Optimum stochastic modeling for GNSS tropospheric delay estimation in real-time

GPS Solutions - In GNSS data processing, the station height, receiver clock and tropospheric delay (ZTD) are highly correlated to each other. Although the zenith hydrostatic delay of the...     

基于北斗的精密单点定位估计对流层天顶延迟精度分析

通过全球导航卫星（GNSS）系统获取对流层天顶延迟对于气象和电波折射修正具有重要应用价值。利用自主研发的静态精密单点定位软件CRPPP,基于国际GNSS地球动力学服务局（IGS）发布的北斗系统（BDS）精密星历和精密钟差,给出了BDS估算天顶延迟结果。以IGS发布的全球定位系统（GPS）结果为参考对比,BDS估算天顶延迟结果平均偏差优于5mm,均方根误差（rms）优于2．3cm．同时,给出了西沙地区GPS与BDS估计结果,结果表明：利用北斗系统估计的对流层天顶延迟精度与GPS相当。     

同时估计电离层延迟的单频精密单点定位方法

提出一种基于单频码和相位观测量的单频精密单点定位方法,将每个观测量的电离层延迟量与接收机钟差、对流层天顶延迟、接收机位置、相位模糊度一起作为未知参数。采用约化参数的平方根信息滤波与平滑算法进行参数解算。该方法适用于实时定位和事后处理,且不需要外部的电离层模型。采用全球分布的32个IGS监测站16 d实测数据进行静态解算试验,结果表明E、N、U方向的RMS分别为0.023 m、0.018 m、0.059 m;基于一组机载GPS数据进行动态解算试验,得到E、N、U方向的RMS(与载波相位动态相对定位结果比较)分别为0.168 m、0.151 m、0.172 m。     

A new GPS/BDS tropospheric delay resolution approach for monitoring deformation in super high-rise buildings

A new approach for deformation monitoring of super high-rise building using GPS/BDS technology is proposed for the case when prior coordinates are known and the baseline is short but has a large height difference. The approach is based on the ambiguity function method (AFM). Considering that the double-differenced (DD) troposphere delay residual error cannot be ignored, the relative zenith tropospheric delay (RZTD) parameter is introduced into the original AFM equation. Thus, the RZTD and 3D coordinate parameters are together obtained through the modified AFM (MAFM). Due to the low computational efficiency of conventional AFM, an improved particle swarm optimization (IPSO) algorithm is used to search the four optimal parameters X/Y/Z/RZTD and replaces the grid search method. In this study, GPS/BDS deformation monitoring data for buildings with approximately 290 m height difference were used to verify the feasibility of the proposed MAFM. Numerical results show a single-epoch average computation time of approximately 0.3 s, which meets the requirements of near-real-time dynamic monitoring. The average accuracy of the GPS single-epoch RZTD solution is better than 1 cm, the combined GPS/BDS MAFM performance outperforms the GPS-only system, and using multi-epoch observations can further improve the accuracy of the RZTD solution. After RZTD correction, GPS/BDS monitoring precision can be improved, particularly the height dimension, whose precision is improved by approximately 6 cm.     

Analysis of distortions in the National Geodetic Network of Saudi Arabia

Summary The first order horizontal control network of Saudi Arabia, which is a purely terrestrial network established in early 1970's by EDM traversing, is analyzed for distortions. The analysis is based on comparisons of the terrestrial network positions with those obtained from a 22 point GPS network uniformly covering the country. An analysis of the discrepancies in slant ranges obtained from the two networks indicates that the terrestrial network scale is smaller than that of the GPS network by about 1.68 parts per million (ppm). The scale appears to change with position suggesting some small systematic distortion of the terrestrial network relative to the GPS network. A similar analysis of the discrepancies in horizontal distance, azimuth and zenith distance also points to some non-uniformities, albeit small ones, in the terrestrial network. The discrepancies appear to be position-dependent and hence non-random in character. The maxima of the magnitudes are 2.5 ppm, 0.4 and 2.7 respectively for the discrepancies in horizontal scale, azimuth and zenith distance.     

Modeling tropospheric wet delays with national GNSS reference network in China for BeiDou precise point positioning

During past decades, precise point positioning (PPP) has been proven to be a well-known positioning technique for centimeter or decimeter level accuracy. However, it needs long convergence time to get high-accuracy positioning, which limits the prospects of PPP, especially in real-time applications. It is expected that the PPP convergence time can be reduced by introducing high-quality external information, such as ionospheric or tropospheric corrections. In this study, several methods for tropospheric wet delays modeling over wide areas are investigated. A new, improved model is developed, applicable in real-time applications in China. Based on the GPT2w model, a modified parameter of zenith wet delay exponential decay wrt. height is introduced in the modeling of the real-time tropospheric delay. The accuracy of this tropospheric model and GPT2w model in different seasons is evaluated with cross-validation, the root mean square of the zenith troposphere delay (ZTD) is 1.2 and 3.6 cm on average, respectively. On the other hand, this new model proves to be better than the tropospheric modeling based on water-vapor scale height; it can accurately express tropospheric delays up to 10 km altitude, which potentially has benefits in many real-time applications. With the high-accuracy ZTD model, the augmented PPP convergence performance for BeiDou navigation satellite system (BDS) and GPS is evaluated. It shows that the contribution of the high-quality ZTD model on PPP convergence performance has relation with the constellation geometry. As BDS constellation geometry is poorer than GPS, the improvement for BDS PPP is more significant than that for GPS PPP. Compared with standard real-time PPP, the convergence time is reduced by 2–7 and 20–50% for the augmented BDS PPP, while GPS PPP only improves about 6 and 18% (on average), in horizontal and vertical directions, respectively. When GPS and BDS are combined, the geometry is greatly improved, which is good enough to get a reliable PPP solution, the augmentation PPP improves insignificantly comparing with standard PPP.     

Kalman-filter-based GPS clock estimation for near real-time positioning

In this article, an algorithm for clock offset estimation of the GPS satellites is presented. The algorithm is based on a Kalman-filter and processes undifferenced code and carrier-phase measurements of a global tracking network. The clock offset and drift of the satellite clocks are estimated along with tracking station clock offsets, tropospheric zenith path delay and carrier-phase ambiguities. The article provides a brief overview of already existing near-real-time and real-time clock products. The filter algorithm and data processing scheme is presented. Finally, the accuracy of the orbit and clock product is assessed with a precise orbit determination of the MetOp satellite and compared to results gained with other real-time products.

Monitoring selective availability dither frequencies and their effect on GPS data

Summary The signals transmitted by Block II satellites of the Global Positioning System (GPS) can be degraded to limit the highest accuracy of the system (10 m or better point positioning) to authorized users. This mode of degraded operation is called Selective Availability (S/A). S/A involves the degradation in the quality of broadcast orbits and satellite clock dithering. We monitored the dithered satellite oscillator and investigated the effect of this clock dithering on high accuracy relative positioning. The effect was studied over short 3-meter and zero-baselines with two GPS receivers. The equivalent S/A effects for baselines ranging from 0 to >10,000 km can be examined with short test baselines if the receiver clocks are deliberately mis-synchronized by a known and varying amount. Our results show that the maximum effect of satellite clock dithering on GPS double difference phase residuals grows as a function of the clock synchronization error according to: S/A _effect =0.04 cm/msec, and it increases as a function of baseline length like: S/A _effect =0.014 cm/100 km. These are equations for maximum observed values of post-fit residuals due to S/A. The effect on GPS baselines is likely to be smaller than the 0.14 mm for a baseline separation of 100 km. We therefore conclude, for our limited data set, and for the level of S/A during our tests, that S/A clock dithering has negligible effect on all terrestrial GPS baselines if double difference processing techniques are employed and if the GPS receivers remain synchronized to better than 10 msec. S/A may constitute a problem, however, if accurate point processing is required, or if GPS receivers are not synchronized. We suggest and test two different methods to monitor satellite frequency offsets due to S/A. S/A modulates GPS carrier frequencies in the range of-2 Hz to +2 Hz over time periods of several minutes. The methods used in this paper to measure the satellite clock dither could be applied by the civilian GPS community to continuously monitor S/A clock dithering. The monitored frequencies may aid high accuracy point positioning applications in a postprocessing mode (Malys and Ortiz 1989), and differential GPS with poorly synchronized receivers (Feigl et al. 1991).     

无气象要素的GPS对流层延迟推算可降水量的研究

本文针对武汉地区GPS气象网资料,进行了GPS对流层延迟直接推算可降水量的研究。在武汉东湖站GPS对流层延迟与无线电探空可降水量的比较中,两者具有很好的相关性,相关系数达到了0.93;推导了对流层延迟直接推算可降水量的模型,对模型结果进行了检验,在武汉东湖站的对流层延迟转换的可降水量与无线电探空可降水量的比较中,均方根为7.8mm,相关性为0.91,这说明了在没有气象数据的地区对流层延迟直接推算的可降水量可以作为气象短期预报的参考。     

Analysis of tropospheric delay prediction models: comparisons with ray-tracing and implications for GPS relative positioning

Ray-tracing is used to examine the accuracy of several well known models for tropospheric delay prediction under varying atmospheric conditions. The models considered include the Hopfield zenith delay model and related mapping functions, the Saastamoinen zenith delay model and mapping function, and three empirical mapping functions based upon the Marini continued fraction form. Modelled delays are benchmarked against ray-tracing solutions for representative atmospheric profiles at various latitudes and seasons. Numerical results are presented in light of the approximations inherent in model formulation. The effect of approximations to the temperature, pressure and humidity structure of the neutral atmosphere are considered; the impact of surface layer anomalies (i.e., inversions) on prediction accuracy is examined; and errors resulting from the neglect of ray bending are illustrated. The influence of surface meteorological parameter measurement error is examined. Finally, model adaptability to local conditions is considered. Recommendations concerning the suitability of the models for GPS relative positioning and their optimal application are made based upon the results presented.     

The precision of geodetic GPS and one way of improving it

We analyse the effect of the combined estimation/elimination of station coordinates, tropospheric zenith delay, dispersive ionosphere and station clock error on the precision achievable with geodetic GPS. We also sketch a method to eliminate the major part of the precision deteriorating effect of this combined estimation of the unknowns, by a dual antenna arrangement. Received 7 December 1995; Accepted 30 October 1996     

利用地面气象观测资料确定对流层加权平均温度

地基GPS气象学的核心思想是通过垂直方向上GPS信号的湿分量延时确定出可降水分 ,而这两个物理量之间的转换必须使用对流层加权平均温度。本文首先讨论了上述转换估计中加权平均温度的几种逼近方式及其容许误差 ,然后利用香港地区的地面和高空气象资料 ,采用逐步回归分析方法 ,建立了适合香港地区的对流层加权平均温度计算公式 ,通过数据分析表明 ,这个公式有效地消除了在香港地区使用Bevis经验公式引起的系统误差 ,较好地满足了地基GPS气象应用中实时性和高精度的要求。本研究也充分表明 ,在地基GPS气象研究中 ,应该利用本地区的气象资料来确定适合本地区的估计对流层加权平均温度的经验公式。     

Evaluation of topographical effects in precise geoid computation from densely sampled heights

In this paper we investigate the behaviour of Newton's kernel in the integration for topographical effects needed for solving the boundary value problem of geodesy. We follow the standard procedure and develop the kernel into a Taylor series in height and look at the convergence of this series when the integral is evaluated numerically on a geographical grid, as is always the case in practice. We show that the Taylor series converges very rapidly for the integration over the distant zone, i.e., the zone well removed from the point of interest. We also show that the series diverges in the vicinity of the point of interest when the grid becomes too dense. Generally, when the grid step is smaller than either the height of the point of interest, or the difference between its height and those of the neighbouring points. Thus we claim that the Taylor series version of Newton's kernel cannot be used for evaluating topographical effects on too dense a topographical mesh.     

A case study of using Raman lidar measurements in high-accuracy GPS applications

This paper investigates the impact of rapid small-scale water vapor fluctuations on GPS height determination. Water vapor measurements from a Raman lidar are used for documenting the water vapor heterogeneities and correcting GPS signal propagation delays in clear sky conditions. We use data from four short observing sessions (6 h) during the VAPIC experiment (15 May–15 June 2004). The retrieval of wet delays from our Raman lidar is shown to agree well with radiosonde retrievals (bias and standard deviation (SD) were smaller than 1 and 2.8 mm, respectively) and microwave radiometers (from two different instruments, bias was 6.0/−6.6 mm and SD 1.3/3.8 mm). A standard GPS data analysis is shown to fail in accurately reproducing fast zenith wet delay (ZWD) variations. The ZWD estimates could be improved when mean post-fit phase residuals were removed. Several methodologies for integrating zenith lidar observations into the GPS data processing are also presented. The final method consists in using lidar wet delays for correcting a priori the GPS phase observations and estimating a scale factor for the lidar wet delays jointly with the GPS station position. The estimation of this scale factor allows correcting for a mis-calibration in the lidar data and provides in the same way an estimate of the Raman lidar instrument constant. The agreement of this constant with an independent determination using radiosonde data is at the level of 1–4%. The lidar wet delays were derived by ray-tracing from zenith pointing measurements: further improvement in GPS positioning is expected from slant path lidar measurements that would properly account for water vapor anisotropy.     

Accuracy improvement of zenith tropospheric delay estimation based on GPS precise point positioning algorithm

In the precise point positioning(PPP),some impossible accurately simulated systematic errors still remained in the GPS observations and will inevitably degrade the precision of zenith tropospheric delay(ZTD) estimation.The stochastic models used in the GPS PPP mode are compared.In this paper,the research results show that the precision of PPP-derived ZTD can be obviously improved through selecting a suitable stochastic model for GPS measurements.Low-elevation observations can cover more troposphere informat...     

提高对流层天顶总延迟解算精度的新方法探讨

对流层天顶总延迟的解算精度,直接影响长基线解算的精度和大气水汽含量的计算精度。文中提出克利金内插法解算天顶总延迟的新方法,并利用南极长城站和周边IGS跟踪站的GPS数据,通过高精度解算软件GAMIT/GLOBK,解算出长城站上空的对流层天顶总延迟,将其与利用内插方法解算的天顶总延迟进行了对比分析,得出:利用该内插方法获取的南极长城站在夏季的天顶总延迟的均方差可达0.2mm,这对今后GPS高精度定位和GPS气象学应用来说,具有重要意义。     

A modified mix-differenced approach for estimating multi-GNSS real-time satellite clock offsets

A modified mixed-differenced approach for estimating multi-GNSS real-time clock offsets is presented. This approach, as compared to the earlier presented mixed-differenced approach which uses epoch-differenced and undifferenced observations, further adds a satellite-differenced process. The proposed approach, based on real-time orbit products and a mix of epoch-differenced and satellite-differenced observations to estimate only satellite clock offsets and tropospheric zenith wet delays, has fewer estimated parameters than other approaches, and thus its implementing procedure is efficient and can be performed and extended easily. To obtain high accuracy, the approach involves three steps. First, the high-accuracy tropospheric zenith wet delay of each station is estimated using mixed-differenced carrier phase observations. Second, satellite clock offset changes between adjacent epochs are estimated using also mixed-differenced carrier phase observations. Third, the satellite clock offsets at the initial epoch are estimated using satellite-differenced pseudorange observations. Finally, the initial epoch clock results and clock offset changes are concatenated to obtain the clock results of the current epoch. To validate the real-time satellite clock results, multi-GNSS post-processing clock products from IGS ACs were selected for comparison. From the comparison, the standard deviations of the GPS, GLONASS, BeiDou and Galileo systems clock results are approximately 0.1–0.4 ns, except for the BeiDou GEO satellites. The root mean squares are about 0.4–2.3 ns, which are similar to those of other international real-time products. When the clock estimates were assessed based on a pseudo-kinematic PPP procedure, the positioning accuracies in the East, North and Up components reach 5.6, 5.5 and 7.6 cm, respectively, which meet the centimeter level and are comparable to the application of other products.     

GPS数据解算对流层天顶总延迟探讨

文中运用GAMIT/GLOBK 软件,解算了南极长城站GPS接收机天线在不同的相位中心和使用不同星历情况下的天顶总延迟,分析了在不同条件下解算结果的差异,探讨了获取高精度的天顶总延迟和实时获取天顶总延迟的具体方法,为今后实现GPS精密定位和实时天气预报提供了依据.     

Numerical simulation of troposphere-induced errors in GPS-derived geodetic time series over Japan

Troposphere-induced errors in GPS-derived geodetic time series, namely, height and zenith total delays (ZTDs), over Japan are quantitatively evaluated through the analyses of simulated GPS data using realistic cumulative tropospheric delays and observed GPS data. The numerical simulations show that the use of a priori zenith hydrostatic delays (ZHDs) derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather model data and gridded Vienna mapping function 1 (gridded VMF1) results in smaller spurious annual height errors and height repeatabilities (0.45 and 2.55 mm on average, respectively) as compared to those derived from the global pressure and temperature (GPT) model and global mapping function (GMF) (1.08 and 3.22 mm on average, respectively). On the other hand, the use of a priori ZHDs derived from the GPT and GMF would be sufficient for applications involving ZTDs, given the current discrepancies between GPS-derived ZTDs and those derived from numerical weather models. The numerical simulations reveal that the use of mapping functions constructed with fine-scale numerical weather models will potentially improve height repeatabilities as compared to the gridded VMF1 (2.09 mm against 2.55 mm on average). However, they do not presently outperform the gridded VMF1 with the observed GPS data (6.52 mm against 6.50 mm on average). Finally, the commonly observed colored components in GPS-derived height time series are not primarily the result of troposphere-induced errors, since they become white in numerical simulations with the proper choice of a priori ZHDs and mapping functions.     

A grid-based tropospheric product for China using a GNSS network

Tropospheric delay accounts for one source of error in global navigation satellite systems (GNSS). To better characterize the tropospheric delays in the temporal and spatial domain and facilitate the safety-critical use of GNSS across China, a method is proposed to generate a grid-based tropospheric product (GTP) using the GNSS network with an empirical tropospheric model, known as IGGtrop. The prototype system generates the GTPs in post-processing and real-time modes and is based on the undifferenced and uncombined precise point positioning (UU-PPP) technique. GTPs are constructed for a grid form (\(2.0{^{\circ }}\times 2.5{^{\circ }}\) latitude–longitude) over China with a time resolution of 5 min. The real-time GTP messages are encoded in a self-defined RTCM3 format and broadcast to users using NTRIP (networked transport of RTCM via internet protocol), which enables efficient and safe transmission to real-time users. Our approach for GTP generation consists of three sequential steps. In the first step, GNSS-derived zenith tropospheric delays (ZTDs) for a network of GNSS stations are estimated using UU-PPP. In the second step, vertical adjustments for the GNSS-derived ZTDs are applied to address the height differences between the GNSS stations and grid points. The ZTD height corrections are provided by the IGGtrop model. Finally, an inverse distance weighting method is used to interpolate the GNSS-derived ZTDs from the surrounding GNSS stations to the location of the grid point. A total of 210 global positioning system (GPS) stations from the crustal movement observation network of China are used to generate the GTPs in both post-processing and real-time modes. The accuracies of the GTPs are assessed against with ERA-Interim-derived ZTDs and the GPS-derived ZTDs at 12 test GPS stations, respectively. The results show that the post-processing and real-time GTPs can provide the ZTDs with accuracies of 1.4 and 1.8 cm, respectively. We also apply the GTPs in real-time kinematic GPS PPP, and the results show that the convergence time of the PPP solutions is shortened. These results confirm that the GTPs can act as an efficient information source to augment GNSS positioning over China.