削弱电离层影响的三频TurboEdit周跳处理方法

针对电离层活跃期或磁暴发生时,现有三频周跳探测方法难以正确探测与修复周跳的问题,借鉴双频TurboEdit思想,提出了能够削弱电离层延迟影响的三频TurboEdit方法。该算法中的三频无几何无电离层码相组合和两次历元差分后的相位无几何组合,均能有效削弱电离层延迟对周跳探测的影响。随后利用三频实测数据对本文算法进行了验证,试验结果表明该方法能够消除电离层延迟影响,实现电离层活跃观测条件下动态非差周跳的实时探测与修复。     

三种电离层延迟多频修正算法的比较

电离层延迟多频修正算法在修正电离层延迟的同时会放大观测噪声等伪距误差的影响。分析了电离层延迟双频修正、三频一阶修正和三频二阶修正三种修正算法及观测噪声的影响。以Galileo系统的四个载波频率为例,对不同频率组合下三种修正算法进行了比较。结果表明电离层延迟多频修正中,并不是观测量的频点数越多或修正掉的高阶项越多修正精度越高,还与观测伪距噪声的大小以及采用的修正方法有关。为多频测距系统的电离层延迟修正算法和最佳频率组合设计提供了一种可行的分析方法。     

三频电离层延迟改正中多路径误差和观测噪声的削弱算法

多频测距系统可以借助多频观测数据削弱电离层延迟的影响,但多频改正算法在改正电离层延迟项的同时会不同程度地放大多路径误差、观测噪声等伪距误差的影响。其中利用三频数据可以将电离层延迟改正至二阶项,也可以只改正至一阶项,分别称为三频二阶改正和三频一阶改正。首次推导了利用三频观测数据削弱伪距中多路径效应和观测噪声等误差的算法,使三频电离层延迟改正中伪距误差的影响大大减小。通过对三频实测数据的处理和分析验证了算法的有效性并给出了一些有益的结论和建议:在利用三频观测数据进行电离层改正时,首先改正伪距中的多路径误差和观测噪声,然后采用三频二阶改正算法将电离层延迟改正至二阶项,将有效提高伪距改正精度。如果不能有效削弱这些误差的影响,宜采用三频一阶改正或双频改正。     

Application of SWACI products as ionospheric correction for single-point positioning: a comparative study

In Global Navigation Satellite Systems (GNSS) using L-band frequencies, the ionosphere causes signal delays that correspond with link related range errors of up to 100 m. In a first order approximation the range error is proportional to the total electron content (TEC) of the ionosphere. Whereas this first order range error can be corrected in dual-frequency measurements by a linear combination of carrier phase- or code-ranges of both frequencies, single-frequency users need additional information to mitigate the ionospheric error. This information can be provided by TEC maps deduced from corresponding GNSS measurements or by ionospheric models. In this paper we discuss and compare different ionospheric correction methods for single-frequency users. The focus is on the comparison of the positioning quality using dual-frequency measurements, the Klobuchar model, the NeQuick model, the IGS TEC maps, the Neustrelitz TEC Model (NTCM-GL) and the reconstructed NTCM-GL TEC maps both provided via the ionosphere data service SWACI (http://swaciweb.dlr.de) in near real-time. For that purpose, data from different locations covering several days in 2011 and 2012 are investigated, including periods of quiet and disturbed ionospheric conditions. In applying the NTCM-GL based corrections instead of the Klobuchar model, positioning accuracy improvements up to several meters have been found for the European region in dependence on the ionospheric conditions. Further in mid- and low-latitudes the NTCM-GL model provides results comparable to NeQuick during the considered time periods. Moreover, in regions with a dense GNSS ground station network the reconstructed NTCM-GL TEC maps are partly at the same level as the final IGS TEC maps.     

GPS现代化后电离层折射误差高阶项的三频改正方法

研究了电离层对GPS观测信号的主要影响及电离层折射误差模型,总结了电离层双频改正模型。针对GPS现代化中增加的第三频率,系统推导了三个频率的电离层改正模型及相位观测值无电离层组合(LC组合)模型。该模型将电离层折射误差模型改正至二阶项,可进一步提高GPS定位精度,同时,为GPS定位中其他误差的改正及分离、周跳的探测等提供了有力的技术手段。     

A procedure for the significance testing of unmodeled errors in GNSS observations

It is a crucial task to establish a precise mathematical model for global navigation satellite system (GNSS) observations in precise positioning. Due to the spatiotemporal complexity of, and limited knowledge on, systematic errors in GNSS observations, some residual systematic errors would inevitably remain even after corrected with empirical model and parameterization. These residual systematic errors are referred to as unmodeled errors. However, most of the existing studies mainly focus on handling the systematic errors that can be properly modeled and then simply ignore the unmodeled errors that may actually exist. To further improve the accuracy and reliability of GNSS applications, such unmodeled errors must be handled especially when they are significant. Therefore, a very first question is how to statistically validate the significance of unmodeled errors. In this research, we will propose a procedure to examine the significance of these unmodeled errors by the combined use of the hypothesis tests. With this testing procedure, three components of unmodeled errors, i.e., the nonstationary signal, stationary signal and white noise, are identified. The procedure is tested by using simulated data and real BeiDou datasets with varying error sources. The results show that the unmodeled errors can be discriminated by our procedure with approximately 90% confidence. The efficiency of the proposed procedure is further reassured by applying the time-domain Allan variance analysis and frequency-domain fast Fourier transform. In summary, the spatiotemporally correlated unmodeled errors are commonly existent in GNSS observations and mainly governed by the residual atmospheric biases and multipath. Their patterns may also be impacted by the receiver.     

Ionospheric correction using NTCM driven by GPS Klobuchar coefficients for GNSS applications

Global Navigation Satellite Systems (GNSS) require mitigation of ionospheric propagation errors because the ionospheric range errors might be larger than tens of meters at the zenith direction. Taking advantage of the frequency-dispersive property of ionospheric refractivity, the ionospheric range errors can be mitigated in dual-frequency applications to a great extent by a linear combination of carrier phases or pseudoranges. However, single-frequency GNSS operations require additional ionospheric information to apply signal delay or range error corrections. To aid single-frequency operations, the global positioning system (GPS) broadcasts 8 coefficients as part of the navigation message to drive the ionospheric correction algorithm (ICA) also known as Klobuchar model. We presented here an ionospheric correction algorithm called Neustrelitz TEC model (NTCM) which can be used as complementary to the GPS ICA. Our investigation shows that the NTCM can be driven by Klobuchar model parameters to achieve a significantly better performance than obtained by the mother ICA algorithm. Our research, using post-processed reference total electron content (TEC) data from more than one solar cycle, shows that on average the RMS modeled TEC errors are up to 40% less for the proposed NTCM model compared to the Klobuchar model during high solar activity period, and about 10% less during low solar activity period. Such an approach does not require major technology changes for GPS users rather requires only introducing the NTCM approach a complement to the existing ICA algorithm while maintaining the simplicity of ionospheric range error mitigation with an improved model performance.     

顾及GEO卫星约束的长距离BDS三频整周模糊度解算

长距离BDS三频载波相位整周模糊度解算受大气误差残余的影响较大,GEO卫星相对于地球静止也非常不利于载波相位整周模糊度的解算。利用GEO卫星的信号传播路径相对较稳定、大气延迟误差的影响不随卫星空间位置变化的特点,对GEO卫星进行更符合实际情况的大气延迟误差约束研究。利用GEO卫星B2和B3载波相位整周模糊度线性关系,降低测站差分电离层延迟误差残余对模糊度备选值的影响,进行B2和B3载波相位整周模糊度备选值的选择。通过三频载波相位整周模糊度间不包含观测误差影响的线性关系对模糊度备选值组合进行检测,并对模糊度搜索空间进行约束。利用历元间GEO卫星的模糊度备选值判断历元间电离层延迟误差残余的变化,对GEO卫星的参数估计进行更符合实际情况的约束。研究了顾及GEO卫星实际大气延迟变化和整周模糊度约束的长距离BDS三频载波相位整周模糊度解算方法。提出了利用历元间模糊度备选值确定电离层延迟约束值的方法,对GEO卫星历元间随机游走的约束值进行符合实际情况的调整。试验结果表明,本文的方法能够提高三频载波相位整周模糊度解算的效率和测站位置的精度。     

利用GPS三频观测值监测电离层TEC及其变化率

三频观测数据为监测电离层总电子含量提供了更多的观测值选择。在双频观测值估算电离层总电子含量的原理基础上,利用不同纬度地区的三频GPS观测资料计算获得了电离层总电子含量值及其变化率。分析结果表明：由于GPS接收机码间偏差的影响,不同频率间组合获得的电离层总电子含量结果出现较大的系统差异,使用不同频率组合获得的电离层TEC变化率有很好的一致性。     

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.     

BDS三频与双频模糊度解算性能分析

全球导航卫星系统(GNSS)已进入多频多系统时代。针对两条短基线,对比分析BDS三频与BDS／GPS三频对于BDS双频与BDS／GPS双频在模糊度固定率、成功率及定位精度等方面的改善情况。结果表明,BDS三频与BDS／GPS三频可有效提高BDS双频与BDS／GPS双频的固定率和成功率,但BDS三频与BDS／GPS三频对于BDS双频与BDS／GPS双频的定位精度基本上没有改善。      

Performance analysis of triple-frequency ambiguity resolution with BeiDou observations

We investigate triple-frequency ambiguity resolution performance using real BeiDou data. We test four ambiguity resolution (AR) methods which are applicable to triple-frequency observations. These are least squares ambiguity decorrelation adjustment (LAMBDA), GF-TCAR (geometry-free three-carrier ambiguity resolution), GB-TCAR (geometry-based three-carrier ambiguity resolution) and GIF-TCAR (three-carrier ambiguity resolution based on the geometry-free and ionospheric-free combination). A comparison between LAMBDA, GF-TCAR and GB-TCAR was conducted over three short baselines and two medium baselines. The results indicated that LAMBDA is optimal in both short baseline and medium baseline cases. However, the performances of GB-TCAR and LAMBDA differ slightly for short baselines. Compared with GF-TCAR, which uses the geometry-free model, the GB-TCAR using the geometry-based model improves the AR performance significantly. Compared with dual-frequency observations, the LAMBDA AR results show a significant improvement when using triple-frequency observations over short baselines. The performance of GIF-TCAR is evaluated using multi-epoch observations. The results indicated that multi-path errors on carrier phases will have a significant influence on GIF-TCAR AR results, which leads to different GIF-TCAR AR performance for different type of satellites. For GEO (Geostationary Orbit) satellites, the ambiguities can barely be correctly fixed because the multi-path errors on carrier phases are very systematic. For IGSO (Inclined Geosynchronous Orbit) and MEO (Medium Earth Orbit) satellites, when the elevation cutoff angle is set as 30°, several tens to several hundreds of epochs are needed for correctly fixing the narrow lane ambiguities. The comparison of positioning performance between dual-frequency observations and triple-frequency observations was also conducted. The results indicated that a minor improvement can be achieved by using triple-frequency observations compared with using dual-frequency observations.     

Ionospheric error contribution to GNSS single-frequency navigation at the 2014 solar maximum

For single-frequency users of the global satellite navigation system (GNSS), one of the main error contributors is the ionospheric delay, which impacts the received signals. As is well-known, GPS and Galileo transmit global models to correct the ionospheric delay, while the international GNSS service (IGS) computes precise post-process global ionospheric maps (GIM) that are considered reference ionospheres. Moreover, accurate ionospheric maps have been recently introduced, which allow for the fast convergence of the real-time precise point position (PPP) globally. Therefore, testing of the ionospheric models is a key issue for code-based single-frequency users, which constitute the main user segment. Therefore, the testing proposed in this paper is straightforward and uses the PPP modeling applied to single- and dual-frequency code observations worldwide for 2014. The usage of PPP modeling allows us to quantify—for dual-frequency users—the degradation of the navigation solutions caused by noise and multipath with respect to the different ionospheric modeling solutions, and allows us, in turn, to obtain an independent assessment of the ionospheric models. Compared to the dual-frequency solutions, the GPS and Galileo ionospheric models present worse global performance, with horizontal root mean square (RMS) differences of 1.04 and 0.49 m and vertical RMS differences of 0.83 and 0.40 m, respectively. While very precise global ionospheric models can improve the dual-frequency solution globally, resulting in a horizontal RMS difference of 0.60 m and a vertical RMS difference of 0.74 m, they exhibit a strong dependence on the geographical location and ionospheric activity.     

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.     

GPS+BDS中长距离RTK定位算法及结果分析

GPS/BDS中长距离RTK定位因为电离层和对流层残余误差的影响,其性能相对于常规RTK有所降低。将GPS/BDS卫星双差电离层误差和对流层误差作为参数,采用卡尔曼滤波进行实时估计。为了验证算法的有效性,利用武汉地区103 km静态基线24 h双频观测数据,分析了GPS和BDS单系统以及二者组合双系统中长距离RTK定位性能。实验结果表明,精确估计的双差电离层残余误差达到米级、对流层误差达到分米级;经过改正后,GPS/BDS单系统的定位精度在1 cm左右,组合双系统则实现了中长距离基线毫米级的高精度定位。     

Calibration errors on experimental slant total electron content (TEC) determined with GPS

The Global Positioning System (GPS) has become a powerful tool for ionospheric studies. In addition, ionospheric corrections are necessary for the augmentation systems required for Global Navigation Satellite Systems (GNSS) use. Dual-frequency carrier-phase and code-delay GPS observations are combined to obtain ionospheric observables related to the slant total electron content (sTEC) along the satellite-receiver line-of-sight (LoS). This observable is affected by inter-frequency biases [IFB; often called differential code biases (DCB)] due to the transmitting and the receiving hardware. These biases must be estimated and eliminated from the data in order to calibrate the experimental sTEC obtained from GPS observations. Based on the analysis of single differences of the ionospheric observations obtained from pairs of co-located dual-frequency GPS receivers, this research addresses two major issues: (1) assessing the errors translated from the code-delay to the carrier-phase ionospheric observable by the so-called levelling process, applied to reduce carrier-phase ambiguities from the data; and (2) assessing the short-term stability of receiver IFB. The conclusions achieved are: (1) the levelled carrier-phase ionospheric observable is affected by a systematic error, produced by code-delay multi-path through the levelling procedure; and (2) receiver IFB may experience significant changes during 1 day. The magnitude of both effects depends on the receiver/antenna configuration. Levelling errors found in this research vary from 1.4 total electron content units (TECU) to 5.3 TECU. In addition, intra-day vaiations of code-delay receiver IFB ranging from 1.4 to 8.8 TECU were detected.     

Enhancement of the accuracy of single-epoch GPS positioning for long baselines by local ionospheric modelling

Single-epoch relative GPS positioning has many advantages, especially for monitoring dynamic targets. In this technique, errors occurring in previous epochs cannot affect the position accuracy at the current epoch, but careful processing is required, and resolving carrier phase ambiguities is essential. Statistical ambiguity resolution functions have been used to determine the best values of these ambiguities. The function inputs include as a minimum the known base station position, the approximate roving antenna “seed” position, and the dual-frequency carrier phase measurements from both receivers. We investigate different solutions to find the ambiguity function inputs that achieve the highest ambiguity resolution success rate. First, we address the rover seed position. A regionally filtered undifferenced pseudorange coordinate solution proves better than a double-differenced one. Multipath errors approximately repeat themselves every sidereal day in the case of static or quasi-static antennas; applying a sidereal filter to the pseudorange-derived positions mitigates their effects. Second, we address the relative carrier phase measurements, which for medium to long baselines are significantly affected by ionospheric propagation errors imperfectly removed during differencing. In addition to the International GNSS Service ionospheric model, we generate a local pseudorange-based ionospheric correction. Applying this correction improves the quality of the phase measurements, leading to more successful ambiguity resolution. Temporally smoothing the correction by means of a Kalman filter further improves the phase measurements. For baselines in the range 60–120 km, the mean absolute deviation of single-epoch coordinates improves to 10–20 cm, from 30–50 cm in the default case.     

GPS/Galileo long baseline computation: method and performance analyses

Modernized GPS and Galileo will provide triple-frequency signals for civil use, generating a high interest to examine the improvement of positioning performance using the triple-frequency signals from both constellations over baselines up to hundreds or thousands of kilometers. This study adopts a generalized GPS/Galileo long-range approach to process the mutually compatible GPS and Galileo triple-frequency measurements for high-precision long baseline determination. The generalized approach has the flexibility to deal with GPS and Galileo constellations separately or jointly, and also the capability to handle dual or triple-frequency measurements. We compared the generalized long-range approach with the Bernese v5.0 software on two test baselines located in East Asia and obtained highly compatible computational results. Further, in order to assess possible improvement of GPS/Galileo long baseline determination compared with the current dual-frequency (L1/L2) GPS, we simulated GPS and Galileo measurements of the test baselines. It is shown that the current level of accuracy of daily baseline solutions can be improved by using the additional Galileo constellation. Both the additional constellation and the triple-frequency measurements can improve ambiguity resolution performance, but single-constellation triple-frequency ambiguity resolution is more resistant to the influences of code noise and multipath than dual-constellation dual-frequency ambiguity resolution. Therefore, in environments where large code noise or multipath is present, the use of triple-frequency measurements is the main factor for improving ambiguity resolution performance.     

Modeling and quality control for reliable precise point positioning integer ambiguity resolution with GNSS modernization

Recent research has demonstrated that the undifferenced integer ambiguities can be recovered using products from a network solution. The standard dual-frequency PPP integer ambiguity resolution consists of two aspects: Hatch-Melbourne-Wübbena wide-lane (WL) and ionosphere-free narrow-lane (NL) integer ambiguity resolution. A major issue affecting the performance of dual-frequency PPP applications is the time it takes to fix these two types of integer ambiguities, especially if the WL integer ambiguity resolution suffers from the noisy pseudorange measurements and strong multipath effects. With modernized Global Navigation Satellite Systems, triple-frequency measurements will be available to global users and an extra WL (EWL) model with very long wavelength can be formulated. Then, the easily resolved EWL integer ambiguities can be used to construct linear combinations to accelerate the PPP WL integer ambiguity resolution. Therefore, we propose a new reliable procedure for the modeling and quality control of triple-frequency PPP WL and NL integer ambiguity resolution. First, we analyze a WL integer ambiguity resolution model based on triple-frequency measurements. Then, an optimal pseudorange linear combination which is ionosphere-free and has minimum measurement noise is developed and used as constraint in the WL and the NL integer ambiguity resolution. Based on simulations, we have investigated the inefficiency of dual-frequency WL integer ambiguity resolution and the performance of EWL integer ambiguity resolution. Using almanacs of GPS, Galileo and BeiDou, the performances of the proposed triple-frequency WL and NL models have been evaluated in terms of success rate. Comparing with dual-frequency PPP, numerical results indicate that the proposed triple-frequency models can outperform the dual-frequency PPP WL and NL integer ambiguity resolution. With 1 s sampling rate, generally, only several minutes of data are required for reliable triple-frequency PPP WL and NL integer ambiguity resolution. Under benign observation situations and good geometries, the integer ambiguity can be reliably resolved even within 10 s.