Troposphere Delay Remote Sensing Using Single GPS Receiver

Time-relative positioning is a recent method for processing GPS phase observations. The operational method undertaken in this paper consists of the following steps: first, recording phase observations at a station of known coordinates; second, moving the GPS receiver to an unknown station (which can be located up to a few hundred meters away, dependint on what type of transportation – e. g., walking, motorcycle – is available) while continuously observing carrier phases; and, third, recording phase observations at a second station of unknown coordinates with a single GPS receiver. To obtain the position of the unknown station relative to the first (known) station, the processing method uses combined observations taken at two different epochs and two different stations with the same receiver. For this reason, the errors that vary between two epochs must be taken into account in an appropriate way, especially errors in satellite clock corrections and ephemerides, and errors related to tropospheric and ionospheric delays. Ionospheric modeling using IONEX files (the ionospheric maps calculated by the International GPS Service) was also tested to correct L1 phase observations. This method has been used to calculate short vectors with an accuracy of a few centimeters (for a processing interval of 30 s) using a single civil GPS receiver. © 2001 John Wiley & Sons, Inc.

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.

Tropospheric delays from GNSS for application in coastal altimetry

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.

In recent years, many national timing laboratories (NMIs) have installed geodetic global positioning system (GPS) receivers together with their traditional GPS/GLONASS Common View (CV) receivers and two way satellite time and frequency transfer (TWSTFT) equipment. Many of these geodetic receivers operate continuously within the international GNSS service (IGS), and their data are regularly processed by IGS Analysis Centers. From its global network of over 350 stations and its Analysis Centers, the IGS generates precise combined GPS precise ephemeredes and station and satellite clock time series referred to the IGS Time Scale. A processing method called precise point positioning (PPP) is in use in the geodetic community allowing precise recovery of GPS antenna position, clock phase and tropospheric delays by taking advantage of the IGS precise products. Natural resources Canada (NRCan) has developed software implementing the PPP methodology. A previous assessment of PPP, as a promising time transfer method, was carried out at INRiM (formerly IEN) in 2003 [7], showing better stability over short/medium term than GPS CV and GPS P3 methods. Further analysis was carried out in 2005 [12] where, running continuously for period of up of two weeks, the NRCan PPP software was able to reduce the day-boundary discontinuities, allowing specific time-limited campaigns (PTFs). This paper reports on follow-on work performed at INRiM and NRCan to further characterize the PPP method for time transfer applications, involving some of the National Metrology Institutes considered in 2005. We take advantage of continuous PPP processing to develop a procedure to improve the continuity of solutions and to reduce the solution boundary discontinuities present in the daily PPP results.

GipsyX/RTGx is the Jet Propulsion Laboratory’s (JPL) next generation software package for positioning, navigation, timing, and Earth science using measurements from three geodetic techniques: Global Navigation Satellite Systems (GNSS), Satellite Laser Ranging (SLR), and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS); with Very Long Baseline Interferometry (VLBI) under development. The software facilitates combined estimation of geodetic and geophysical parameters using a Kalman filter approach on real or simulated data in both post-processing and in real-time. The estimated parameters include station coordinates and velocities, satellite orbits and clocks, Earth orientation, ionospheric and tropospheric delays. The software is also capable of full realization of a dynamic terrestrial reference through analysis and combination of time series of ground station coordinates.Applying lessons learned from its predecessors, GIPSY-OASIS and Real Time GIPSY (RTG), GipsyX/RTGx was re-designed from the ground up to offer improved precision, accuracy, usability, and operational flexibility. We present some key aspects of its new architecture, and describe some of its major applications, including Real-time orbit determination and ephemeris predictions in the U.S. Air Force Next Generation GPS Operational Control Segment (OCX), as well as in JPL’s Global Differential GPS (GDGPS) System, supporting User Range Error (URE) of <5 cm RMS; precision post-processing GNSS orbit determination, including JPL’s contributions to the International GNSS Service (IGS) with URE in the 2 cm RMS range; Precise point positioning (PPP) with ambiguity resolution, both statically and kinematically, for geodetic applications with 2 mm horizontal, and 6.5 mm vertical repeatability for static positioning; Operational orbit and clock determination for Low Earth Orbiting (LEO) satellites, such as NASA’s Gravity Recovery and Climate Experiment (GRACE) mission with GRACE relative clock alignment at the 20 ps level; calibration of radio occultation data from LEO satellites for weather forecasting and climate studies; Satellite Laser Ranging (SLR) to GNSS and LEO satellites, DORIS-based and multi-technique orbit determination for LEO; production of terrestrial reference frames and Earth rotation parameters in support of JPL’s contribution to the International Terrestrial Reference Frame (ITRF).

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.

Observation data sets from three different periods and 23 International GNSS Service (IGS) stations spread over the world were processed in static mode using four online free precise point positioning (PPP) services: Automatic Precise Positioning Service (APPS), GPS Analysis and Positioning Software, Canadian Spatial Reference System precise point positioning service, and Magic-PPP. The estimated positions of the 23 IGS stations were compared with the published values. The estimated zenith tropospheric delays (ZTDs) at these stations were compared with the corresponding IGS troposphere products published on the IGS Web site. Furthermore, in order to analyze PPP precision for short observation periods, GPS observation data sets with a sampling rate of 1 s collected by one CORS station were also processed by the four online PPP services. Calculation shows that the precision of daily solutions for north and east (N/E) components estimated by the four online PPP services can reach millimeter level, the precision of ellipsoid elevation (H) can reach 1---2 cm, and precision of ZTDs estimation results is approximately 1---2 cm. Compared with the corresponding values published on the IGS Web site, the precision of ZTDs estimated by APPS is higher than those estimated by the other three PPP online services; the differences between ZTDs by APPS and IGS values are mostly within ±1 cm. For PPP with short observation periods, the precision of N/E components within 2, 1, and 0.5 h observation periods can reach about 2---3, 2---7, and 3---8 cm, respectively, while the precision of H components is about 3---5, 5---12, and 10---18 cm, respectively.

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.

Tropospheric delay is one of the major error sources in GNSS (Global Navigation Satellite Systems) positioning. Over the years, many approaches have been devised which aim at accurately modeling tropospheric delays, so-called troposphere models. Using the troposphere data of over 16,000 global stations in the last 10 years, as calculated by the Nevada Geodetic Laboratory (NGL), this paper evaluates the performance of the empirical troposphere model GPT3, which is the latest version of the GPT (Global Pressure and Temperature) series model. Owing to the large station number, long time-span and diverse station distribution, the spatiotemporal properties of the empirical model were analyzed using the average deviation (BIAS) and root mean square (RMS) error as indicators. The experimental results demonstrate that: (1) the troposphere products of NGL have the same accuracy as the IGS (International GNSS Service) products and can be used as a reference for evaluating general troposphere models. (2) The global average BIAS of the ZTD (zenith total delay) estimated by GPT3 is −0.99 cm and the global average RMS is 4.41 cm. The accuracy of the model is strongly correlated with latitude and ellipsoidal height, showing obviously seasonal variations. (3) The global average RMS of the north gradient and east gradient estimated by GPT3 is 0.77 mm and 0.73 mm, respectively, which are strongly correlated with each other, with values increasing from the equator to lower latitudes and decreasing from lower to higher latitudes.

GNSS zenith delays and gradients in the analysis of VLBI Intensive sessions

Acousto-optic devices using lead molybdate and related compounds: Bell Telephone Labs Inc US patent 3617931 (1971) filed 5 May 1969

Ground-based GNSS ZTD/IWV estimation system for numerical weather prediction in challenging weather conditions

Measuring deformations using SAR interferometry and GPS observables with geodetic accuracy: Application to Tokyo, Japan

Existing apriori tropospheric models are not sufficiently accurate to remove tropospheric delay from GPS observations. Remaining effects of residual tropospheric delay need to be estimated to ensure high accuracy and reliability of GPS positioning. Other researchers have shown that implementations of network- based positioning techniques can adequately model the residual tropospheric delay as well as ionospheric delay and orbit biases. However, the effectiveness in removing residual tropospheric delay is highly dependent on the degree to which the wet component from the troposphere can be estimated or mitigated, an effect which shows strong variation with time and space. The aim of this paper is to illustrate the performance of an existing apriori tropospheric model and to discuss some issues concerning the estimation of the (total) tropospheric delay in the equatorial area. Finally, the network approach is applied to mitigate the effect of residual tropospheric delay. Some preliminary results from test experiments using GPS network data from an equatorial region, a location with the highest effect of tropospheric delay, are presented.