几种附电离层约束GNSS单频PPP性能评估

针对单频精密单点定位(PPP)两种常用的定位模型:非组合模型和附加电离层约束模型,同时综合考虑电离层约束模型三种不同约束策略(常数约束,时空约束,逐步松弛),对比分析了其使用GPS单系统及GPS+BDS双系统观测值的定位收敛时间,定位精度及其优缺点.实验结果表明:使用GPS单系统,附加不同电离层约束对单频PPP收敛时间...     

Application of the TaiWan Ionospheric Model to single-frequency ionospheric delay corrections for GPS positioning

The performance of a three-dimensional ionospheric electron density model derived from FormoSat3/COSMIC GPS Radio Occultation measurements, called the TaiWan Ionosphere Model (TWIM), in removing the ionospheric delays in single-frequency pseudorange observations is presented. Positioning results using TWIM have been compared with positioning results using other ionospheric models, such as the Klobuchar (KLOB) and the global ionospheric model (GIM). C/A code pseudoranges have been observed at three International GPS Service reference stations that are representative of mid-latitude (BOR1 and IRKJ) and low-latitude (TWTF) regions of the ionosphere. The observations took place during 27 geomagnetically quiet days from April 2010 to October 2011. We perform separate solutions using the TWIM, KLOB, GIM ionospheric models and carry out a solution applying no ionospheric correction at all. We compute the daily mean horizontal errors (DMEAN) and the daily RMS (DRMS) for these solutions with respect to the published reference station coordinates. It has demonstrated that TEC maps generate using the TWIM exhibit a detailed structure of the ionosphere, particularly at low-latitude region, whereas the Klobuchar and the GIM only provide the basic diurnal and geographic features of the ionosphere. Also, it is shown that even for lower satellite elevations, the TWIM provides better positioning than the Klobuchar and GIM models. Specifically, using TWIM, the difference of the uncorrected solution (no ionospheric correction), and the other solutions, relative to the uncorrected solution, is 45 % for the mean horizontal error (DMEAN) and 42 % for the horizontal root-mean-square error (DRMS). Using Klobuchar and GIM, the percent for DMEAN only reaches to about 12 % and 3 %, while the values for the DRMS are only 12 and 4 %, respectively. In the vertical direction, all models have a percentage of about 99 and 70 % for the mean vertical error (VMEAN) and vertical root-mean-square error (VRMS), respectively. These percentages show the greater impact of TWIM on the ionospheric correction compared to the other models. In at least 40 % of the observed days and across all stations, TWIM has the smallest DMEAN, VMEAN, DRMS, and VRMS daily values. These values reach 100 % at station TWTF. This shows the overall performance of TWIM is better than the Klobuchar and GIM.     

Enhancing differential GPS using regional ionospheric error models

Distance-dependent errors due to ionospheric refraction complicate ambiguity resolution and limit the accuracy attainable in GPS baseline determination. This paper presents an approach for modelling these errors from the observations of several permanent GPS-stations surrounding the area of interest. Regional ionospheric correction models are produced epoch-by-epoch and satellite-by-satellite. It is shown that after their application, observation residuals, fractional parts of estimated ambiguities, and single-frequency coordinate errors are greatly reduced, thus improving ambiguity resolution even under disturbed ionospheric conditions, with short observation sessions, in the case of baseline lengths of more than 10 km, and with singlefrequency and dual-frequency data.     

不同截止高度角GPS/BDS组合伪距差分定位性能分析

针对在不同截止卫星高度角时,GPS,BDS,GPS/BDS系统间伪距差分定位精度的差异,文中对多系统融合伪距差分定位的数学模型方法进行研究。以香港CORS站6.9km和34.0km的两条基线为例,在截止卫星高度角10°、20°、30°、40°的情况下,进行GPS,BDS,GPS/BDS伪距差分基线解算。结果表明,与34.0km基线相比,6.9km基线伪距差分定位具有更高的精度,在不同截止高度角下,GPS/BDS组合系统在E,N,U方向的定位精度都优于单GPS,BDS系统,且定位结果更加稳定,特别在截止高度角为40°的极端条件下,GPS/BDS组合伪距差分定位精度仍能达到m级左右。     

基于GPS单频接收机的精密单点定位研究

介绍了利用单频GPS接收机进行精密单点定位的数学模型及解算方案,并采用选权拟合法得到比较准确的状态参数初值及其方差-协方差,加快了卡尔曼滤波的收敛。算例结果表明,利用精密卫星星历及卫星钟改正数并采用单频观测值,半个小时后的定位精度可达1~2分米的水平。     

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.     

基于单频GPS精密单点定位算法研究

研究单频GPS精密单点定位的算法,包括单频精密单点定位的回归方程及卡尔曼滤波用于单频精密单点定位.探讨卡尔曼滤波的观测方程和状态方程,给出状态转移矩阵及系统噪声矩阵.通过算例验证在1 s采样率的情况下,定位达到了分米级的精度.     

Real-time kinematic positioning of LEO satellites using a single-frequency GPS receiver

Due to their low cost and low power consumption, single-frequency GPS receivers are considered suitable for low-cost space applications such as small satellite missions. Recently, requirements have emerged for real-time accurate orbit determination at sub-meter level in order to carry out onboard geocoding of high-resolution imagery, open-loop operation of altimeters and radio occultation. This study proposes an improved real-time kinematic positioning method for LEO satellites using single-frequency receivers. The C/A code and L1 phase are combined to eliminate ionospheric effects. The epoch-differenced carrier phase measurements are utilized to acquire receiver position changes which are further used to smooth the absolute positions. A kinematic Kalman filter is developed to implement kinematic orbit determination. Actual flight data from China’s small satellite SJ-9A are used to test the navigation performance. Results show that the proposed method outperforms traditional kinematic positioning method in terms of accuracy. A 3D position accuracy of 0.72 and 0.79 m has been achieved using the predicted portion of IGS ultra-rapid products and broadcast ephemerides, respectively.     

Geometrical aspects of differential GPS positioning

Differential GPS positioning is considered from the purely geometric point of view. The tetrahedron formed by two ground stations and two satellite locations is the basic geometrical building block for differential satellite positioning. Relationships between the various vectors involved in this tetrahedron are described. These relationships are used to develop linear mathematical models which relate the vector baseline between the two ground stations to various kinds of differential GPS observations. Geometrically, all proposed observation types can be considered as either differential range observations or differential range difference observations. In the absence of instrumental and refraction effects, it is found that differential range observations are geometrically superior to differential range difference observations. Some implications of these geometrical considerations to practical differential GPS positioning are discussed.     

Influence of different GPS receiver antenna calibration models on geodetic positioning

To better understand how receiver antenna calibration models contribute to GPS positioning error budget, we compare station positions estimated with different calibration models: igs05.atx, igs08.atx and individual antenna calibrations. First, the impact of switching from the igs05.atx antenna calibration model to the igs08.atx antenna calibration model is investigated using the EUREF Permanent Network historical data set from 1996 until April 2011. It is confirmed that these position offsets can be effectively represented by the igs05.atx to igs08.atx latitude-dependent model. Then, we demonstrate that the position offsets resulting from the use of individual calibrations instead of type mean igs08.atx calibrations can reach up to 1 cm in the up component, while in the horizontal, the offsets generally stay below 4 mm. Finally, using six antennas individually calibrated by a robot as well as in an anechoic chamber, we observe a position agreement of 2 mm in the horizontal component and a bias of 5 mm in the up component. Larger position offsets, dependent on the antenna/radome type, are, however, found when these individual calibrations are compared to type mean calibrations of two tested antennas.     

An improvement to ionospheric delay correction for single-frequency GPS users – the APR-I scheme

 For the commonly used GPS wide-area augmentation systems (WAAS) with a grid ionospheric model, the efficient modelling of ionospheric delays in real time, for single-frequency GPS users, is still a crucial issue which needs further research. This is particularly necessary when differential ionospheric delay corrections cannot be broadcast, when users cannot receive them, or when there are ionospheric anomalies. Ionospheric delays have a severe effect on navigation performance of single-frequency receivers. A new scheme is proposed which can efficiently address the above problems. The robust recurrence technique is based on the efficient combination of single-frequency GPS observations by users and the high-precision differential ionospheric delay corrections from WAAS. Its effectiveness is verified with examples. Received: 24 December 1999 / Accepted 21 February 2001     

The wavelet method as an alternative for reducing ionospheric effects from single-frequency GPS receivers

The ionospheric effect is one of the major errors in GPS data processing over long baselines. As a dispersive medium, it is possible to compute its influence on the GPS signal with the ionosphere-free linear combination of L1 and L2 observables, requiring dual-frequency receivers. In the case of single-frequency receivers, ionospheric effects are either neglected or reduced by using a model. In this paper, an alternative for single-frequency users is proposed. It involves multiresolution analysis (MRA) using a wavelet analysis of the double-difference observations to remove the short- and medium-scale ionosphere variations and disturbances, as well as some minor tropospheric effects. Experiments were carried out over three baseline lengths from 50 to 450 km, and the results provided by the proposed method were better than those from dual-frequency receivers. The horizontal root mean square was of about 0.28 m (1σ).     

单频GPS实时定位精度分析

电离层延迟误差是单频GPS实时/事后定位误差的一个重要来源,目前尚无有效的方法来削弱其影响。针对这一状况,该文首先介绍了单频GPS改正电离层延迟误差的常用方法,通过分析说明了电离层格网数据能够有效改善单频GPS实时/事后定位误差。给出了电离层格网数据的建立、预报方法,并详细介绍了刺入点地心经纬度VTEC值的计算方法、四点格网法内插刺入点天顶方向的总电子含量以及单层模型投影函数。结合算例,分析比较了不同类型电离层改正数据与卫星星历数据对单频GPS实时/事后定位精度的影响。实验结果表明,利用电离层格网预报数据能够显著改善单频GPS的实时/事后导航定位精度,对提高单频GPS定位精度具有一定实用价值。     

Multi-GNSS precise point positioning with raw single-frequency and dual-frequency measurement models

GPS Solutions - The emergence of multiple satellite navigation systems, including BDS, Galileo, modernized GPS, and GLONASS, brings great opportunities and challenges for precise point positioning...     

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...     

BDS/GPS网络差分定位试验分析

针对在传统网络差分定位中,单GPS系统在观测条件不好情况下会出现可用卫星数量偏少甚至不够、观测值存在粗差而影响定位等问题,该文提出BDS/GPS双系统组合网络伪距差分定位的数学模型,并加入基于最小二乘残差法探测粗差观测数据的质量控制算法。基于省CORS网实时BDS/GPS双系统数据,以国产的手持机终端作为流动端,利用BDS/GPS伪距差分平台进行了车载动态试验,根据试验对比和分析,动态定位平面精度优于1m,在加入质量控制算法模式下,定位精度和可靠性都有一定提高。     

Impact of the Halloween 2003 ionospheric storm on kinematic GPS positioning in Europe

Using dual-frequency data from 36 GPS stations from the EUREF Permanent Network (EPN), the influence of the October 30, 2003 Halloween geomagnetic storm on kinematic GPS positioning is investigated. The Halloween storm induced ionospheric disturbances above the northern part of Europe and Scandinavia. It is shown that kinematic position repeatabilities for this period are mainly affected for stations in northern Europe with outliers reaching 12 cm in the horizontal, and 26 cm in the vertical. These magnitudes are shown to be possibly due to the second-order ionospheric delays on GPS signals, not accounted for in the kinematic GPS positioning analysis performed. In parallel, we generate hourly TEC (Total Electron Content) maps on a 1° × 1° grid using the dense EPN network. These TEC maps do not use any interpolation but provide a high resolution in the time and space and therefore allow to better evidence small structures in the ionosphere than the classical 2-hourly 2.5° × 5° grid Global Ionospheric TEC Maps (GIM). Using the hourly 1° × 1° TEC maps, we reconstruct and refine exactly the zones of intense ionosphere activity during the storm, and we show the correlation between the ionospheric activity and assess the quality of GPS-based kinematic positioning performed in the European region.     

电离层VTEC与气象要素对GPS定位结果的影响

本文对FJCORS基准站定位误差序列进行了分析,发现观测误差呈明显的季节性变化,峰值出现在7月,同时分析了定位误差与电离层VTEC和气象要素的关系。结果表明,定位误差与VTEC不相关,而与气象要素存在较强的相关性,气压降低或气温、水汽压升高直接导致误差呈线性增加。     

差分GPS水下立体定位系统的迭代算法分析

差分GPS水下立体定位系统通过将差分GPS定位技术和水下声学定位技术进行集成,实现高精度水下定位。本文基于差分GPS水下立体定位系统的基本观测方程,简要介绍了迭代法的基本原理,从双曲线差分定位观测方程出发,使用求解非线性方程组常用的牛顿迭代法构造迭代方程式,并用实测数据验证了该算法的可行性。