Impact of systematic errors on precise long-baseline kinematic GPS positioning

Many kinematic GPS applications rely on high accuracy, which usually requires the ambiguities to be fixed. Normally, a reference station in the rover’s vicinity is needed for successful ambiguity resolution. Alternatively, a network surrounding the rover and allowing one to derive area correction parameters is needed. Unfortunately, both approaches are not feasible in certain situations. This paper is a contribution to precise kinematic positioning over long baselines. Atmospheric refraction becomes critical in the error budget, but progress has been made to use numerical weather models to derive tropospheric corrections, for instance. The spatial correlation of both ionospheric and tropospheric propagation delays is investigated in this paper and special attention is paid on the systematic error behavior of tropospheric refraction. The principles developed are applied to an extended reliability test of the ambiguities. Finally, it is demonstrated in positioning experiments that kinematic positioning retrieval with fixed ambiguities is actually possible for baselines between 150 and 300 km with an accuracy of approximately 2 cm in post-mission processing.

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Spatially convergent GPS kinematic positioning

It is a known fact that obtaining accurate GPS carrier-phase measurements involves fixed, unknown whole-cycle ambiguity parameters. As the use of cosine functions to eliminate any double-difference integer ambiguities causes spatial ambiguity problems, both reasonably approximated positions and wavelength-dependent convergence ranges are of the utmost importance. Differential GPS-based position solutions are first smoothed to create a polynomial trajectory, leading to less variable position approximations. Long-wavelength wide-lane phase combinations will then be utilized to facilitate convergent GPS positioning, on a stage-by-stage basis. Although double-difference ionospheric path delays are often interpreted as nuisance parameters, they can be obtained when the respective cosines of the original L1 and L2 carrier phases undergo a simultaneous least-squares estimation. In particular, quadratic forms of the estimated phase residuals will be linked with hypothesis testing to allow for a meaningful statistical inference. Some low-dynamics experiments are then performed to prove the feasibility of the proposed hierarchical positioning concept. Electronic Publication     

基于LAMBDA方法的GPS动态相对定位

基于载波相位观测值的RTK(Real time kinematic)定位技术能够在野外实时得到厘米级定位精度,核心技术是在动态条件下快速固定整周模糊度,解算动态条件下的模糊度参数.采用LAMBDA方法快速固定整周模糊度完成初始化,实时探测周跳,搜索并固定新的模糊度.用C++编制软件实现该算法,通过实测数据的计算,验证文...     

GPS rapid static and kinematic positioning based on GPS active network

This paper presents a data processing strategy for GPS kinematic Positioning by using a GPS active network to model the GPS errors in double difference observable.Firstly,the double difference residuals are estimated between the reference stations in the active network.Then the errors at a user station are predicted as the network corrctions to user measurements,based on the location of the user,Finally conventional kinematic positioning algorithms can be applied to determine the position of the user station.As an example,continuous 24-hour GPS data in March 2001 has been processed by this method.It clearly demonstrates that,after applying these corrections to a user within the network,both the success rate for ambiguity resolution and the positioning accuracy have been significantly improved.     

GPS动态定位自适应卡尔曼滤波算法研究

Sage-Husa滤波和强跟踪滤波是2种常规的自适应卡尔曼滤波,有各自的优缺点。综合2种滤波的特点,给出一种抗粗差的修正算法,实验效果比较好,能有效抑制少部分粗差带来的影响,计算结果表明效果比较理想。     

Removing attitude-related variations in the line-of-sight for kinematic GPS positioning

We are presenting a method for removing attitude-related variations (ATTRVs) in dynamic 1 Hz GPS positioning. The ATTRVs are separated into vertical and horizontal components. These result from the translational and rotational motions of the vehicle, which is a marine research vessel in our case. We have developed new observation equations that use corrected pseudoranges and carrier phases to account for ATTRVs. In the present contribution, we are only focusing on the vertical signals. These modeled ATTRVs are included as corrections in the line-of-sight (LoS) to each GPS satellite in the RINEX data sets using a new software called RNXATTCOR. Precise IGS sp3-orbits are used as inputs together with precise lever arm coordinates of the onboard GPS antennas, observations from the marine inertial navigation system and a priori 3D position of the vessel. The corrected RINEX data sets are then processed using kinematic processing or sequential processing in Precise Point Positioning (PPP) mode. The reduction of the standard deviation from a running mean in the final processed GPS time series is about 95%. The current method is being proposed for marine geodesy science applications such as along-track calibration/validation of altimetry products, and also for applications related to offshore kinematic high precision GPS positioning such as drilling, offshore platforms stability, marine pipeline positioning, earthquake monitoring and tsunami detection.     

A windowing-recursive approach for GPS real-time kinematic positioning

All conventional Kalman filtering methods depend to a great extent on dynamic models for describing the motion state of vehicle. However, low-cost GPS navigation systems do not provide velocity and acceleration measurements to construct dynamic models. Therefore, it is rather difficult to establish reasonable dynamic models. A windowing-recursive approach (WRA) which employs previous positions to predict the current position is proposed, and the transition matrix is modeled for transforming the previous positions to the current one. Two typical transition matrices are constructed by numerical polynomial fitting and extrapolation. A real vehicular GPS experiment is carried out to demonstrate the WRA performances in two relative positioning scenarios. The data are processed by the least squares approach and by WRA using the two developed transition matrices. The results show that the WRA performed excellently in a high sampling rate data. In case of a lower sampling rate, higher-order polynomial fitting and extrapolation models work better than lower-order models for a given window. In addition, the extrapolation models can alleviate the computation burdens significantly relative to the polynomial fitting models.     

GPS observations of the ionospheric F2-layer behavior during the 20th November 2003 geomagnetic storm over South Korea

The ionospheric F2-layer peak density (NmF2) and its height (hmF2) are of great influence on the shape of the ionospheric electron density profile Ne (h) and may be indicative of other physical processes within the ionosphere, especially those due to geomagnetic storms. Such parameters are often estimated using models such as the semiempirical international reference ionosphere (IRI) models or are measured using moderately priced to expensive instrumentation, such as ionosondes or incoherent scatter radars. Global positioning system (GPS) observations have become a powerful tool for mapping high-resolution ionospheric structures, which can be used to study the ionospheric response to geomagnetic storms. In this paper, we describe how 3-D ionospheric electron density profiles were produced from data of the dense permanent Korean GPS network using the tomography reconstruction technique. These profiles are verified by independent ionosonde data. The responses of GPS-derived parameters at the ionospheric F2-layer to the 20th November 2003 geomagnetic storm over South Korea are investigated. A fairly large increase in the electron density at the F2-layer peak (the NmF2) (positive storm) has been observed during this storm, which is accompanied by a significant uplift in the height of the F2 layer peak (the hmF2). This is confirmed by independent ionosonde observations. We suggest that the F2-layer peak height uplift and NmF2 increase are mainly associated with a strong eastward electric field, and are not associated with the increase of the O/N₂ ratio obtained from the GUVI instruments aboard the TIMED satellite. It is also inferred that the increase in NmF2 is not caused by the changes in neutral composition, but is related to other nonchemical effects, such as dynamical changes of vertical ion motions induced by winds and E × B drifts, tides and waves in the mesosphere/lower thermosphere region, which can be dynamically coupled upward to generate ionospheric perturbations and oscillations.     

GPS导航中的抗差自适应Kalman滤波算法

GPS导航与定位的质量取决于对动态载体函数模型和随机模型的认知。本文首先基于机动载体的当前统计模型 ,设计了离散系统的Kalman滤波器 ,进而基于方差分量估计给出了一种适合GPS动态定位的抗差自适应卡尔曼滤波算法。该算法模型简单 ,实时性好。实测数据计算结果表明 ,滤波导航解能有效地控制观测异常和动态扰动异常对导航解的影响 ,使导航解更能反映导航目标的真实情况     

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。     

The ionospheric impact of the October 2003 storm event on Wide Area Augmentation System

The United States Federal Aviation Administrations (FAA) Wide-Area Augmentation System (WAAS) for civil aircraft navigation is focused primarily on the Conterminous United States (CONUS). Other Satellite-Based Augmentation Systems (SBAS) include the European Geostationary Navigation Overlay Service (EGNOS) and the Japanese Multi-transport Satellite-based Augmentation System (MSAS). Navigation using WAAS requires accurate calibration of ionospheric delays. To provide delay corrections for single frequency global positioning system (GPS) users, the wide-area differential GPS systems depend upon accurate determination of ionospheric total electron content (TEC) along radio links. Dual-frequency transmissions from GPS satellites have been used for many years to measure and map ionospheric TEC on regional and global scales. The October 2003 solar-terrestrial events are significant not only for their dramatic scale, but also for their unique phasing of solar irradiance and geomagnetic events. During 28 October, the solar X-ray and EUV irradiances were exceptionally high while the geomagnetic activity was relatively normal. Conversely, 29–31 October was geomagnetically active while solar irradiances were relatively low. These events had the most severe impact in recent history on the CONUS region and therefore had a significant effect on the WAAS performance. To help better understand the event and its impact on WAAS, we examine in detail the WAAS reference site (WRS) data consisting of triple redundant dual-frequency GPS receivers at 25 different locations within the US. To provide ground-truth, we take advantage of the three co-located GPS receivers at each WAAS reference site. To generate ground-truth and calibrate GPS receiver and transmitter inter-frequency biases, we process the GPS data using the Global Ionospheric Mapping (GIM) software developed at the Jet Propulsion Laboratory. This software allows us to compute calibrated high resolution observations of TEC. We found ionospheric range delays up to 35 m for the day-time CONUS during quiet conditions and up to 100 m during storm time conditions. For a quiet day, we obtained WAAS planar fit slant residuals less than 2 m (0.4 m root mean square (RMS)) and less than 25 m (3.4 m RMS) for the storm day. We also investigated ionospheric gradients, averaged over distances of a few hundred kilometers. The gradients were no larger than 0.5 m over 100 km for a quiet day. For the storm day, we found gradients at the 4 m level over 100 km. Similar level gradients are typically observed in the low-latitude region for quiet or storm conditions.     

Reparameterization of single difference and undifferenced kinematic GPS positioning models

A series of advantages of single difference(SD)and undifferenced(ZD)models are given as compared with the double difference(DD)model.However,rank defects exist in SD and ZD models.The reparameterization method is provided to resolve this rank defect problem by estimating some combinations of the unknowns rather than the unknowns themselves.The reparameterization of SD and ZD functional models is discussed in detail with their stochastic models.The theoretical confirmation of the equivalence of undifferenced and differenced models is described in a straightforward way.The relationship between SD and ZD residuals is given and verified for some special purposes,e.g.research on the stochastical properties of GPS observations.     

Use of phase data for accurate differential GPS kinematic positioning

DifferentialGPS land kinematic positioning tests conducted at velocities of20 to100 km/h over a baseline of1,000 km using a combination of pseudo-range and phase measurements are described. An algorithm designed for high reliability and accuracy of1 to2 m in real time field operational mode was utilized. The relatively long baseline used for the tests provided valuable information on the effects of broadcast ephemeris errors on the differential results. The tests were conducted with two Texas InstrumentsTI4100 receivers using both theP andC/A codes to assess the effect of both code measurement noise, and ionospheric irregularities on differential positioning over such a baseline. The use of cesium clocks to constrain time was also tested. Accuracies (in terms of repeatabilities) of the order of1 to3 ppm, i.e.,1 to3 m, were obtained.     

Performance evaluation of different ionospheric models in single-frequency code-based differential GPS positioning

Differential ionospheric slant delays are obtained from a quiet-time, three-dimensional ionospheric electron density model, called the TaiWan Ionosphere Model (TWIM), to be used in code-based differential GPS positioning. The code observations are acquired from nine continuously operating GPS stations around Taiwan whose baseline ranged from 19 to 340 km. Daily 24-hour epoch-per-epoch positioning obtained for 70 most geomagnetic quiet days (2008–2010) for each of the 72 baselines. The performance of TWIM has been compared with the standard operational Klobuchar model (KLB) used by typical single-frequency receivers and the IGS global ionospheric model (GIM). Generally, TWIM performed well in reducing the differential ionospheric delay especially for long baselines and different levels of low solar activity. It has a much better performance compared to the operational KLB model. TWIM also performed similarly with GIM, though GIM has the best performance overall. GIM has the best ionospheric gradient estimates among the three models whose differential ionospheric delay-to-horizontal error ratio is more than 0.25. This is followed closely by TWIM with about 0.20. KLB only has a ratio of <0.10. The similarity of the performance of TWIM and GIM demonstrates the feasibility of TWIM in correcting for differential ionospheric delays in the C/A code pseudorange that is caused by electron density gradients in the ionosphere. It can provide decimeter-to-centimeter level accuracy in differential GPS positioning for single-frequency receivers during geomagnetic quiet conditions across all seasons and different levels of low solar activities.     

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.     

An analysis of carrier phase differential kinematic GPS positioning using DynaPos

A series of activities have been carried out at the University of New Brunswick in an effort to evaluate advances in long-range marine kinematic differential positioning. These activities involved processing and analysis of GPS carrier phase kinematic data sets. Some of the data was collected by UNB and some was provided by The XYZs of GPS Inc. Data were collected using Trimble 5700 and Ashtech Z-12 receivers. The data sets were processed using the software DynaPos provided by the The XYZs of GPS Inc. The best results obtained in our analysis indicate an agreement of 5 cm RMS for the horizontal component and 12 cm RMS for the vertical component between two ionospheric-delay free solutions, in baselines varying from 40 to 100 km.     

基于GPS的2003年10月28日太阳耀斑的电离层响应研究

本文利用VTEC(the Vertical Total Electron Contents)增量和VTEC变化率分析了电离层在2003年10月28日太阳耀斑期间中国的四个IGS跟踪站的响应情况.通过分析比较说明用VTEC变化率似更适合探测电离层对太阳耀斑的响应,并有望发现耀斑期间电离层的一些扰动现象,但在能得到高精度的绝对离层延迟的情况下,利用VTEC增量能准确全面地反映电离层对耀斑响应的整体变化情况.     

Performance assessment of single- and dual-frequency BeiDou/GPS single-epoch kinematic positioning

The first results of the short baseline single-epoch kinematic positioning based on dual-frequency real BeiDou/GPS data are presented. The performance of the BeiDou/GPS single-epoch positioning is demonstrated in both static and kinematic modes and compared with corresponding GPS-only performance. It is shown that the availability and reliability of the single-frequency BeiDou/GPS and dual-frequency BeiDou single-epoch kinematic positioning are comparable to those of the dual-frequency GPS. The fixed rate and reliability of ambiguity resolution for the single- and dual-frequency BeiDou/GPS are remarkably improved as compared to that of GPS-only, especially in case of high cutoff elevations. For positioning accuracy with fixed ambiguities, the BeiDou/GPS single-epoch solutions are improved by 23 and 4 % relative to the GPS-only case for two short baseline tests of 8 km, respectively. These results reveal that dual-frequency BeiDou real-time kinematic (RTK) is already applicable in Asia–Pacific areas and that single-frequency BeiDou/GPS RTK is also achievable but only with initialization of several seconds. More promisingly, the dual-frequency BeiDou/GPS RTK can overcome the difficulties with GPS-only RTK under the challenging conditions assuming, of course, that the additional BeiDou satellites are visible.     

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.