GPS 시각 전송에서의 대류층 천정지연 모델과 매핑 함수에 따른 시각오프셋 비교

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.

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.

The complexity of the atmosphere renders the modelling of the atmospheric delay in multi temporal InSAR difficult. This limits the potential of achieving millimetre accuracy of InSAR-derived deformation measurements. In this paper we review advances in tropospheric delay modelling in InSAR, tropospheric correction methods and integration of the correction methods within existing multi temporal algorithms. Furthermore, we investigate ingestion of the correction techniques by different InSAR applications, accuracy performance metrics and uncertainties of InSAR derived measurements attributed to tropospheric delay. Spatiotemporal modelling of atmospheric delay has evolved and can now be regarded as a spatially correlated turbulent delay with varying degree of anisotropy random in time and topographically correlated seasonal stratified delay. Tropospheric corrections methods performance is restricted to a case by case basis and ingestion of these methods by different applications remains limited due to lack of their integration into existing algorithms. Accuracy and uncertainty assessments remain challenging with most studies adopting simple statistical metrics. While advances have been made in tropospheric modelling, challenges remain for the calibration of atmospheric delay due to lack of data or limited resolution and fusion of multiple techniques for optimal performance.

In the context of a High accuracy SBAS-PPP service, we require a different tropospheric delay model than the existing model provided in DO-229F (RTCA, 2020). This will yield more reliable results, but also reduce convergence times with desired accuracy to assist a faster convergence time for the PPP solution, which is imperative for employing the SBAS-PPP corrections for high integrity safety-of-life applications. In this paper we describe a real-time capable global methodology to estimate tropospheric zenith delay and the associated standard deviation values for SBAS applications based on ERA-5 ECMWF forecast weather data. In addition, a new messaging format is developed to disseminate the tropospheric corrections and the associated standard deviation values to the users via the SBAS signal-in-space with least impact on the signal data rate. Validating the proposed methodology against 10 years of more accurate re-analysis ERA-5 ECMWF weather data illustrates the potential of the approach presented in this paper to estimate tropospheric zenith delays in the order of sub-cm level at most locations. This is a significant improvement with respect to the current 0.12 m sigma used in the DO-229F (RTCA, 2020).

Global Navigation Satellite System (GNSS) are one of the promising fields of applied astronautics. They give coordinates and time high quality measurements supporting land, sea, air and space applications. In the article, the possible sources of errors in the algorithm for calculating the navigation parameters are analyzed and algorithm for calculating the navigation parameters of the GNSS receiver using raw measurements is introduced. The influence of the troposphere on the GNSS signals is manifested in the form of an additional delay that add to time the signal passing from the satellite to the receiver is taking, this delay depends on temperature, pressure, humidity, as well as on the antennas of the transmitter and receiver. The main feature of the troposphere is that it is a non-dispersive medium to electromagnetic waves up to 15 GHz, thus, tropospheric effects do not change with the frequency of the GNSS signals. Tropospheric delays are usually calculated using Neil mapping function, which has its drawbacks. Thus, this article considers a new algorithm for tropospheric delay estimation by using a genetic algorithm for calculating the navigation parameters of a stationary GNSS receiver. Genetic algorithm, as an effective method of search and optimization, is used to improve the characteristics of the GNSS, reduce the total calculation time and achieve faster convergence to the optimal solution. In the article, a genetic algorithm for tropospheric delay estimation based on the iterative least squares method is presented. In the final part, the results of the genetic algorithm are presented and a comparison of the results of the algorithm with the Niell mapping function.

Atmospheric refraction in the troposphere causes the propagation speed of electromagnetic signals to be less than the light speed. This creates a difference between the actual propagation path delay and the distance of the geometrical straight-line path, i.e., a quantity known as the tropospheric delay. As classical imaging algorithms for spaceborne synthetic aperture radar (SAR) do not take the tropospheric delay into account, imaging filters are designed based on the assumption of rectilinear propagation with the light speed. Therefore, a residual phase exists in imaging results, which affects focusing quality under the condition of high resolution. In order to compensate for the impact of tropospheric delay on focusing performance, this paper modifies the spaceborne SAR echo model and then proposes an imaging compensation algorithm. The key to this algorithm is to fit a range delay coefficient based on the European Geostationary Navigation Overlay Service model of zenith delay and Niell mapping function, which projects the zenith delay onto the looking direction. After range compensation, classical imaging, and azimuth compensation, which compose the proposed algorithm, the processed results are well focused.

The high spatial and temporal variability of the troposphere is well known, as is its effect-through propagation delays-on GPS positioning. This effect can be particularly problematical in airborne kinematic differential positioning where the altitude difference between reference station and aircraft is typically quite large. The use of zenith delay models and mapping functions at ground stations is fairly well understood, however their use for processing data collected on board aircraft is less well understood. Previous tests have indicated that some of the models often used for navigation purposes (e.g. Altshuler, NATO and the proposed WAAS model) perform poorly compared to those generally used for static positioning. These tests were not done under kinematic conditions however, but as comparisons with ray tracing through radiosonde data. This paper outlines the work recently done at UNB on testing the reliability of tropospheric models in precise airborne GPS navigation. Particular attention has been paid to the performance of the currently proposed WAAS model. The data used to test the models is from an adverse weather flight dynamics experiment undertaken off Newfoundland, Canada, in March 1995. The paper includes an analysis of the GPS flight data to determine the influence of different tropospheric models on the reliability and accuracy of the solutions.

Abstract. In the field of space geodetic techniques, such as global navigation satellite systems (GNSSs), tropospheric zenith hydrostatic delay (ZHD) is chosen as the a priori value of tropospheric total delay. Therefore, the inaccuracy of ZHD will definitely affect parameters like the wet delay and the horizontal gradient of tropospheric delay, accompanied by an indirect influence on the accuracy of geodetic parameters, if not dealt with well at low elevation angles. In fact, however, the most widely used ZHD model currently seems to contain millimeter-level biases from the precise integral method. We explored the bias of traditional ZHD models and analyzed the characteristics in different aspects on a global annual scale. It was found that biases differ significantly with season and geographical location, and the difference between the maximum and minimum values exceeds 30 mm, which should be fully considered in the field of high-precision measurement. Then, we constructed a global grid correction model, which is named ZHD_crct, based on the meteorological data of the year 2020 from the ECMWF (European Centre for Medium-Range Weather Forecasts), and it turned out that the bias of traditional models in the current year could be reduced by ∼ 50 % when the ZHD_crct was added. When we verified the effect of ZHD_crct on the biases in the next year, it worked almost the same as the former year. The mean absolute biases (MABs) of ZHD will be narrowed within ∼ 0.5 mm for most regions, and the SDs (standard deviations) will be within ∼ 0.7 mm. This improvement will be helpful for research on meteorological phenomena as well.

Para se corrigir a refração troposférica, que consiste em uma das principais fontes de erro que afetam as observações do Sistema de Posicionamento Global (GPS), usam-se modelos troposféricos e funções de mapeamento que estimam o valor do atraso nos sinais GPS provocado por esta refração. Tais modelos foram desenvolvidos usando dados meteorológicos coletados predominantemente no hemisfério norte. Este artigo apresenta um estudo comparativo sobre o efeito, no posicionamento geodésico com o GPS, provocado por modelos troposféricos, mais precisamente os de Saastamoinen, Hopfield e Ifadis, combinados às funções de mapeamento de Ifadis, Hopfield, Saastamoinen, Herring e Lanyi. Dados GPS coletados pela Rede Brasileira de Monitoramento Contínuo de Sistema GPS (RBMC) foram utilizados. As estações da RBMC estão distribuídas de modo que cada uma das regiões geográficas do Brasil tenha pelo menos uma delas. Visto que também a RBMC cobre as cinco regiões climáticas do país, foram estabelecidas três linhas de base configuradas de acordo com a região climática em que se localizam, tendo cada uma dessas bases características específicas quanto ao seu comprimento, variação altimétrica, dentre outras. Os dados GPS utilizados correspondem a quatro diferentes épocas do ano de 1997, e foram tratados com o programa DIPOP, de posicionamento diferencial. A análise do resultado do processamento indica uma maior homogeneidade com a utilização das funções de mapeamento de Ifadis, Herring e Lanyi independentemente dos modelos.

Troposphere Delay Remote Sensing Using Single GPS Receiver

In addition to the non-dispertic medium, the tropospheric medium changes with time, and it is difficult to use a simple and unified mathematical model to determine the degree of change, especially in the long baseline relative positioning, the tropospheric delay between two stations often shows a weak spatial correlation. In this paper, this study will briefly introduce the main methods to reduce or eliminate various kinds of errors in order to build a real-time tropospheric delay model. The main body of this paper is to introduce and discuss the existing direct calculation model and mapping function of tropospheric delay. Based on the meteorological data of Shijiazhuang meteorological station provided by the official website of China Meteorological Administration, the appropriate tropospheric delay correction model and projection function (Saastamoinen +Marini-Murray model) are selected. The hourly tropospheric delay correction model along the propagation path direction in Shijiazhuang city on April 1, 2023 is established, and the accuracy and reliability of the model are analyzed.

Improving the accuracy of zenith tropospheric delay (ZTD) models is an important task. However, the existing ZTD models still have limitations, such as a lack of appropriate vertical adjustment function and being unsuitable for China, which has a complex climate and great undulating terrain. A new approach that considers the time-varying vertical adjustment and delicate diurnal variations of ZTD was introduced to develop a new grid ZTD model (NGZTD). The NGZTD model employed the Gaussian function and considered the seasonal variations of Gaussian coefficients to express the vertical variations of ZTD. The effectiveness of vertical interpolation for the vertical adjustment model (NGZTD-H) was validated. The root mean squared errors (RMSE) of the NGZTD-H model improved by 58% and 22% compared to the global pressure and temperature 3 (GPT3) model using ERA5 and radiosonde data, respectively. The NGZTD model’s effectiveness for directly estimating the ZTD was validated. The NGZTD model improved by 22% and 31% compared to the GPT3 model using GNSS-derived ZTD and layered ZTD at radiosonde stations, respectively. Seasonal variations in Gaussian coefficients need to be considered. Using constant Gaussian coefficients will generate large errors. The NGZTD model exhibited outstanding advantages in capturing diurnal variations and adapting to undulating terrain. We analyzed and discussed the main error sources of the NGZTD model using validation of spatial interpolation accuracy. This new ZTD model has potential applications in enhancing the reliability of navigation, positioning, and interferometric synthetic aperture radar (InSAR) measurements and is recommended to promote the development of space geodesy techniques.

Global pressure and temperature 2 wet (GPT2w) is an empirical troposphere delay model providing the mean values plus annual and semiannual amplitudes of pressure, temperature and its lapse rate, water vapor pressure and its decrease factor, weighted mean temperature, as well as hydrostatic and wet mapping function coefficients of the Vienna mapping function 1. All climatological parameters have been derived consistently from monthly mean pressure level data of ERA-Interim fields (European Centre for Medium-Range Weather Forecasts Re-Analysis) with a horizontal resolution of 1°, and the model is suitable to calculate slant hydrostatic and wet delays down to 3° elevation at sites in the vicinity of the earth surface using the date and approximate station coordinates as input. The wet delay estimation builds upon gridded values of the water vapor pressure, the weighted mean temperature, and the water vapor decrease factor, with the latter being tuned to ray-traced zenith wet delays. Comparisons with zenith delays at 341 globally distributed global navigation satellite systems stations show that the mean bias over all stations is below 1 mm and the mean standard deviation is about 3.6 cm. The GPT2w model with the gridded input file is provided at http://ggosatm.hg.tuwien.ac.at/DELAY/SOURCE/GPT2w/.

The tropospheric delay is one of the main error sources that degrades the accuracy of Global Navigation Satellite Systems (GNSS) Single Point Positioning (SPP). Although an empirical model is usually applied for correction and thereby to improve the positioning accuracy, the residual tropospheric delay is still drowned in measurement noise, and cannot be further compensated by parameter estimation. How much this type of residual error would sway the SPP positioning solutions on a global scale are still unclear. In this paper, the biases on SPP solutions introduced by the residual tropospheric delay when using nine conventionally Zenith Tropospheric Delay (ZTD) models are analyzed and discussed, including Saastamoinen+norm/Global Pressure and Temperature (GPT)/GPT2/GPT2w/GPT3, University of New Brunswick (UNB)3/UNB3m, European Geostationary Navigation Overlay System (EGNOS) and Vienna Mapping Functions (VMF)3 models. The accuracies of the nine ZTD models, as well as the SPP biases caused by the residual ZTD (dZTD) after model correction are evaluated using International GNSS Service (IGS)-ZTD products from around 400 globally distributed monitoring stations. The seasonal, latitudinal, and altitudinal discrepancies are analyzed respectively. The results show that the SPP solution biases caused by the dZTD mainly occur on the vertical direction, nearly to decimeter level, and significant discrepancies are observed among different models at different geographical locations. This study provides references for the refinement and applications of the nine ZTD models for SPP users.

Satellite laser ranging (SLR) constitutes a fundamental space geodetic technique providing global geodetic parameters, such as geocenter coordinates, Earth rotation parameters, and low-degree gravity field coefficients. The tropospheric delay correction is one of the crucial corrections that have to be taken into account when processing SLR data. Current conventional models of the troposphere delays assume a full symmetry of the atmosphere above SLR stations. Neglecting horizontal gradients in SLR solutions introduces a systematic error in SLR products, especially for the observations at low elevation angles, and leads to a deterioration of the consistency between SLR and other space geodetic techniques, such as global navigational satellite systems and very-long-baseline interferometry. We derive new mapping function coefficients, as well as first- and second-order horizontal gradients, all of which are based on numerical weather models, in order to properly consider the azimuthal asymmetry in SLR solutions. We test the enhanced mapping function and horizontal gradients on the solutions based on 11 years of SLR observations to LAGEOS-1/2 satellites and 1 year of SLR observations to Sentinel-3A. The consideration of azimuthal asymmetry of the atmosphere above the SLR stations has a systematic effect on SLR-derived products, such as station and geocenter coordinates and pole coordinates. Horizontal gradients in SLR solutions improve the consistency between SLR-derived pole coordinates and the combined IERS-C04 series by means of reducing the offset for the X and Y pole coordinates by 20 {upmu }mathrm{as}. The second-order horizontal gradients are negligible in SLR solutions; thus, including first-order gradients is sufficient for SLR solutions.