Practical analysis of using PPPH and raPPPid for Precise Point Positioning in Europe

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

The accurate modeling of tropospheric path delay is significant for data processing of radio space-geodetic techniques such as Global Navigation Satellite System (GNSS) and Very-Long-Baseline Interferometry (VLBI). The Vienna Mapping Function 1 (VMF1) model, based on continuous update of Numerical Weather Prediction (NWP) data from the European Centre for Medium-Range Weather Forecasts (ECMWF), is recommended for this purpose in post-processing. The VMF1 coefficients determined from forecast data of the ECMWF are now readily and freely available. However, little or no implementation of this forecast VMF1 (VMF1-FC) model in real-time GNSS or VLBI applications has occurred. This study investigates the performance of the VMF1-FC model in terms of its three components which are critical for the modeling of tropospheric path delay: the Zenith Hydrostatic Delay (ZHD), the Zenith Wet Delay (ZWD) and mapping functions. All three components are assessed in the context of GNSS Precise Point Positioning (PPP) using 28 global stations over a 70-day period. The Zenith Total Delays (ZTD) derived with the VMF1-FC (implemented in real-time PPP) are shown to agree well with the tropospheric delay product from the Center for Orbit Determination Europe (CODE). Root mean square (RMS) errors associated with these ZTD estimates are < 10 mm at all 28 stations. The results also show that the VMF1-FC model performs better than empirical models such as the widely used Global Pressure and Temperature 2 (GPT2) and GPT2 wet (GPT2w), with smaller RMS errors associated with the ZTD estimates. It is recommended that VMF1-FC be applied for future tropospheric delay modeling in real-time GNSS and VLBI applications.

Accurate estimation of tree position, diameter at breast height (DBH), and tree height measurements is an important task in forest inventory. Mobile Laser Scanning (MLS) is an important solution. However, the poor global navigation satellite system (GNSS) coverage under the canopy makes the MLS system unable to provide globally-consistent point cloud data, and thus, it cannot accurately estimate the forest attributes. SLAM could be an alternative for solutions dependent on GNSS. In this paper, a mobile phone with RGB-D SLAM was used to estimate tree position, DBH, and tree height in real-time. The main aims of this paper include (1) designing an algorithm to estimate the DBH and position of the tree using the point cloud from the time-of-flight (TOF) camera and camera pose; (2) designing an algorithm to measure tree height using the perspective projection principle of a camera and the camera pose; and (3) showing the measurement results to the observer using augmented reality (AR) technology to allow the observer to intuitively judge the accuracy of the measurement results and re-estimate the measurement results if needed. The device was tested in nine square plots with 12 m sides. The tree position estimations were unbiased and had a root mean square error (RMSE) of 0.12 m in both the x-axis and y-axis directions; the DBH estimations had a 0.33 cm (1.78%) BIAS and a 1.26 cm (6.39%) root mean square error (RMSE); the tree height estimations had a 0.15 m (1.08%) BIAS and a 1.11 m (7.43%) RMSE. The results showed that the mobile phone with RGB-D SLAM is a potential tool for obtaining accurate measurements of tree position, DBH, and tree height.

Nowadays, Precise Point Positioning (PPP) is a very popular technique for Global Navigation Satellite System (GNSS) positioning. The advantage of PPP is its low cost as well as no distance limitation when compared with the differential technique. Single-frequency receivers have the advantage of cost effectiveness when compared with the expensive dual-frequency receivers, but the ionosphere error makes a difficulty to be completely mitigated. This research aims to assess the effect of using observations from both GPS and GLONASS constellations in comparison with GPS only for kinematic purposes using single-frequency observations. Six days of the year 2018 with single-frequency data for the Ethiopian IGS station named “ADIS” were processed epoch by epoch for 24 hours once with GPS-only observations and another with GPS/GLONASS observations. In addition to “ADIS” station, a kinematic track in the New Aswan City, Aswan, Egypt, has been observed using Leica GS15, geodetic type, dual-frequency, GPS/GLONASS GNSS receiver and single-frequency data have been processed. Net_Diff software was used for processing all the data. The results have been compared with a reference solution. Adding GLONASS satellites significantly improved the satellite number and Position Dilution Of Precision (PDOP) value and accordingly improved the accuracy of positioning. In the case of “ADIS” data, the 3D Root Mean Square Error (RMSE) ranged between 0.273 and 0.816 m for GPS only and improved to a range from 0.256 to 0.550 m for GPS/GLONASS for the 6 processed days. An average improvement ratio of 24%, 29%, 30%, and 29% in the east, north, height, and 3D position components, respectively, was achieved. For the kinematic trajectory, the 3D position RMSE improved from 0.733 m for GPS only to 0.638 m for GPS/GLONASS. The improvement ratios were 7%, 5%, 28%, and 13% in the east, north, height, and 3D position components, respectively, for the kinematic trajectory data. This opens the way to add observations from the other two constellations (Galileo and BeiDou) for more accuracy in future research.

Abstract. The spatiotemporal variations of integrated precipitable water vapor (IPWV) are very important in understanding the regional variability of water vapor. Traditional in situ measurements of IPWV in the Indian region are limited, and therefore the performance of satellite and Copernicus Atmosphere Meteorological Service (CAMS) retrievals with the Indian Global Navigation Satellite System (GNSS) as reference were analyzed. In this study the CAMS reanalysis data of 1 year (2018) and the Indian GNSS and INSAT-3DR sounder retrieval data for 1.5 years (January 2017 to June 2018) were utilized, and statistics were computed. It is noticed that seasonal correlation coefficient (CC) values between INSAT-3DR and Indian GNSS data mainly lie within the range of 0.50 to 0.98 for all the selected 19 stations except Thiruvananthapuram (0.1), Kanyakumari (0.31) and Karaikal (0.15) during the monsoon season and Panjim (0.2) during the post-monsoon season. The seasonal CC values between CAMS and GNSS IPWV range from 0.73 to .99 except for Jaipur (0.16) and Bhubaneswar (0.29) during the pre-monsoon season, Panjim (0.38) during the monsoon season, Nagpur (0.50) during the post-monsoon season, and Dibrugarh (0.49) Jaipur (0.58) and Bhubaneswar (0.16) during the winter season. The root mean square error (RMSE) values are higher under the wet conditions (pre-monsoon and monsoon season) than under dry conditions (post-monsoon and winter season), and we found differences in magnitude and sign of bias for INSAT-3DR and CAMS with respect to GNSS IPWV from station to station and season to season. This study will help to improve understanding and utilization of CAMS and INSAT-3DR data more effectively along with GNSS data over land, coastal and desert locations in terms of the seasonal flow of IPWV, which is an essential integrated variable in forecasting applications.

Abstract. In the fields of mapping, surveying, and three-dimensional (3D) modeling, unmanned aerial vehicle (UAV) systems have become essential equipment in recent times. UAVs are increasingly widely used, especially in the field of photogrammetry. The integration of technologies such as digital cameras, inertial measurement unit (IMU), and Global Navigation Satellite System (GNSS) has improved the quality and accuracy of photogrammetric products. In comparison to conventional methodologies, UAVs present a cost-effective alternative to traditional aerial photogrammetry. Recent advancements in technology substantiate their efficacy across a variety of applications. The utilization of direct georeferencing minimizes the reliance on ground control points (GCP). With the advancements in positioning techniques, the accuracy of the products is concurrently improving. Real-Time Kinematic (RTK) and Post-Processed Kinematic (PPK) techniques play a critical role in enhancing the accuracy of UAV-based photogrammetry. Both techniques are widely used in UAV-based photogrammetry. However, relative positioning poses limitations to the study in terms of infrastructure and cost. PPP (Precise Point Positioning), a specific form of absolute positioning, is utilized effectively across various applications. The PPP method, used globally with a single GNSS receiver, is more cost-effective than relative methods. In this study, the performance of the PPP-AR technique as an alternative to the relative methods RTK and PPK is evaluated. Thus, the applicability of the PPP technique, which has improved accuracy and precision with ambiguity resolution, in UAV-based photogrammetry is examined. RTK and PPK techniques achieve Root Mean Square Error (RMSE) values of less than 10 centimeters. In contrast, RMSE values at the decimeter level are observed in the PPP-AR technique.

&amp;lt;p&amp;gt;The recent release of mass-marked dual-frequency receivers opens up the opportunity to facilitate the cost-efficient estimation of Zenith Tropospheric Delays (ZTDs) from Global Navigation Satellite System (GNSS) observations. We present results of ZTD estimations from a low-cost dual-frequency GNSS receiver (U-blox ZED-F9) equipped with a range of different quality and priced antennas. It is demonstrated that the receiver itself is able to produce high quality ZTD estimations with higher grade antennas. However, the noise introduced by applying the ionosphere-free linear combination in Precise Point Positioning (PPP), makes the low-cost antenna performance initially a major challenge. With Root Mean Square Errors (RMSE) between 15 mm and 24 mm for low-cost antennas the results were at first not adequate for meteorological purposes. We demonstrate an easy-to-apply relative antenna calibration that increased the ZTD accuracy significantly for the tested low-cost antennas. After applying antenna corrections the error is reduced to a level that is adequate for meteorological applications (RMSE ~4 mm).&amp;lt;/p&amp;gt;

Global Navigation Satellite Systems (GNSS) tomography is a well-recognized modeling technique for reconstruction, which can be used to investigate the spatial structure of water vapor with a high spatiotemporal resolution. In this study, a refined near real-time tomographic model is developed based on multi-source data including GNSS observations, Global Forecast System (GFS) products and surface meteorological data. The refined tomographic model is studied using data from Hong Kong from 2 to 11 October 2021. The result is compared with the traditional model with physical constraints and is validated by the radiosonde data. It is shown that the root mean square error (RMSE) values of the proposed model and traditional model are 0.950 and 1.763 g/m3, respectively. The refined model can decrease the RMSE by about 46%, indicating a better performance than the traditional one. In addition, the accuracy of the refined tomographic model is assessed under both rainy and non-rainy conditions. The assessment shows that the RMSE in the rainy period is 0.817 g/m3, which outperforms the non-rainy period with the RMSE of 1.007 g/m3.

BackgroundThe multileaf collimator (MLC) is a critical component to accurate intensity-modulated radiotherapy (IMRT) delivery. This study examined MLC positional accuracy via MLC logs from Varian machines from six institutions and three delivery techniques to evaluate typical positional accuracy and treatment and mechanical parameters that affect accuracy. Typical accuracy achieved was compared against TG-142 recommendations for MLC performance; more appropriate recommendations are suggested.MethodsOver 85,000 Varian MLC treatment logs were collected from six institutions and analyzed with FractionCHECK. Data were binned according to institution and treatment type to determine overall root mean square (RMS) and 95th percentile error values, and then to look for correlations between those errors and with mechanical and treatment parameters including mean and maximum leaf speed, gantry angle, beam-on time, mean leaf error, and number of segments.ResultsResults of treatment logs found that leaf RMS error and 95th percentile leaf error were consistent between institutions, but varied by treatment type. The step and shoot technique had very small errors: the mean RMS leaf error was 0.008 mm. For dynamic treatments the mean RMS leaf error was 0.32 mm, while volumetric-modulated arc treatment (VMAT) showed an RMS leaf error of 0.46 mm. Most MLC leaf errors were found to be well below TG-142 recommended tolerances. For the dynamic and VMAT techniques, the mean and maximum leaf speeds were significantly linked to the leaf RMS error. Additionally, for dynamic delivery, the mean leaf error was correlated with RMS error, whereas for VMAT the average gantry speed was correlated. For all treatments, the RMS error and the 95th percentile leaf error were correlated.ConclusionsRestricting the maximum leaf speed can help improve MLC performance for dynamic and VMAT deliveries. Furthermore, the tolerances of leaf RMS and error counts for all treatment types should be tightened from the TG-142 values to make them more appropriate for clinical performance. Values of 1 mm for the 95th percentile of leaf RMS error and 1.5 mm for the 95th percentile leaf error are suggested as action levels for all treatment types.

Global Navigation Satellite System (GNSS) signals arrive at the Earth in a nonlinear and slightly curved way due to the refraction effect caused by the troposphere. The troposphere delay of the GNSS signal consists of hydrostatic and wet parts. In particular, tropospheric wet delay prediction and interpolation are more difficult than those of the dry component due to the rapid temporal and spatial variation of the water vapor content. Wet delay estimation and interpolation with a sufficient accuracy is an important issue for all parameters obtained by GNSS positioning techniques. In particular, in real-time positioning applications, errors caused by interpolation of the wet troposphere delay are reflected in the height component of about 1 to 2 cm. Furthermore, the amount of water vapor in the troposphere is very important information in weather forecast applications obtained as a function of wet delay. Therefore, real-time monitoring of the troposphere can be achieved with a higher resolution and accuracy by utilizing neural network models for interpolation of the wet tropospheric delay. In addition, in the absence of the GNSS station, wet delays can be interpolated by means of the surrounding stations to the desired location. In this study, a back propagation artificial neural network (BPNN) model based on meteorological parameters obtained from The New Austrian Meteorological Measuring Network (TAWES) was used to interpolate wet troposphere delay. Analysis was carried out at 40 reference stations of the Echtzeit Positionierung Austria (EPOSA) GNSS Network covering the whole of Austria. The interpolation of zenith wet delays based on the artificial neural network was performed by using latitude, longitude, altitude and meteorological parameters (temperature, pressure, weighted mean temperature, and water vapor pressure). These parameters were then subtracted from the artificial neural network model one by one and six different artificial neural networks were designed. In addition, the linear interpolation method (LIN) and inverse distance weighted interpolation method (IDW) were used as conventional interpolation methods. In order to investigate the effect of the network density on interpolation methods, three networks, including 40, 30, and 20 reference stations, were formed and the increased distance effect on interpolation methods was evaluated. In addition, analyses were conducted in winter, spring, and summer to evaluate the seasonal effects on interpolation methods. According to the statistical analysis, the root mean square error (RMSE) values of the IDW, LIN, and BPNN methods were found to be 12.6, 13.4, and 5.9 mm, respectively.

Background and purposeThe study evaluated the differences in leaf positioning deviations by the log files of three advanced accelerators with two delivery techniques, and established specific assessment parameters of leaf positioning deviations for different types of accelerators.MethodsA total of 420 treatment plans with 5 consecutive treatment log files were collected from the Trilogy, TrueBeam and Halcyon accelerators. Millennium MLC was equipped on the Trilogy and TrueBeam accelerators. A jawless design and dual-layer MLC were adopted on the Halcyon accelerator. 70 IMRT and 70 VMAT plans were selected randomly on each accelerator. The treatment sites of all plans included head and neck, chest, breast, pelvis and other sites. The parsing tasks for 2100 log files were proceeded by SunCheck software from Sun Nuclear Corporation. The maximum leaf root mean square (RMS) errors, 95th percentile errors and percentages of different leaf positioning errors were statistically analyzed. The correlations between these evaluation parameters and accelerator performance parameters (maximum leaf speed, mean leaf speed, gantry and arc angle) were analyzed.ResultsThe average maximum leaf RMS errors of the Trilogy in the IMRT and VMAT plans were 0.44 ± 0.09 mm and 0.79 ± 0.07 mm, respectively, which were higher than the TrueBeam's 0.03 ± 0.01 mm, 0.03 ± 0.01 mm and the Halcyon's 0.05 ± 0.01 mm, 0.07 ± 0.01 mm. Similar data results were shown in the 95th percentile error. The maximum leaf RMS errors were strongly correlated with the 95th percentile errors (Pearson index > 0.5). The leaf positioning deviations in VMAT were higher than those in IMRT for all accelerators. In TrueBeam and Halcyon, leaf position errors above 1 mm were not found in IMRT and VMAT plans. The main influencing factor of leaf positioning deviation was the leaf speed, which has no strong correlation with gantry and arc angles.ConclusionsCompared with the quality assurance guidelines, the MLC positioning deviations tolerances of the three accelerators should be tightened. For both IMRT and VMAT techniques, the 95th percentile error and the maximum RMS error are suggested to be tightened to 1.5 and 1 mm respectively for the Trilogy accelerator. In TrueBeam and Halcyon accelerators, the 95th percentile error and maximum RMS error of 1 and 0.5 mm, respectively, are considered appropriate.

The delays of radio signals transmitted by global navigation satellite system (GNSS) satellites and induced by neutral atmosphere, which are usually represented by zenith tropospheric delay (ZTD), are required as critical information both for GNSS positioning and navigation and GNSS meteorology. Establishing a stable and reliable ZTD model is one of the interests in GNSS research. In this study, we proposed a regional ZTD model that makes full use of the ZTD calculated from regional GNSS data and the corresponding ZTD estimated by global pressure and temperature 3 (GPT3) model, adopting the artificial neutral network (ANN) to construct the correlation between ZTD derived from GPT3 and GNSS observations. The experiments in Hong Kong using Satellite Positioning Reference Station Network (SatRet) were conducted and three statistical values, i.e., bias, root mean square error (RMSE), and compound relative error (CRE) were adopted for our comparisons. Numerical results showed that the proposed model outperformed the parameter ZTD model (Saastamoinen model) and the empirical ZTD model (GPT3 model), with an approximately 56%/52% and 52%/37% RMSE improvement in the internal and external accuracy verification, respectively. Moreover, the proposed method effectively improved the systematic deviation of GPT3 model and achieved better ZTD estimation in both rainy and rainless conditions.

In recent years, geodesy based on spaceborne microwave remote sensing has gained significant advances. However, whether the observations from the Global Navigation Satellite System (GNSS) or Interferometric Synthetic Aperture Radar (InSAR), the results are inevitably influenced by atmospheric tropospheric delay. Although the tropospheric zenith total delay (ZTD) can be estimated through the gridded meteorological data products and empirical models provided by the ERA5 reanalysis product, its accuracy is still insufficient to meet the needs of modern geodesy. To overcome this challenge, we propose leveraging machine learning techniques to learn local spatio-temporal patterns of tropospheric delay for inferring total zenith delay (ZTD) and zenith wet delay (ZWD) at any location within the learning area.Our findings indicate that artificial neural networks can establish a robust mapping between ZTD estimated by empirical models and GNSS-measured ZTD. Then employing the ensemble learning strategy and the time series dynamics model, the ZTD at any location within the sample area can be inferred. To evaluate our approach, we conducted tests during the active water vapor season in the T&amp;#252;bingen region of Baden-W&amp;#252;rttemberg, Germany, from June 25 to July 9, 2022. In comparative experiments with the root mean square error (RMSE) of Zenith Total Delay (ZTD) derived from ERA5, our proposed method yielded a significant reduction in RMSE, decreasing it from 16.4292mm to 7.2108mm. This reflects a remarkable accuracy improvement of 56.11%.The proposed approach holds promise for enhancing the precision of GNSS positioning, InSAR earth observation, and generating more dependable water vapor products.

For precise positioning in arctic regions with Global Navigation Satellite Systems (GNSS), such as GPS and Glonass, there are a number of issues to be resolved or taken into account. The most important ones are satellite geometry, ionospheric effects and distribution of correction data. Precise Point Positioning (PPP) is currently the standard for precise offshore positioning. PPP requires a sparse global network of GNSS reference stations to estimate precise satellite orbit and clock parameters in real-time. These parameters are transmitted to users, who can compute their position with an accuracy of 0.1 m using code and carrier observations. The main disadvantage of PPP is that in general it takes a long time to converge to this accuracy, about 30–45 minutes. GNSS carrier observations are similar to pseudo ranges, but have an additional bias which needs to be estimated. Under certain conditions, these biases are integer. This property is used in what is generally referred to as Real-Time Kinematic (RTK) positioning, a technique which uses corrections generated at reference stations to make sure these ambiguities are integer. Integer Ambiguity Resolution (IAR) results in RTK accuracies of 0.01–0.03 m or better and short convergence times, ranging from instantaneous to several minutes for long inter-station distances. The disadvantage is the limited area of applicability, because RTK in general does not use precise orbits and clocks. Current research focuses on the combination of PPP and RTK techniques. The main goal is to achieve cm accuracy with a sparse network of reference stations. Another goal is to reduce convergence time. Applications are in the field of precise real-time offshore positioning in general, and subsidence monitoring and tidal estimation in particular. Results will be presented from standard PPP and PPP combined with IAR for arctic regions and from a test bed in the Gulf of Mexico. These results, although preliminary, indicate centimeter level accuracy is indeed possible, also in the arctic. We will also look at further improvements, mainly in convergence time, using all operational satellites and signals from current and future navigation systems.

Accurate water vapor information is crucial for improving the quality of numerical weather forecasting. Previous studies have incorporated tropospheric water vapor data obtained from a global navigation satellite system (GNSS) into numerical weather models to enhance the accuracy and reliability of rainfall forecasts. However, research on evaluating forecast accuracy for different rainfall levels and the development of corresponding forecasting platforms is lacking. This study develops and establishes a rainfall forecasting platform supported by the GNSS-assisted weather research and forecasting (WRF) model, quantitatively assessing the effect of GNSS precipitable water vapor (PWV) on the accuracy of WRF model forecasts for light rain (LR), moderate rain (MR), heavy rain (HR), and torrential rain (TR). Three schemes are designed and tested using data from seven ground meteorological stations in Xi’an City, China, in 2021. The results show that assimilating GNSS PWV significantly improves the forecast accuracy of the WRF model for different rainfall levels, with the root mean square error (RMSE) improvement rates of 8%, 15%, 19%, and 25% for LR, MR, HR, and TR, respectively. Additionally, the RMSE of rainfall forecasts demonstrates a decreasing trend with increasing magnitudes of assimilated PWV, particularly effective in the range of [50, 55) mm where the lowest RMSE is 3.58 mm. Moreover, GNSS-assisted numerical weather model shows improvements in statistical forecasting indexes such as probability of detection (POD), false alarm rate (FAR), threat score (TS), and equitable threat score (ETS) across all rainfall intensities, with notable improvements in the forecasts of HR and TR. These results confirm the high precision, visualization capabilities, and robustness of the developed rainfall forecasting platform.