, GPS-over-fiber architecture with real-time delay monitoring, designed and implemented to improve the vertical precision is presented. The improvement in vertical precision arises from the elimination of the relative receiver clock error in single difference, between antennas, and the precision real-time calibration of the relative hardware delay. Experiments were conducted with a zero baseline and a short baseline configuration. The results show, as expected by the theory and the simulations, a two to three times improvement in the precision of the vertical component such that it reached the same level of performance as the horizontal components. These promising results will enable the use of this type of configuration in several applications where the same precision in all 3D components is essential and could not be achieved before with standard GPS positioning techniques.     

An approach to GLONASS ambiguity resolution

 When processing global navigation satellite system (GLONASS) carrier phases, the standard double-differencing (DD) procedure cannot cancel receiver clock terms in the DD phase measurement equations due to the multiple frequencies of the carrier phases. Consequently, a receiver clock parameter has to be set up in the measurement equations in addition to baseline components and DD ambiguities. The resulting normal matrix unfortunately becomes singular. Methods to deal with this problem have been proposed in the literature. However, these methods rely on the use of pseudo-ranges. As pseudo-ranges are contaminated by multi-path and hardware delays, biases in these pseudo-ranges are significant, which may result in unreliable ambiguity resolution. A new approach is addressed that is not sensitive to the biases in the pseudo-ranges. The proposed approach includes such steps as converting the carrier phases to their distances to cancel the receiver clock errors, and searching for the most likely single-differenced (SD) ambiguity. Based on the results from the theoretical investigation, a practical procedure for GLONASS ambiguity resolution is presented. The initial experimental results demonstrate that the proposed approach is useable in cases of GLONASS and combined global positioning system (GPS) and GLONASS positioning. Received: 19 August 1998 / Accepted: 12 November 1999     

估计接收机差分码偏差的GPS/BDS非组合精密单点定位模型

在传统多系统非差非组合精密单点定位（precise point positioning,PPP）模型中,电离层延迟会吸收部分接收机码硬件延迟,其估计值可能为负数。提出了一种估计接收机差分码偏差（differential code bias,DCB）参数的GPS（Global Positioning System）/BDS（BeiDou Navigation Satellite System）非组合PPP模型,将每个系统第1个频率上的接收机码硬件延迟约束为零,对接收机DCB进行参数估计,达到了分离电离层延迟和接收机码硬件延迟的目的,降低了接收机钟差和电离层延迟的相关程度。利用4个多星座实验（multi-GNSS experiment,MGEX）跟踪站的GPS/BDS数据进行了静态和动态PPP试验,结果表明,与不估计DCB参数的PPP模型相比,采用估计DCB参数PPP模型后,静态模式下定位精度和收敛速度平均提高了29.3%和29.8%,动态模式下定位精度和收敛速度平均提高了15.7%和21.6%。     

Analyzing GNSS data in precise point positioning software

This work demonstrates that precise point positioning (PPP) can be used not only for positioning, but for a variety of other tasks, such as signal analysis. The fact that the observation model used for accurate error modeling has to take into consideration the several effects present in GPS signals, and that observations are undifferenced, makes PPP a powerful data analysis tool sensitive to a variety of parameters. The PPP application developed at the University of New Brunswick, which is called GAPS (GPS Analysis and Positioning Software), has been designed and built in order to take advantage of available precise products, resulting in a data analysis tool for determining parameters in addition to position, receiver clock error, and neutral atmosphere delay. These other estimated parameters include ionospheric delays, code biases, satellite clock errors, and code multipath among others. In all cases, the procedures were developed in order to be suitable for real-time as well as post-processing applications. One of the main accomplishments in the development described here is the use of very precise satellite products, coupled with a very complete observation error modeling to make possible a variety of analyses based on GPS data. In this paper, several procedures are described, their innovative aspects are pointed out, and their results are analyzed and compared with other sources. The procedures and software are readily adaptable for using data from other global navigation satellite systems.     

Stochastic modeling of high-stability ground clocks in GPS analysis

In current global positioning system (GPS) applications, receiver clocks are typically estimated epoch-wise in the data analyses even for clocks with high performance like Hydrogen-masers (H-maser). Applying an appropriate clock model for high-stability receiver clocks should, in view of the strong correlation between the station height and the clock parameters, significantly improve the positioning results. Recent experiments have shown that modeling the deterministic behavior of high-quality receiver clocks can improve the kinematic precise point positioning considerably. In this paper, well-behaving ground clocks are studied in detail applying constraints between subsequent and near-subsequent clock parameters. The influence of different weights for these relative clock constraints on the positioning quality, especially on the height, is investigated. For excellent clocks, an improvement of up to a factor of 3 can be obtained for the repeatability of the kinematic height estimates. This may be essential to detect small but sudden changes in the vertical component (e.g., caused by earthquakes). Troposphere zenith path delays (ZPD) are also heavily correlated with the receiver clock estimates and station heights. All these parameters are usually estimated simultaneously. We show that the use of relative clock constraints allows for a higher time resolution of the ZPD estimates (smaller than 2 h) without compromising the quality of the kinematic height estimates.     

A proposed GPS method with multi-antennae and single receiver

A method based on multi-antennae linked to a common GPS receiver is proposed. The goal of the technique is to improve height determination for baselines a few kilometres in length. The advantage of this technique resides in the elimination of relative clock parameters in the between-antenna single difference observations. Because single difference observations are free of clock errors more geometrical strength remains to determine the baseline components. This statement is valid as long as intercable biases can be carefully calibrated. For millimetre height determination, the intercable calibration must be done at the same level of accuracy. Under this assumption it is shown that in general the height standard deviation improves by a factor of about three compared to standard GPS data processing. With the proposed method, the effect of relative tropospheric zenith delay errors becomes a bit smaller (in absolute value), compared to standard data processing. To absorb this error, a relative tropospheric zenith delay parameter may be estimated. Even with this additional parameter in the solution the height standard deviation remains two times smaller than the results of standard processing techniques (without tropospheric zenith delay parameter), and at least five times smaller than in the results obtained from standard processing including one tropospheric zenith delay parameter.     

Monitoring selective availability dither frequencies and their effect on GPS data

Summary The signals transmitted by Block II satellites of the Global Positioning System (GPS) can be degraded to limit the highest accuracy of the system (10 m or better point positioning) to authorized users. This mode of degraded operation is called Selective Availability (S/A). S/A involves the degradation in the quality of broadcast orbits and satellite clock dithering. We monitored the dithered satellite oscillator and investigated the effect of this clock dithering on high accuracy relative positioning. The effect was studied over short 3-meter and zero-baselines with two GPS receivers. The equivalent S/A effects for baselines ranging from 0 to >10,000 km can be examined with short test baselines if the receiver clocks are deliberately mis-synchronized by a known and varying amount. Our results show that the maximum effect of satellite clock dithering on GPS double difference phase residuals grows as a function of the clock synchronization error according to: S/A _effect =0.04 cm/msec, and it increases as a function of baseline length like: S/A _effect =0.014 cm/100 km. These are equations for maximum observed values of post-fit residuals due to S/A. The effect on GPS baselines is likely to be smaller than the 0.14 mm for a baseline separation of 100 km. We therefore conclude, for our limited data set, and for the level of S/A during our tests, that S/A clock dithering has negligible effect on all terrestrial GPS baselines if double difference processing techniques are employed and if the GPS receivers remain synchronized to better than 10 msec. S/A may constitute a problem, however, if accurate point processing is required, or if GPS receivers are not synchronized. We suggest and test two different methods to monitor satellite frequency offsets due to S/A. S/A modulates GPS carrier frequencies in the range of-2 Hz to +2 Hz over time periods of several minutes. The methods used in this paper to measure the satellite clock dither could be applied by the civilian GPS community to continuously monitor S/A clock dithering. The monitored frequencies may aid high accuracy point positioning applications in a postprocessing mode (Malys and Ortiz 1989), and differential GPS with poorly synchronized receivers (Feigl et al. 1991).     

Analysis of estimated satellite clock biases and their effects on precise point positioning

This study provides a systemic analysis to identify the biases in estimated satellite clocks and illustrates their effects in precise point positioning (PPP). First, the precise satellite clock estimation method considering pseudorange and carrier phase hardware delays is derived. Two methods for satellite clock estimation are compared, and their equivalency is discussed. The results show that apart from the well-known constant code hardware biases, the time-variant phase hardware biases are also absorbed by the estimated clocks. Also, the satellite clocks contain biases caused by modeling errors. To analyze the effects of these biases, they are grouped into initial clock biases (ICBs) and time-dependent biases (TDBs). Then, a detailed analysis of the impact of the biases on PPP-based troposphere and coordinate estimates is conducted. The experimental analysis demonstrates that TDBs affect positioning and tropospheric estimates, and their impacts are more significant in the static mode. The ICBs affect coordinate accuracy, zenith total delay mean bias, and its standard deviations only at the millimeter level for kinematic and static PPP, which is negligible. However, the ICBs affect the convergence period for both static and real kinematic PPP, and the magnitude of their impact largely depends on data quality. Note that satellites clocks are generally estimated with the P1/P2 and L1/L2 ionospheric-free combinations, and that hardware-specific parts of ICBs and TDBs cancel if users employ the same type of observables as the clock providers. Otherwise, the effects of biases cannot be ignored, especially for triple-frequency applications. Also, modeling-specific parts of ICBs and TDBs are significant in real-time clocks, which also affect user applications. Our conclusion is applicable for understanding the effects of these biases.     

Precise Point Positioning Using IGS Orbit and Clock Products

The contribution details a post-processing approach that used undifferentiated dual-frequency pseudorange and carrier phase observations along with IGS procise orbit products, for stand-alone precise geodetic point positioning (static or kinematic) with cm precision. This is possible if one takes advantage of the satellite clock estimates available with the satellite coordinates in the IGS precise orbit products and models systematic effects that cause cm variations in the satelite to user range. This paper will describe the approach, summarize the adjustment procedure, and specify the earth- and space-based models that must be implementetd to achieve cm-level positioning in static mode. Furthermore, station tropospheric zenth path delays with cm precision and GPS receiver clock estimates procise to 0.1 ns are also obtained. ? 2001 John Wiley & Sons, Inc.     

基于接收机钟差约束的精密单点定位时间传递研究

精密单点定位(PPP)技术起初主要面向定位与导航等位置应用.近年来,PPP技术逐渐成为时间传递等非定位应用的一种重要且有效的手段.如今,具有更高稳定性的氢原子钟也被越来越多的测站用来提供时间频率基准.而传统的PPP时间传递方法通常在数据处理时将接收机钟差参数视为白噪声(WN)参数进行处理,并未充分利用原子钟的高稳定特性...     

基于星间单差法的GEO卫星精密定轨

提出了一种利用星间单差法消除接收机钟差的GEO卫星精密定轨方案。通过仿真,详细探讨了相关原理、参数设置、测站分布以及单差选星等关键问题。仿真研究表明,该方法消去了接收机钟差、大部分与测站相关的系统误差以及用模型未完全改正的对流层及电离层延迟残差,能够直接解算卫星轨道参数,减轻测站接收机时钟同步的负担;通过方案对比,确定了一种优化方案,选取合适的卫星对,在现有条件下采用合适的测站分布,利用星间单差方法解算22参数,可以获得高精度的GEO卫星轨道。     

导航卫星星地/星间链路联合定轨中设备时延的方法

导航卫星系统播发的卫星钟差改正数包含了卫星的导航信号设备群时延。从保持与用户算法一致性的角度考虑,指出利用星间测距数据求解的卫星钟差也应该包含导航信号设备群时延。由此发现星间链路设备时延以组合时延的形式出现在观测方程中：接收设备时延与导航信号群时延之和构成组合接收时延,发射设备时延与导航信号群时延之差构成组合发射时延。探讨了处理星间链路设备时延的方法,提出两种在定轨和钟差解算数据处理的同时估计设备时延参数的方法：一是估计每颗卫星的组合接收时延和组合发射时延;二是估计每条(有向)链路的时延偏差参数(组合接收时延与组合发射时延之和)。通过仿真实验,证明了所提方法正确性和有效性。结果表明,利用提出的方法可以显著地降低设备时延对轨道和钟差解算精度的影响,效果几乎接近设备时延被准确标定的理想情况。     

Performance analysis of integrated GPS/GLONASS carrier phase-based positioning

Due to the different signal frequencies for the GLONASS satellites, the commonly-used double-differencing procedure for carrier phase data processing can not be implemented in its straightforward form, as in the case of GPS. In this paper a novel data processing strategy, involving a three-step procedure, for integrated GPS/GLONASS positioning is proposed. The first is pseudo-range-based positioning, that uses double-differenced (DD) GPS pseudo-range and single-differenced (SD) GLONASS pseudo-range measurements to derive the initial position and receiver clock bias. The second is forming DD measurements (expressed in cycles) in order to estimate the ambiguities, by using the receiver clock bias estimated in the above step. The third is to form DD measurements (expressed in metric units) with the unknown SD integer ambiguity for the GLONASS reference satellite as the only parameter (which is constant before a cycle slip occurs for this satellite). A real-time stochastic model estimated by residual series over previous epochs is proposed for integrated GPS/GLONASS carrier phase and pseudo-range data processing. Other associated issues, such as cycle slip detection, validation criteria and adaptive procedure(s) for ambiguity resolution, is also discussed. The performance of this data processing strategy will be demonstrated through case study examples of rapid static positioning and kinematic positioning. From four experiments carried out to date, the results indicate that rapid static positioning requires 1 minute of single frequency GPS/GLONASS data for 100% positioning success rate. The single epoch positioning solution for kinematic positioning can achieve 94.6% success rate over short baselines (<6 km).     

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。     

PERFORMANCE ANALYSIS OF INTEGRATED GPS/GLONASS CARRIER PHASE-BASED POSITIONING

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精密单点定位用户自主式完备性监测算法

精密单点定位PPP是当前GNSS高精度定位中的关键技术之一,使用的PPP采用扩展卡尔曼滤波估计,未知参数包括站点坐标,接收机钟差,对流层延迟以及虚拟未知数。在QR奇偶检校法的基础上,重点考察设计矩阵向量间的相关距离,将其作为粗差探测和识别的研究对象。通过向量相关距离时间序列,可以区分单个粗差和多个粗差的粗差集。提出精密单点定位的RAIM算法,解决了精密单点定位中的质量控制问题,使得多个粗差的识别更加清晰和快捷。