GPS,Galileo, QZSS and IRNSS differential ISBs: estimation and application

Knowledge of inter-system biases (ISBs) is essential to combine observations of multiple global and regional navigation satellite systems (GNSS/RNSS) in an optimal way. Earlier studies based on GPS, Galileo, BDS and QZSS have demonstrated that the performance of multi-GNSS real-time kinematic positioning is improved when the differential ISBs (DISBs) corresponding to signals of different constellations but transmitted at identical frequencies can be calibrated, such that only one common pivot satellite is sufficient for inter-system ambiguity resolution at that particular frequency. Recently, many new GNSS satellites have been launched. At the beginning of 2016, there were 12 Galileo IOV/FOC satellites and 12 GPS Block IIF satellites in orbit, while the Indian Regional Navigation Satellite System (IRNSS) had five satellites launched of which four are operational. More launches are scheduled for the coming years. As a continuation of the earlier studies, we analyze the magnitude and stability of the DISBs corresponding to these new satellites. For IRNSS this article presents for the first time DISBs with respect to the L5/E5a signals of GPS, Galileo and QZSS for a mixed-receiver baseline. It is furthermore demonstrated that single-frequency (L5/E5a) ambiguity resolution is tremendously improved when the multi-GNSS observations are all differenced with respect to a common pivot satellite, compared to classical differencing for which a pivot satellite is selected for each constellation.     

Geometry-free undifferenced, single and double differenced analysis of single frequency GPS, EGNOS and GIOVE-A/B measurements

This paper demonstrates a geometry-free GNSS measurement analysis approach and presents results of single frequency GPS, EGNOS and GIOVE short and zero baseline measurements. The purpose is to separate the different contributions to the measurement noise of pseudo range code and carrier phase observations at the receiver. The influence of multipath on the different combinations of observations is also determined. Quantitative results are presented for the thermal code and phase measurement noise and for the correlation between the observations. Comparison of the results with theoretical approximations confirms the validity of the used approach. Results from field measurements clearly show less thermal noise on the Galileo E1BC observations than on the GPS L1C/A observations due to the new signal modulation. The feasibility of ambiguity resolution with a geometry-free model is also discussed including the significant impact of multipath thereon.     

BDS-3和Galileo组合的RTK定位性能分析

北斗三号卫星导航系统（BeiDou-3 navigation satellite system, BDS-3）已全面建成并向全球用户提供可靠的定位、导航和授时（positioning, navigation and timing, PNT）服务。为了实现与其他全球卫星导航系统（global navigation satellite system, GNSS）的兼容性和互操作性,BDS-3在BDS-2的基础上调制了B1C和B2a两个新信号,与伽利略系统（Galileo）的E1和E5a实现了频率的复用。系统间偏差（inter-system bias, ISB）对于实现不同GNSS之间的融合处理至关重要,为此提出了基于单差模型的ISB估计与应用算法,并对BDS-3与Galileo重叠频率之间的ISB进行了分析。基于可跟踪BDS-3新信号的几类接收机,揭示了BDS-3和Galileo之间的ISB的特性,在此基础上分析了BDS-3和Galileo组合的实时动态（real-time kinematic, RTK）定位性能。结果表明,基于相同类型的接收机B1C-E1和B2a-E5a之间是不存在ISB...     

Combined GPS and BDS for single-frequency continuous RTK positioning through real-time estimation of differential inter-system biases

Double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can be fixed to integers if the associated differential inter-system biases (DISBs) are well known. In this case, only one common pivot satellite is sufficient for inter-system ambiguity resolution. This will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning especially when only a few satellites are observed. However, for GPS and current operational BDS-2, there are no overlapping frequencies. Due to the influence of different frequencies, the inter-system DD ambiguities still cannot be fixed to integers even if the DISBs are precisely known. In this contribution, we present an inter-system differencing model for combined GPS and BDS single-frequency RTK positioning through real-time estimation of DISBs. The stability of GPS L1 and BDS B1 DISBs is analyzed with different receiver types. Along with parameterization and using the short-term stability of DISBs, the DD ambiguities between GPS and BDS pivot satellites and the between-receiver single-difference ambiguity of the GPS pivot satellite can be estimable jointly with the differential phase DISB term from epoch to epoch. Then the inter-system differencing model can benefit from the near time-constant DISB parameters and thus has better multi-epoch positioning performance than the classical intra-system differencing model. The combined GPS and BDS single-frequency RTK positioning performance is evaluated with various simulated satellite visibilities. It will be shown that compared with the classical intra-system differencing model, the proposed model can effectively improve the positioning accuracy and reliability, especially for severely obstructed situations with only a few satellites observed.     

BeiDou B2/Galileo E5b短基线紧组合相对定位模型及性能评估

随着GPS和GLONASS系统的现代化以及Galileo和BeiDou卫星导航系统的建设,GNSS正朝多频多系统的方向发展。本文对BeiDou B2/Galileo E5b短基线紧组合相对定位的模型与算法进行了研究,详细推导了BeiDou B2/Galileo E5b短基线紧组合相对定位的模型与算法,并对其定位性能进行了分析。重点分析了BeiDou B2与Galileo E5b频点的接收机间差分系统间偏差的长期稳定性,结果表明:基线两端的接收机类型(包括固件版本)相同时,差分系统间偏差接近于0;基线两端的接收机类型不同时,差分系统间偏差较大,但具有长期稳定性,因此能够事先标定并作为改正数用于后续的定位中。最后基于BeiDou B2/Galileo E5b单频单历元相对定位试验对系统间紧组合模型的定位效果进行了比较验证。结果表明,相对于传统的松组合模型,使用改正系统间偏差的紧组合模型能够显著提高模糊度固定的成功率,尤其是在遮挡比较严重、单系统可观测到的卫星数较少的情况下,模糊度固定成功率可以提高10%~25%。     

Characterization of GPS/GIOVE sensor stations in the CONGO network

The Cooperative Network for GIOVE Observation (CONGO) is a global network of real-time capable multi-constellation GNSS receivers, which has been established by the German Aerospace Center (DLR) and the German Federal Agency for Cartography and Geodesy (BKG) as a test bed for experimentation with the new Galileo signals. The CONGO network employs a variety of different antennas and receivers which have become available for public use over the last 2 years. Following an overview of the network and the employed user equipment, the paper discusses the achieved GPS/GIOVE tracking performance. This includes a characterization of antenna gain patterns as well as receiver noise and multipath errors. Special attention is given to the discussion of inter-system biases. The nature and variation of these biases is illustrated based on a set of three different receivers operated in a zero-baseline configuration at the Wettzell site.     

多频多模接收机差分码偏差的精密估计与特性分析

全球导航卫星系统（Global Navigation Satellite System,GNSS）探测大气电离层需要精确处理由接收机差分码偏差（differential cade bias,DCB）引起的系统误差。准确掌握接收机DCB的多时间尺度精细变化等特性是联合美国GPS、中国北斗卫星导航系统（BeiDou navigation satellite system,BDS）和欧盟Galileo等多GNSS技术监测电离层所面临的主要科学问题之一。为此,提出了基于零基线精密估计站间单差接收机DCB的方法,并对站间单差接收机DCB的日加权平均值进行了分析。基于4台多模接收机采集于2013年的双频观测值,揭示了站间单差接收机DCB的变化可能受3种因素的影响,即接收机内置软件的版本升级（实验中引起了约3 ns的显著增加）、拆卸个别接收机所导致的观测条件改变（实验中引起了约1.3 ns的显著减少）和估计方法的误差（引起了与导航系统卫星几何结构重复性相一致的周期性变化）等。     

多模GNSS融合PPP系统间偏差特性分析

多模全球导航卫星系统（Global Navigation Satellite System,GNSS）精密单点定位（precise point positioning,PPP）存在系统间偏差（inter-system bias,ISB）,构建了顾及系统间偏差的多模GNSS融合PPP算法,对多星座实验（the multi-GNSS experiment,MGEX）监测网中的7个测站观测数据进行静态解算,获得Galileo、GLONASS、北斗与全球定位系统之间的ISB值。分析结果表明,四系统PPP融合定位在水平分量和高程分量的精度分别为8.9 mm、5.3 mm和10.9 mm,体现出较高的融合定位精度。不同系统ISB值在单天内的稳定性较好,均优于0.12 ns。从多天ISB序列看,ISB存在不规律跳变,变化幅度可达近20 ns。不同类型接收机ISB存在一定差异,同一类型接收机结果相近。综合来看,Galileo ISB值最稳定且结果最优,北斗与GLONASS结果相当。     

BDS–GPS inter-system bias of code observation and its preliminary analysis

Navigation applications will benefit significantly from the improved reliability, availability, and accuracy offered by combining BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS). In the BDS/GPS navigation data fusion model, the effect of inter-system bias (ISB) must be considered. We present a detailed analysis of the pseudorange measurements for BDS and GPS and demonstrate the existence of code ISB in BDS/GPS measurements. The ISB mainly consists of the time system offset, the coordinate system difference, and the inter-system hardware delay bias. A method based on statistical hypothesis testing is proposed to assess the stability and difference of the BDS–GPS ISB. Real data from 18 stations equipped with six types of receivers are used to compute the ISB. The results illustrate that (a) receiver-dependent ISBs are evident and comparatively consistent, with the maximum ISB observed in our experiments being ?1516 ns, (b) these receiver-dependent ISBs exhibit great stability in terms of their standard deviation and intra-day variation, and (c) the estimated ISBs for each BDS satellite type with respect to GPS are consistent.     

An enhanced calibration method of GLONASS inter-channel bias for GNSS RTK

A user of heterogeneous GPS and GLONASS receiver pairs in differential positioning mode will experience ambiguity fixing challenges due to the presence of inter-channel biases. These biases cannot be canceled by differencing GLONASS observations, whether pseudorange or carrier phase. Fortunately, pre-calibration of GLONASS pseudorange and carrier phase observations can make ambiguity fixing for GPS/GLONASS positioning much easier. We propose an effective algorithm that transforms an RTK (real-time kinematic) solution in a mixed receiver baseline from a float to a fixed ambiguity solution. Carrier phase and code inter-channel biases are estimated from a zero baseline. Then, GLONASS both carrier phase and code observations are corrected accordingly. The results show that a mixed baseline can be transformed from a float (~100 %) to a fixed (more than 92 %) solution.     

GPS/BDS接收机端系统偏差稳定性对整周模糊度固定的影响

GNSS接收机端的UPD与接收到的信号频率有关,这导致GPS和BDS系统间的双差模糊度不具有整数特性,为了恢复其整数特性,两系统间的系统偏差需要进行估计或改正。在顾及GPS和BDS之间的时间系统、坐标系统和频率间偏差的基础上,推导出GPS/BDS系统偏差计算模型,并利用不同实验对系统偏差的稳定性进行验证。实验结果表明,不同品牌接收机在GPS/BDS系统偏差方面在一定条件下均具有稳定性;天线类型和天线连接线长度没有对GPS/BDS系统偏差产生显著影响。加入系统偏差改正的GPS/BDS紧组合定位在恶劣环境下表现良好,可将模糊度固定平均所需时间缩短33%,模糊度固定成功率提高31%。     

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.     

Revisit the calibration errors on experimental slant total electron content (TEC) determined with GPS

The calibration errors on experimental slant total electron content (TEC) determined with global positioning system (GPS) observations is revisited. Instead of the analysis of the calibration errors on the carrier phase leveled to code ionospheric observable, we focus on the accuracy analysis of the undifferenced ambiguity-fixed carrier phase ionospheric observable determined from a global distribution of permanent receivers. The results achieved are: (1) using data from an entire month within the last solar cycle maximum, the undifferenced ambiguity-fixed carrier phase ionospheric observable is found to be over one order of magnitude more accurate than the carrier phase leveled to code ionospheric observable and the raw code ionospheric observable. The observation error of the undifferenced ambiguity-fixed carrier phase ionospheric observable ranges from 0.05 to 0.11 total electron content unit (TECU) while that of the carrier phase leveled to code and the raw code ionospheric observable is from 0.65 to 1.65 and 3.14 to 7.48 TECU, respectively. (2) The time-varying receiver differential code bias (DCB), which presents clear day boundary discontinuity and intra-day variability pattern, contributes the most part of the observation error. This contribution is assessed by the short-term stability of the between-receiver DCB, which ranges from 0.06 to 0.17 TECU in a single day. (3) The remaining part of the observation errors presents a sidereal time cycle pattern, indicating the effects of the multipath. Further, the magnitude of the remaining part implies that the code multipath effects are much reduced. (4) The intra-day variation of the between-receiver DCB of the collocated stations suggests that estimating DCBs as a daily constant can have a mis-modeling error of at least several tenths of 1 TECU.     

Assessment of GPS + Galileo and multi-frequency Galileo single-epoch precise positioning with network corrections

Several processing strategies that use dual-frequency GPS-only solution, multi-frequency Galileo-only solution, and finally tightly combined dual-frequency GPS + Galileo solution were tested and analyzed for their applicability to single-epoch long-range precise positioning. In particular, a multi-system GPS + Galileo solution was compared to GPS double-frequency solution as well as to Galileo double-, triple-, and quadruple-frequency solutions. Also, the performance of the strategies was analyzed under clear-sky and obstructed satellite visibility in both single-baseline and multi-baseline modes. The results indicate that tightly combined GPS + Galileo instantaneous positioning has a clear advantage over single-system solutions and provides an accurate and reliable solution. It was also confirmed that application of multi-frequency observations in case of Galileo system has an advantage over a dual-frequency solution.     

Particle filter-based estimation of inter-system phase bias for real-time integer ambiguity resolution

Although double-differenced (DD) observations between satellites from different systems can be used in multi-GNSS relative positioning, the inter-system DD ambiguities cannot be fixed to integer because of the existence of the inter-system bias (ISB). Obviously, they can also be fixed as integer along with intra-system DD ambiguities if the associated ISBs are well known. It is critical to fix such inter-system DD ambiguities especially when only a few satellites of each system are observed. In most of the existing approaches, the ISB is derived from the fractional part of the inter-system ambiguities after the intra-system DD ambiguities are successfully fixed. In this case, it usually needs observations over long times depending on the number of observed satellites from each system. We present a new method by means of particle filter to estimate ISBs in real time without any a priori information based on the fact that the accuracy of a given ISB value can be qualified by the related fixing RATIO. In this particle filter-based method, the ISB parameter is represented by a set of samples, i.e., particles, and the weight of each sample is determined by the designed likelihood function related to the corresponding RATIO, so that the true bias value can be estimated successfully. Experimental validations with the IGS multi-GNSS experiment data show that this method can be carried out epoch by epoch to provide precise ISB in real time. Although there are only one, two, or at most three Galileo satellites observed, the successfully fixing rate increases from 75.5% for GPS only to 81.2%. In the experiment with five GPS satellites and one Galileo satellites, the first successfully fixing time is reduced to half of that without fixing the inter-system DD ambiguities.     

Multi-GNSS precise point positioning (MGPPP) using raw observations

A joint-processing model for multi-GNSS (GPS, GLONASS, BDS and GALILEO) precise point positioning (PPP) is proposed, in which raw code and phase observations are used. In the proposed model, inter-system biases (ISBs) and GLONASS code inter-frequency biases (IFBs) are carefully considered, among which GLONASS code IFBs are modeled as a linear function of frequency numbers. To get the full rank function model, the unknowns are re-parameterized and the estimable slant ionospheric delays and ISBs/IFBs are derived and estimated simultaneously. One month of data in April, 2015 from 32 stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) tracking network have been used to validate the proposed model. Preliminary results show that RMS values of the positioning errors (with respect to external double-difference solutions) for static/kinematic solutions (four systems) are 6.2 mm/2.1 cm (north), 6.0 mm/2.2 cm (east) and 9.3 mm/4.9 cm (up). One-day stabilities of the estimated ISBs described by STD values are 0.36 and 0.38 ns, for GLONASS and BDS, respectively. Significant ISB jumps are identified between adjacent days for all stations, which are caused by the different satellite clock datums in different days and for different systems. Unlike ISBs, the estimated GLONASS code IFBs are quite stable for all stations, with an average STD of 0.04 ns over a month. Single-difference experiment of short baseline shows that PPP ionospheric delays are more precise than traditional leveling ionospheric delays.     

Precise position determination using a Galileo E5 single-frequency receiver

The European Galileo system offers one dedicated signal that is superior to all other signals currently available in space, namely the broadband signal E5. This signal has a bandwidth of at least 51 MHz using an AltBOC modulation. It features a code range noise at centimeter level. Additionally, the impact of multipath effects on this signal is significantly lower compared to all other available GNSS signals. These unique features of Galileo E5 drastically improve the precision of code range measurements and hence enable precise single-frequency positioning. Certain scientific and non-scientific applications in the positioning domain could likely benefit from the exploitation of E5 measurements. A positioning approach based on an additive combination of code range and carrier phase measurements (CPC—“code-plus-carrier”) to eliminate the ionospheric delay could be used to perform precise positioning over long distances. Unfortunately, this derived observable contains the ambiguity term as an additional unknown what normally requires longer observation windows in order to allow sufficient convergence of the ambiguity parameters. For this reason, a rapid convergence algorithm based on Kalman filtering was implemented in addition to the conventional CPC approach that is also discussed. The CPC-based results yield a positioning precision of 2–5 cm after a convergence time of about 3 h. The rapid convergence filter allows fixing the ambiguity terms within a few minutes, and the obtained position results are at the sub-decimeter level. Regarding one selected test, real data from Galileo experimental satellite GIOVE A were used in order to confirm our assumptions. However, since the current Galileo constellation is not sufficient for real-world positioning trials yet, all major results are based on simulated data.     

Ambiguity resolved precise point positioning with GPS and BeiDou

This paper focuses on the contribution of the global positioning system (GPS) and BeiDou navigation satellite system (BDS) observations to precise point positioning (PPP) ambiguity resolution (AR). A GPS + BDS fractional cycle bias (FCB) estimation method and a PPP AR model were developed using integrated GPS and BDS observations. For FCB estimation, the GPS + BDS combined PPP float solutions of the globally distributed IGS MGEX were first performed. When integrating GPS observations, the BDS ambiguities can be precisely estimated with less than four tracked BDS satellites. The FCBs of both GPS and BDS satellites can then be estimated from these precise ambiguities. For the GPS + BDS combined AR, one GPS and one BDS IGSO or MEO satellite were first chosen as the reference satellite for GPS and BDS, respectively, to form inner-system single-differenced ambiguities. The single-differenced GPS and BDS ambiguities were then fused by partial ambiguity resolution to increase the possibility of fixing a subset of decorrelated ambiguities with high confidence. To verify the correctness of the FCB estimation and the effectiveness of the GPS + BDS PPP AR, data recorded from about 75 IGS MGEX stations during the period of DOY 123-151 (May 3 to May 31) in 2015 were used for validation. Data were processed with three strategies: BDS-only AR, GPS-only AR and GPS + BDS AR. Numerous experimental results show that the time to first fix (TTFF) is longer than 6 h for the BDS AR in general and that the fixing rate is usually less than 35 % for both static and kinematic PPP. An average TTFF of 21.7 min and 33.6 min together with a fixing rate of 98.6 and 97.0 % in static and kinematic PPP, respectively, can be achieved for GPS-only ambiguity fixing. For the combined GPS + BDS AR, the average TTFF can be shortened to 16.9 min and 24.6 min and the fixing rate can be increased to 99.5 and 99.0 % in static and kinematic PPP, respectively. Results also show that GPS + BDS PPP AR outperforms single-system PPP AR in terms of convergence time and position accuracy.     

Short and zero baseline analysis of GPS L1 C/A, L5Q, GIOVE E1B, and E5aQ signals

Stochastic properties of GNSS range measurements can accurately be estimated using a geometry-free short and zero baseline analysis method. This method is now applied to dual-frequency measurements from a new field campaign. Results are presented for the new GPS L5Q and GIOVE E5aQ wideband signals, in addition to the GPS L1 C/A and GIOVE E1B signals. As expected, the results clearly show the high precision of the new signals, but they also show, rather unexpectedly, significant, slowly changing variations in the pseudorange code measurements that are probably a result of strong multipath interference on the data. Carrier phase measurement noise is assessed on both frequencies, and finally successful mixed GPS-GIOVE double difference ambiguity resolution is demonstrated.     

Multifrequency algorithms for precise point positioning: MAP3

We present the new MAP3 algorithms to perform static precise point positioning (PPP) from multifrequency and multisystem GNSS observations. MAP3 represents a two-step strategy in which the least squares theory is applied twice to estimate smoothed pseudo-distances, initial phase ambiguities, and slant ionospheric delay first, and the absolute receiver position and its clock offset in a second adjustment. Unlike the classic PPP technique, in our new approach, the ionospheric-free linear combination is not used. The combination of signals from different satellite systems is accomplished by taking into account the receiver inter-system bias. MAP3 has been implemented in MATLAB and integrated within a complete PPP software developed on site and named PCube. We test the MAP3 performance numerically and contrast it with other external PPP programs. In general, MAP3 positioning accuracy with low-noise GPS dual-frequency observations is about 2.5 cm in 2-h observation periods, 1 cm in 10 h, and 7 mm after 1 day. This means an improvement in the accuracy in short observation periods of at least 7 mm with respect to the other PPP programs. The MAP3 convergence time is also analyzed and some results obtained from real triple-frequency GPS and GIOVE observations are presented.