On the short-term temporal variations of GNSS receiver differential phase biases

As a first step towards studying the ionosphere with the global navigation satellite system (GNSS), leveling the phase to the code geometry-free observations on an arc-by-arc basis yields the ionospheric observables, interpreted as a combination of slant total electron content along with satellite and receiver differential code biases (DCB). The leveling errors in the ionospheric observables may arise during this procedure, which, according to previous studies by other researchers, are due to the combined effects of the code multipath and the intra-day variability in the receiver DCB. In this paper we further identify the short-term temporal variations of receiver differential phase biases (DPB) as another possible cause of leveling errors. Our investigation starts by the development of a method to epoch-wise estimate between-receiver DPB (BR-DPB) employing (inter-receiver) single-differenced, phase-only GNSS observations collected from a pair of receivers creating a zero or short baseline. The key issue for this method is to get rid of the possible discontinuities in the epoch-wise BR-DPB estimates, occurring when satellite assigned as pivot changes. Our numerical tests, carried out using Global Positioning System (GPS, US GNSS) and BeiDou Navigation Satellite System (BDS, Chinese GNSS) observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, suggest two major findings. First, epoch-wise BR-DPB estimates can exhibit remarkable variability over a rather short period of time (e.g. 6 cm over 3 h), thus significant from a statistical point of view. Second, a dominant factor driving this variability is the changes of ambient temperature, instead of the un-modelled phase multipath.     

多频多模GNSS接收机差分相位偏差的短期时变特性

随着中国北斗三号全球导航卫星系统(BeiDou-3 Navigation Satellite System,BDS-3)的建成、欧盟伽利略系统(Galileo)及日本准天顶卫星系统(quasi-zenith satellite system,QZSS)的发展,越来越多的卫星可用于反演大气电离层.通常,接收机差分码偏差(differential code biases,DCB)的短时变化被认为是利用全球导航卫星系统(Global Navigation Satellite System,GNSS)反演电离层的重要误差来源,然而,有研究表明,接收机差分相位偏差(differential phase biases,DPB)的短时变化也有可能影响电离层反演的精度和可靠性.为此,本文提出了基于站间单差模型并采用不变换参考星策略来估计接收机DPB的方法,可实现接收机DPB的连续估计.基于几台可跟踪BDS-3信号的多频多模接收机采集的数据,对BDS-3、Galileo、GPS和QZSS重叠频率组合的DPB进行了分析.结果表明,四系统的接收机DPB日变化都是很明显的,并且和温度有很强的相关性;基于不同系统重叠频率组合的DPB之间存在强相关;基于相同类型接收机的DPB的变化也存在明显的相关性.     

Estimation and analysis of Galileo differential code biases

When sensing the Earth’s ionosphere using dual-frequency pseudorange observations of global navigation satellite systems (GNSS), the satellite and receiver differential code biases (DCBs) account for one of the main sources of error. For the Galileo system, limited knowledge is available about the determination and characteristic analysis of the satellite and receiver DCBs. To better understand the characteristics of satellite and receiver DCBs of Galileo, the IGGDCB (IGG, Institute of Geodesy and Geophysics, Wuhan, China) method is extended to estimate the satellite and receiver DCBs of Galileo, with the combined use of GPS and Galileo observations. The experimental data were collected from the Multi-GNSS Experiment network, covering the period of 2013–2015. The stability of both Galileo satellite and receiver DCBs over a time period of 36 months was thereby analyzed for the current state of the Galileo system. Good agreement of Galileo satellite DCBs is found between the IGGDCB-based DCB estimates and those from the German Aerospace Center (DLR), at the level of 0.22 ns. Moreover, high-level stability of the Galileo satellite DCB estimates is obtained over the selected time span (less than 0.25 ns in terms of standard deviation) by both IGGDCB and DLR algorithms. The Galileo receiver DCB estimates are also relatively stable for the case in which the receiver hardware device stays unchanged. It can also be concluded that the receiver DCB estimates are rather sensitive to the change of the firmware version and that the receiver antenna type has no great impact on receiver DCBs.     

GPS differential code biases considering the second-order ionospheric term

GPS Solutions - Differential code biases (DCBs) of the global positioning system (GPS) are generally estimated together with total electron content (TEC) along the signal transmission path through...     

FY-3D and FY-3C onboard observations for differential code biases estimation

GPS Solutions - As parameter estimation and statistical testing are often intimately linked in the processing of observational data, the uncertainties involved in both estimation and testing need...     

Two-step method for the determination of the differential code biases of COMPASS satellites

The differential code bias (DCB) in satellites of the Global Navigation Satellite Systems (GNSS) should be precisely corrected when designing certain applications, such as ionospheric remote sensing, precise point positioning, and time transfer. In the case of COMPASS system, the data used for estimating DCB are currently only available from a very limited number of global monitoring stations. However, the current GPS/GLONASS satellite DCB estimation methods generally require a large amount of geographically well-distributed data for modeling the global ionospheric vertical total electron content (TEC) and are not particularly suitable for current COMPASS use. Moreover, some satellites with unstable DCB (i.e., relatively large scatter) may affect other satellite DCB estimates through the zero-mean reference that is currently imposed on all satellites. In order to overcome the inadequacy of data sources and to reduce the impact of unstable DCB, a new approach, designated IGGDCB, is developed for COMPASS satellite DCB determination. IGG stands for the Institute of Geodesy and Geophysics, which is located in Wuhan, China. In IGGDCB, the ionospheric vertical TEC of each individual station is independently modeled by a generalized triangular series function, and the satellite DCB reference is selected using an iterative DCB elimination process. By comparing GPS satellite DCB estimates calculated by the IGGDCB approach based on only a handful (e.g., seven) of tracking stations against that calculated by the currently existing methods based on hundreds of tracking stations, we are able to demonstrate that the accuracies of the IGGDCB-based DCB estimates perform at the level of about 0.13 and 0.10?ns during periods of high (2001) and low (2009) solar activity, respectively. The iterative method for DCB reference selection is verified by statistical tests that take into account the day-to-day scatter and the duration that the satellites have spent in orbit. The results show that the impact of satellites with unstable DCB can be considerably reduced using the IGGDCB method. It is also confirmed that IGGDCB is not only specifically valid for COMPASS but also for all other GNSS.     

Joint estimation of vertical total electron content (VTEC) and satellite differential code biases (SDCBs) using low-cost receivers

Vertical total electron content (VTEC) parameters estimated using global navigation satellite system (GNSS) data are of great interest for ionosphere sensing. Satellite differential code biases (SDCBs) account for one source of error which, if left uncorrected, can deteriorate performance of positioning, timing and other applications. The customary approach to estimate VTEC along with SDCBs from dual-frequency GNSS data, hereinafter referred to as DF approach, consists of two sequential steps. The first step seeks to retrieve ionospheric observables through the carrier-to-code leveling technique. This observable, related to the slant total electron content (STEC) along the satellite–receiver line-of-sight, is biased also by the SDCBs and the receiver differential code biases (RDCBs). By means of thin-layer ionospheric model, in the second step one is able to isolate the VTEC, the SDCBs and the RDCBs from the ionospheric observables. In this work, we present a single-frequency (SF) approach, enabling the joint estimation of VTEC and SDCBs using low-cost receivers; this approach is also based on two steps and it differs from the DF approach only in the first step, where we turn to the precise point positioning technique to retrieve from the single-frequency GNSS data the ionospheric observables, interpreted as the combination of the STEC, the SDCBs and the biased receiver clocks at the pivot epoch. Our numerical analyses clarify how SF approach performs when being applied to GPS L1 data collected by a single receiver under both calm and disturbed ionospheric conditions. The daily time series of zenith VTEC estimates has an accuracy ranging from a few tenths of a TEC unit (TECU) to approximately 2 TECU. For 73–96% of GPS satellites in view, the daily estimates of SDCBs do not deviate, in absolute value, more than 1 ns from their ground truth values published by the Centre for Orbit Determination in Europe.     

GNSS receiver implementations to mitigate the effects of commensurate sampling frequencies on DLL code tracking

The sampling frequency of a digitized intermediate frequency signal has a strong effect on the measurement accuracy of Global Navigation Satellite System (GNSS) receivers. The delay-locked loop tracking error is significant when the sampling frequency is an integer multiple of the code chipping rate, the so-called commensurate sampling frequency, and the number of distinct instantaneous residual code phases is low. This results in distortions of the correlation shape and discriminator functions that lead to a significant accuracy degradation. These effects are most pronounced when the sampling frequency is low. Notwithstanding, it is generally good for receivers to keep the sampling frequency to a minimum owing to the processing load and power consumption. It creates a challenge for existing GNSS signal processing techniques. Random, sine and sawtooth jitters have been found to mitigate these distortions considerably. A software algorithm and two hardware receiver implementations of these solutions are proposed. A register-based architecture can be directly applied to the conventional receiver architecture, while the increase in resource and power consumption is insignificant. A RAM-based design cannot only considerably minimize utilized resources but also slightly reduce the power consumption compared to the conventional architecture.     

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.     

Calibration of the clock-phase biases of GNSS networks: the closure-ambiguity approach

In global navigation satellite systems (GNSS), the problem of retrieving clock-phase biases from network data has a basic rank defect. We analyse the different ways of removing this rank defect, and define a particular strategy for obtaining these phase biases in a standard form. The minimum-constrained problem to be solved in the least-squares (LS) sense depends on some integer vector which can be fixed in an arbitrary manner. We propose to solve the problem via an undifferenced approach based on the notion of closure ambiguity. We present a theoretical justification of this closure-ambiguity approach (CAA), and the main elements for a practical implementation. The links with other methods are also established. We analyse all those methods in a unified interpretative framework, and derive functional relations between the corresponding solutions and our CAA solution. This could be interesting for many GNSS applications like real-time kinematic PPP for instance. To compare the methods providing LS estimates of clock-phase biases, we define a particular solution playing the role of reference solution. For this solution, when a phase bias is estimated for the first time, its fractional part is confined to the one-cycle width interval centred on zero; the integer-ambiguity set is modified accordingly. Our theoretical study is illustrated with some simple and generic examples; it could have applications in data processing of most GNSS networks, and particularly global networks using GPS, Glonass, Galileo, or BeiDou/Compass satellites.     

GNSS接收机数据质量及常见问题分析

GNSS接收机数据质量是接收机实现各项功能、向用户提供各项服务的基础。针对当前GNSS数据质量核验方法和评价指标较为单一,分析方法不系统的问题,文中分析一种综合利用TEQC、GAMIT、RTKLIB三款软件进行GNSS数据质量分析的方法,并给出相应质量分析指标。以北京市全球卫星定位系统网络中基准站数据为基础,对北斗三模接收机和GPS/GLONASS双模接收机数据质量进行对比分析,对比结果显示,石景山和牛口峪两个站数据质量整体较差,mp1大于0.5m,mp2大于0.75m,周跳比小于2 000。对影响数据质量的原因进行初步分析,通过实地勘测验证理论分析结果,对比分析结果表明:采用文中提出的质量分析方法所判断出的问题同实地勘察结果一致,验证本方法的实用性。最后针对基准站存在的问题向相关部门提出改善建议,并对改善后该站观测数据进行质量分析,各项指标均达标。     

Method for evaluating real-time GNSS satellite clock offset products

Real-time satellite clock offset products are frequently utilized in navigation and positioning service fields. The precision of such products is a key issue for their application. The evaluation methods existed for satellite clock offset products are mostly based on post-processed satellite clock offset solutions, which will encounter problems in real-time product evaluation, especially for real-time satellite clock offset products estimated from data with regional stations only. We propose an improved evaluation method for global navigation satellite system (GNSS) satellite clock offset products. In the proposed method, we use all-satellite reference method instead of single-satellite reference method to eliminate the timescale in satellite clock offset products. Moreover, a preprocessing step is suggested to detect gross errors and initial clock bias before evaluating the precision of the satellite clock offsets. We conduct two examples to verify our method, and the experimental results show that the proposed method is more reasonable in assessing the GNSS satellite clock offset precision, and it also provides a reliable approach to analyzing the estimated satellite clock offset in both real-time and post-processed, or globally and regionally.     

An advanced GNSS code multipath detection and estimation algorithm

A novel maximum likelihood-based range estimation algorithm is designed to provide robustness to multipath, which is recognized as a dominant error source in DS-CDMA-based navigation systems. The detection–estimation problem is jointly solved to sequentially estimate the parameters of each individual multipath component and predict the existence of a next possible component. A comparison between contemporary maximum likelihood-based multipath estimation techniques and this new technique is provided. A selection of realistic channel simulation models is used to assess relative performance under different operating situations. A set of real GPS L1/CA data processing results are also presented to further assess the applicability of the proposed algorithm for urban navigation.     

GPS receiver phase biases estimable in PPP-RTK networks: dynamic characterization and impact analysis

The integer ambiguity resolution enabled precise point positioning (PPP-RTK) has been proven advantageous in a wide range of applications. The realization of PPP-RTK concerns the isolation of satellite phase biases (SPBs) and other corrections from a network of Global Positioning System (GPS) reference receivers. This is generally based on Kalman filter in order to achieve real-time capability, in which proper modeling of the dynamics of various types of unknowns remains crucial. This paper seeks to gain insight into how to reasonably deal with the dynamic behavior of the estimable receiver phase biases (RPBs). Using dual-frequency GPS data collected at six colocated receivers over days 50–120 of 2015, we analyze the 30-s epoch-by-epoch estimates of L1 and wide-lane (WL) RPBs for each receiver pair. The dynamics observed in these estimates are a combined effect of three factors, namely the random measurement noise, the multipath and the ambient temperature. The first factor can be overcome by turning to a real-time filter and the second by considering the use of a sidereal filtering. The third factor has an effect only on the WL, and this effect appears to be linear. After accounting for these three factors, the low-pass-filtered, sidereal-filtered, epoch-by-epoch estimates of L1 RPBs follow a random walk process, whereas those of WL RPBs are constant over time. Properly modeling the dynamics of RPBs is vital, as it ensures the best convergence of the Kalman-filtered, between-satellite single-differenced SPB estimates to their correct values and, in turn, shortens the time-to-first-fix at user side.     

On the impact of GNSS ambiguity resolution: geometry,ionosphere, time and biases

Integer ambiguity resolution (IAR) is the key to fast and precise GNSS positioning and navigation. Next to the positioning parameters, however, there are several other types of GNSS parameters that are of importance for a range of different applications like atmospheric sounding, instrumental calibrations or time transfer. As some of these parameters may still require pseudo-range data for their estimation, their response to IAR may differ significantly. To infer the impact of ambiguity resolution on the parameters, we show how the ambiguity-resolved double-differenced phase data propagate into the GNSS parameter solutions. For that purpose, we introduce a canonical decomposition of the GNSS network model that, through its decoupled and decorrelated nature, provides direct insight into which parameters, or functions thereof, gain from IAR and which do not. Next to this qualitative analysis, we present for the GNSS estimable parameters of geometry, ionosphere, timing and instrumental biases closed-form expressions of their IAR precision gains together with supporting numerical examples.     

Coherent integration time limit of a mobile receiver for indoor GNSS applications

There is an emerging requirement for processing global navigation satellite system (GNSS) signals indoor where the signal is very weak and subjected to spatial fading. Typically, longer coherent integration intervals provide the additional processing gain required for the detection and processing of such weak signals. However, the arbitrary physical motion of the handset imputed by the user limits the effectiveness of longer coherent integration intervals due to the spatial decorrelation of the multipath-faded GNSS signal. In this paper, limits of coherent integration due to spatial decorrelation are derived and corroborated with experimental verification. A general result is that the processing gain resulting from direct coherent integration saturates after the antenna has moved through a certain distance, which for typical indoor propagation, is about half a carrier wavelength. However, a refined Doppler search coupled with a prolonged coherent integration interval extends this limit, which is effectively a manifestation of selective diversity.