衛星型GNSS補強システムにおける対流圏遅延補正方式

The Satellite Based Augmentation System (SBAS) can transmit a variety of correction information through satellite, such as ephemeris error, satellite clock error, ionospheric delay and integrity information, which will provide better navigation information for civil aviation aircrafts. Compared with the Instrument Landing System (ILS) commonly used in civil commercial aviation, the SBAS has the advantages of low environmental requirements and lower equipment cost. And the SBAS can provide lower-cost navigation services for civil aviation (including general aviation), so that the significant economic and social benefits will be produced. Based on SBAS satellite broadcast signals, using the navigation receiver with SBAS functions to get the broadcast correction information and integrity information from the Multi-Functional Satellite Augmentation System (MSAS) of Japan. The raspberry pi will receive the information through the USB interface and select them. Finally, the data will be Displayed on the external display. The user uses the display to input fixed instructions to select and compare whether to use SBAS positioning accuracy, which provides a visual demonstration platform for civil aviation teaching.

Tropospheric delay acts as a systematic error source in the Global Navigation Satellite Systems (GNSS) positioning. Empirical models UNB3, UNB3m, UNB4 and EGNOS have been developed for use in Satellite-Based Augmentation Systems (SBAS). Model performance, however, is limited due to the low spatial resolution of the look-up tables for meteorological parameters. A new design has been established in this study for improving performance of the tropospheric delay model by more effectively eliminating the error produced by tropospheric delay. The spatiotemporal characteristics of the Zenith Tropospheric Delay (ZTD) were analyzed with findings that ZTD exhibits different annual variations at different locations and decreases exponentially with height increasing. Spherical harmonics are utilized based on the findings to fit the annual mean and amplitude of the ZTD on a global scale and the exponential function is utilized for height corrections, yielding the ZTrop model. On a global scale, the ZTrop features an average deviation of -1.0 cm and Root Mean Square (RMS) of 4.7 cm compared with the International GNSS Service (IGS) ZTD products, an average deviation of 0.0 cm and RMS of 4.5 cm compared with the Global Geodetic Observing System (GGOS) ZTD data, and an average deviation of -1.3 cm and RMS of 5.2 cm compared with the ZTD data from the Constellation Observing System of Meteorology, Ionosphere, and Climate (COSMIC). The RMS of the ZTrop model is 14.5% smaller than that of UNB3, 6.0% smaller than that of UNB3m, 16% smaller than that of UNB4, 14.5% smaller than that of EGNOS and equivalent to the sophisticated GPT2+Saas model in comparison with the IGS ZTD products. The ZTrop, UNB3m and GPT2+Saas models are finally evaluated in GPS-based Precise Point Positioning (PPP), as the models act to aid in obtaining PPP position error less than 1.5 cm in north and east components and relative large error (>5 cm) in up component with respect to the random walk approach.

L1-SAIF signal is one of the navigation signals of Quasi-Zenith Satellite System, which provides an augmentation function for mobile users in Japan. This paper presents the detail of the tropospheric delay correction in L1-SAIF augmentation. The tropospheric delay correction information is generated at the ground station using the data collected at GEONET (GPS Earth Observation NETwork) stations. The correction message contains the information of the zenith tropospheric delay (ZTD) values at 105 Tropospheric Grid Points (TGP) in the experiment area. From this message a mobile user can acquire the ZTD value at some neighboring TGPs, and estimate the local ZTD value accurately by using a suitable ZTD model function. Only 3 L1-SAIF messages are necessary to provide all of the tropospheric correction information. Several investigations using the actual data observed at many GEONET stations overall Japan have proved that it is possible to achieve the correction accuracy of 13.2mm (rms).

Tropospheric delay is a major error source that affects the performance of the Global Navigation Satellite Systems (GNSS) Real Time Kinematic (RTK) positioning especially for the medium/long-range baseline. Although high precision tropospheric delay can be estimated by GNSS carrier phase measurement, together with position and ambiguity, a relatively long period of convergence time is necessary. In this study, we develop a new GPS/BDS RTK algorithm constrained with a tropospheric delay parameters from Numerical weather prediction (NWP) model for medium/long-range baselines. The accuracy of the tropospheric delays derived from NWP is assessed through comparisons with the results of GAMIT (GNSS at MIT). The positioning performance with standard GPS RTK, standard GPS/BDS RTK, the developed NWP-constrained GPS RTK and NWP-constrained GPS/BDS RTK over medium/long-range baselines are compared in terms of the initialization time and the positioning accuracy. Experiment results show that the mean differences between the NWP and GAMIT zenith tropospheric delay (ZTD) are between −5.50 mm and 5.60 mm, and the RMS values of the NWP ZTD residuals are from 24.02 mm to 32.62 mm. A reduction in the initialization time of over 41% and 58% for medium- and long-range baselines can be achieved with the NWP-constrained RTK (both GPS alone and GPS/BDS RTK solutions) compared to the standard RTK solution, respectively. An improvement of over 30% can be found with the GPS/BDS RTK compared with that of the GPS alone RTK for both standard and the NWP-constrained modes. The positioning precision of NWP-constrained GPS/BDS RTK is better than 3 cm in the horizontal direction and better than 5 cm in the vertical direction, which satisfies the requirement of the precise positioning service.

In order to solve the problem of low precision of tropospheric delay interpolation under the long-distance sparse reference station, a method of tropospheric delay interpolation estimation based on support vector machine (SVM) theory was proposed. Firstly, the troposphere was assumed to be an infinitely thin single-layer membrane, and with the known information of reference stations, the puncture point coordinates and zenith tropospheric delay of each reference station on each visible satellite in the single-layer membrane were obtained. Then, the puncture point coordinates and zenith tropospheric delay were taken as training samples to optimize the appropriate core parameters of SVM and establish the SVM model of tropospheric delay. Finally, two sets of network RTK data with different lengths were selected to compare and analyze the effect of the interpolated tropospheric delay. The results showed that under the long-distance reference station, with the SVM tropospheric delay model established in this paper, the tropospheric delay accuracy of the interpolation estimation is better than 2cm, and the estimation error is generally stable, and the interpolation effect of satellite in different systems is basically the same.

GGOS tropospheric delay forecast product performance evaluation and its application in real-time PPP

<p>Tropospheric delays have been a major error source for space geodetic techniques and the performance of their modeling is significantly limited due to the high spatiotemporal variability of the moisture in the lower atmosphere. In this study, tropospheric zenith wet delay (ZWD) modeling was realized based on the machine learning (random forest approach, RF) and using 10 years (2010-2019) of radiosonde measurements at 586 globally distributed stations. Subsequently, the ZWD modeling accuracy was validated based on the sounding profiles across the globe for the year 2020. We find that ZWD modeling accuracy is significantly improved by taking account meteorological parameters in the functional formulation, especially for surface water vapor pressure. When surface meteorological data are available, the RF-based ZWD models with meteorological parameterization can achieve an overall accuracy of 2.9 cm and the bias close to zero across the globe, which clearly outperforms current empirical models, such as the GPT3, or other models based on surface meteorological measurements. From the analyses of spatial characteristics of the ZWD accuracy, it can be concluded that the RF-based ZWD models especially mitigate the systematic biases in the regions with monsoon climate and tropical rainforest climate types. </p>

The electromagnetic signals of the Global Navigation Satellite Systems (GNSS) satellites suffer delays while propagating through the troposphere. The tropospheric delay is a significant systematic error of GNSS positioning. For safety-of-life applications of positioning many systematic error effects are either mitigated or eliminated in the positioning solution. Space based augmentation systems provide corrections for the orbital and satellite clock error, the ionospheric effects, etc. Moreover advanced GNSS provide dual frequency code observations for civilian users to eliminate the ionospheric delays caused by the electron content of the upper atmosphere. Nevertheless tropospheric delays are still taken into account using empirical models.For safety-of-life applications besides the accuracy of the positioning, the integrity of the positioning service is an important factor, too. The integrity information includes the maximal positioning error at an extremely rare probability level, called protection level to ensure highly reliable position solution in the aviation. The Radio Technical Commission for Aeronautics Minimum Operational Performance Standard (RTCA MOPS) recommends 0.12 m as the maximum zenith tropospheric error in terms of standard deviation. Previous studies show that this recommendation seems to be too conservative leading to a lower service availability. Therefore a more realistic integrity model has to be derived for the estimation of maximal residual tropospheric delay error.In the recent years many advanced empirical tropospheric delay models have been formulated compared to the one recommended by the RTCA. Recently new integrity models have been derived for estimating the maximum residual tropospheric delay error using numerical weather models under real extreme weather.The aim of this paper is to study the reliability of these models conditions. In order to achieve this, high-resolution numerical weather models were ray-traced using an improved ray-tracing algorithm to evaluate the slant and zenith tropospheric delays with the geographical resolution of 0.1° × 0.1°.

Tropospheric delay is a significant error source in Global Navigation Satellite Systems (GNSS) positioning. Slant Path Delay (SPD) is commonly derived by multiplying Zenith Tropospheric Delay (ZTD) with a mapping function. However, mapping functions, assuming atmospheric isotropy, restrict the accuracy of derived SPDs. To improve the accuracy, a horizontal gradient correction is introduced to account for azimuth-dependent SPD variations, treating the atmosphere as anisotropic. This study uncovers that, amidst atmospheric dynamics and spatiotemporal changes in moisture content, the SPD deviates from that based on traditional isotropy or anisotropy assumption. It innovatively introduces the concept that SPD exhibits non-isotropy with respect to azimuth angles. Hypothesis validation involves assessing SPD accuracy using three mapping functions at five International GNSS Service (IGS) stations, referencing the SPD with the ray-tracing method. It subsequently evaluates the SPD accuracy with horizontal gradient correction based on Vienna Mapping Function 3 (VMF3) estimation. Lastly, the non-isotropic of SPD is analyzed through the ray-tracing method. The results indicate the smallest residual (1.1–82.7 mm) between the SPDs with VMF3 and those with the ray-tracing. However, introducing horizontal gradient correction yields no significant improvement of SPD accuracy. Considering potential decimeter-level differences in SPD due to non-isotropic tropospheric delay across azimuth angles, a precise grasp and summary of these variations is pivotal for accurate tropospheric delay modeling. This finding provides vital support for future high-precision tropospheric delay modeling.

When processing code- and carrier-phase ranges sampled at individual epochs, the control baseline of a pair of reference receivers can bring forth relative integer-valued ambiguities and tropospheric delays. The estimates are usually so accurate that they may act as constraints, when a roving user who operates in the network of references requires instantaneous position solutions. This paper has the objective of taking advantage of a tropospheric zenith delay surface for the user’s ranging corrections. A local network of six reference stations was used to study the single-epoch position estimation, which revealed that with the increased reliability of ambiguity resolution on both L1 and L2 carriers, global positioning system-derived height accuracy was refined by more than 60%.

The Global Navigation Satellite System (GNSS) precise point positioning (PPP) technology is currently used to process GNSS water vapor observations in real time or near real time. Further developments are required to improve the accuracy and real-time performance of processing tropospheric delays from which the water vapor observations are extracted. In real-time BDS/GPS precise clock correction estimation with square-root information filtering and PPP solution with Kalman filtering, a fixed variance is often assigned for the process noise of the troposphere dynamics model. However, this fixed value may deviate from reality as the weather conditions change, especially for extreme weather. In this paper, a new adaptive Kalman filter is proposed for tropospheric delay processing, in which the variance of the process noise for the zenith tropospheric delay (ZTD) dynamics model is tuned in real time using the least-squares variance component estimation technique. MGEX/IGS data of 15 consecutive days were processed in a stepwise manner. Namely: Real-time BDS/GPS precise clock corrections were estimated firstly, followed by comparison among ZTD solutions of four schemes based on these real-time clocks of first step and GFZ multi-GNSS precise clock (GBM) final clocks: (1) real-time solution of ZTD (G(GPS), GC(GPS and BDS)) without VCE; (2) real-time solution of ZTD (G, GC) with VCE; (3) final solution of ZTD (G, GC, GR (GPS and GLONASS), GE (GPS and GALILEO), GRC (GPS, GLONASS and BDS), GREC (GPS, GLONASS, GALILEO and BDS) without VCE; and (4) final solution of ZTD (G, GC, GR, GE, GRC, GREC) with VCE. The performance of the ZTD and positioning solution was analyzed. Results showed that the accuracy of estimated real-time satellite clock correction was 0.27, 1.31, 0.29, and 0.21 ns for GPS, BDS/GEO, BDS/IGSO, and BDS/MEO, respectively. For the ZTD solutions, the results of schemes 1 and 2 were 12.8 mm (GC) and 10.1 mm (GC) in terms of mean root-mean-square (RMS) values and 2.1 mm (GC) and 1.6 mm (GC) in terms of minimum RMS values, respectively, thereby showing an improvement for scheme 2 of 1.8–81.4% over scheme 1 with average increasing rates of 20.7% (GC) and 20.2% (G). The results for schemes 3 and 4 were 7.6 mm (G) and 6.3 mm (GRC) in terms of mean RMS values and 2.1 mm (G) and 1.9 mm (GRCE) in terms of minimum RMS values, respectively, thereby showing an improvement in scheme 4 over scheme 3 by 1.3–85.6% with average increasing rates of 22.1% (GRCE), 21.9% (GRC), 18.4% (GR), 15.9% (GC), 15.2% (GE), and 12.1% (G). Similar results can be observed for the positioning solution, especially in the height component. These findings clearly show the advantage of the proposed method, which is consistent with the theoretical analysis. Notably, the advantage of the adaptive VCE becomes significant with the inclusion of additional satellite systems.

This paper presents an investigation into the performance of real-time Global Navigation Satellite Systems (GNSS) Precise Point Positioning (PPP) in New Zealand. The motivation of the research is to evaluate the feasibility of using PPP technique and a satellite based augmentation system such as the Japanese Quasi-Zenith Satellite System (QZSS) to deliver a real-time precise positioning solution in support of a nation-wide high accuracy GNSS positioning coverage in New Zealand. Two IGS real-time correction streams are evaluated alongside with the PPP correction messages transmitted by the QZSS satellite known as MDC1. MDC1 corrections stream is generated by Japan Aerospace Exploration Agency (JAXA) using the Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA) software and are currently transmitted in test mode by the QZSS satellite. The IGS real-time streams are the CLK9B real-time corrections stream generated by the French Centre National D’études Spatiales (CNES) using the PPP-Wizard software, and the CLK81 real-time corrections stream produced by GMV using their MagicGNSS software. GNSS data is collected from six New Zealand CORS stations operated by Land Information New Zealand (LINZ) over a one-week period in 2015. GPS and GLONASS measurements are processed in a real-time PPP mode using the satellite orbit and clock corrections from the real-time streams. The results show that positioning accuracies of 6 cm in horizontal component and 15 cm in vertical component can be achieved in real-time PPP. The real-time GPS+GLONASS PPP solution required 30 minutes to converge to within 10 cm horizontal positioning accuracy.

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.

Regional modeling of tropospheric delay considering vertically and horizontally separation of station for regional augmented PPP

<p>Microwave signals passing through the troposphere are delayed by refraction. Its high variations, both in time and space, are caused mainly by water vapor. The tropospheric delay used to be considered only as a source of error that needed to be removed. Nowadays, these delays are also a source of interest, for example, tropospheric delays or integrated water vapor information are being assimilated into nowcasting or numerical weather prediction (NWP) models. Moreover, long time series of tropospheric observations have become an important source of information for climate studies. On the other hand, the meteorological data is supporting the space-geodetic community by providing models that can be used to reduce the troposphere impact on the signal propagation.</p><p>There are several ways of observing the troposphere, especially considering water vapor.  First one are the classical meteorological: in-situ measurements, radiosondes or radiometers, from which we can sense directly the amount of water vapor. Another, indirect way of observing the water vapor distribution is by using the Global Navigation Satellite Systems (GNSS). This method is called GNSS meteorology. Other microwave techniques such as Very Long Baseline Interferometry (VLBI), Interferometric Synthetic Aperture Radar (InSAR) or space-based Radio Occultations (RO) can also be used in a similar way to GNSS.</p><p>This contribution presents an overview of the troposphere sensing techniques with examples of their applications. We present a multi-comparison of the tropospheric products, i.e. refractivity, tropospheric delays in zenith and slant directions and integrated water vapor. The integration of the different data sources often leads to an improved accuracy of the tropospheric products but requires a careful preparation of data. The combination of the data sources allows for using techniques of complementary properties, for example InSAR with very high spatial resolution with GNSS observations of high temporal resolution. With the emergence of new technologies, some traditional ways of tropospheric measurements can be augmented with the new methods. For example, we have tested meteo-drones as an alternative to radiosondes. The comparisons with GNSS data shows a good agreement of the drone and microwave data, even better than with radiosondes.</p>