GNSS Applications Research Articles

Enhancing GNSS tropospheric delay corrections through an innovative lapse rate grid and adiabatic modelling

Since measurements of meteorological parameters like air pressure, water vapor pressure, and temperature are typically not conducted at the receiving antenna’s height, accurate vertical adjustments are indispensable for the tropospheric delay calculation in GNSS applications. We developed an enhanced GPT3 model named as GPT3a, incorporating a new temperature lapse rate grid model and the adiabatic method. The capabilities of GPT3a in predicting atmospheric parameter profiles are assessed by comparison with radiosonde data, NCEP reanalysis data, and GNSS data. Compared with GPT3, IGPT, UNB3, and the constant model with a value of 6.5 K/km, the accuracy of the GPT3a is improved by 50 %, 26 %, 21 %, and 31 % respectively in predicting lapse rate. The RMSEs of GPT3a, GPT3 and IGPT, across temperature profiles (4.2 K, 10.7 K and 6.6 K, respectively), pressure profiles (5.7 hPa, 18.7 hPa and 6.8 hPa, respectively), and ZHD profiles (16.4 mm, 36.4 mm and 17.5 mm, respectively), demonstrate that GPT3a performs superiorly to the GPT3 and IGPT models. Moreover, in the GNSS-based water vapor retrieval, when there is a large height difference between GNSS sites and the model, the GPT3a obviously outperforms GPT3. In short, GPT3a can be used as an enhancement of GPT3 to support GNSS positioning, GNSS meteorology and atmospheric research, which extends the applicability of GPT3 beyond the Earth’s surface to airspace.

Derivation of the Sagnac (Earth-rotation) correction and analysis of its accuracy for GNSS applications

Global Navigation Satellite Systems (GNSS) applications require computation of the geometric range between the satellite vehicle at the time-of-signal transmission and the receiver antenna location at the time-of-signal reception. This computation requires attention to the frames of reference due to the rotation of the Earth-Centered Earth-Fixed (ECEF) frame during the time-of-signal propagation. Three range computation approaches are commonplace and will be discussed herein. The first is the Global Positioning System Interface Control Document recommendation to rotate the ECEF frames to a common reference time. The other two are forms of the Sagnac correction. The Sagnac derivations already in the literature are either limited to stationary receivers or lack the connection between the Earth-centered inertial (ECI) and ECEF frames. Neither form of the Sagnac correction exactly reproduces the geometric range. They are approximations. The literature does not currently contain an analysis of the error involved in using either form of the Sagnac correction. This article makes two contributions: (1) it presents derivations for both forms of the Sagnac correction that are valid for moving receivers and that maintain the connection between the ECI and ECEF frames; and (2) it analyzes the error of the Sagnac correction for orbits of different radius. The analysis shows that Sagnac corrections introduce range errors less than 7.57×10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.57\ imes 10^{-4}$$\\end{document} meters for GNSS satellites at medium Earth orbit.

On the applicability of low-cost GNSS antennas to precise surveying applications

Abstract This study addresses the scientific question of the applicability of low-cost antennas to the most precise GNSS applications. First of all, we inspect the implications of the availability and quality of low-cost antenna PCC models for precise positioning. From this point of view, we analyze the selected performance indicators of multi-constellation positioning with the representative set of low-cost mass-market GNSS receiver antennas. The processing strategy was based on the relative positioning model, considered the most reliable and precise one. To isolate the antenna-related errors from atmospheric propagation ones, we conducted an experiment based on an ultra-short baseline. As the main indications of low-cost antenna performance, we considered distance and height residuals, defined as the difference between benchmarks and the retrieved from GNSS measurements. We found that the low-cost antenna's PCV effect may significantly affect the final results. On the other hand, the results obtained using certain configurations of low-cost antennas were characterized by only slightly higher standard deviations and discrepancies with respect to benchmark values than those obtained with surveying or geodetic equipment. We identify several sets of low-cost antennas where distance residuals do not exceed 4 mm and height residuals do not exceed 6 mm, which shows the low-cost antenna performance comparable to those achieved using high-grade antennas. On this basis, we conclude that selected low-cost antennas can meet the requirements of high-precision surveying applications.

Single-Fed CP Antenna With Abrupt Sense Reversal for GNSS and SATCOM Application

Single-Fed CP Antenna With Abrupt Sense Reversal for GNSS and SATCOM Application

Sensitivity of GNSS to vertical land motion over Europe: effects of geophysical loadings and common-mode errors

We perform a statistical sensitivity analysis on a parametric fit to vertical daily displacement time series of 244 European Permanent GNSS stations, with a focus on linear vertical land motion (VLM), i.e., station velocity. We compare two independent corrections to the raw (uncorrected) observed displacements. The first correction is physical and accounts for non-tidal atmospheric, non-tidal oceanic and hydrological loading displacements, while the second approach is an empirical correction for the common-mode errors. For the uncorrected case, we show that combining power-law and white noise stochastic models with autoregressive models yields adequate noise approximations. With this as a realistic baseline, we report improvement rates of about 14% to 24% in station velocity sensitivity, after corrections are applied. We analyze the choice of the stochastic models in detail and outline potential discrepancies between the GNSS-observed displacements and those predicted by the loading models. Furthermore, we apply restricted maximum likelihood estimation (RMLE), to remove low-frequency noise biases, which yields more reliable velocity uncertainty estimates. RMLE reveals that for a number of stations noise is best modeled by a combination of random walk, flicker noise, and white noise. The sensitivity analysis yields minimum detectable VLM parameters (linear velocities, seasonal periodic motions, and offsets), which are of interest for geophysical applications of GNSS, such as tectonic or hydrological studies.

LEO enhanced GNSS (LeGNSS) precise point positioning with emphasis on model comparison

With the rapid construction of the low-earth-orbit (LEO) constellation, LEO Enhanced Global Navigation Satellite System (LeGNSS) has become a hotspot in the research of GNSS applications and services, especially for fast convergence of precise point positioning (PPP). In this study, we analyze the impact of LEO satellites on the spatial geometry based on simulated LEO and real GNSS data, and evaluate the LeGNSS PPP performance with ionosphere-free (IF), undifferenced and uncombined (UDUC), and ionosphere-weighted (IW) models. Eight Multi-GNSS Experiment (MGEX) stations are selected for static and kinematic experiments. Results show that Position Dilution of Precision (PDOP) values of LeGNSS are about 0.5–1.2, which are improved by 38 % and 22 % compared with GPS-only and combined GPS, Galileo, and BDS (G\\E\\C) solutions. With LEO satellites, the positioning accuracy in east (E), north (N), and up (U) directions are improved by about 50 %, 30 %, and 50 % for the static mode, and about 35 %, 30 %, and 67 % for the kinematic mode. Moreover, the positioning accuracies of the IF, UDUC, and IW models are comparable. For convergence time, the static and kinematic results with LEO satellites are about 1.1 and 1.3 min, respectively, while those without LEO satellites are longer than 10.0 min. In addition, the model with inter-system bias (ISB) constraints can reduce the convergence time by within 1.0 min.

A novel piecewise linear transformation to moderate regional boundary effect on Real-Time regional ionospheric map (RT-RIM)

RT-RIM with high accuracy and dense spatiotemporal resolution of the ionospheric total electron content is crucial to diverse real-time GNSS applications. However, the uneven ionospheric pierce points distribution and boundary effect severely restrict the RT-RIM accuracy. We dedicate to the rapid and straightforward method to address the limited accuracy issue caused by the two crucial challenges. A novel piecewise linear transformation-adjusted spherical cap harmonic (PLT-ASCH) method is proposed to moderate the localized accuracy decrease in various latitudes areas for both active and stable ionospheric conditions. Especially, in the active ionospheric condition, the RMS improvements referring to IGS products are about 38.85%, 17.04%, 16.73% in Europe and 53.12%, 4.36%, 4.35% in South America, comparing to the inverse distance weighting, ASCH, and adjusted spherical harmonics adding Kriging methods. Moreover, the RMS improvements referring to differential slant TEC are about 48.11%, 16.53%, 16.99% in Europe and 61.01%, 4.87%, 4.33% in South America.

EVALUATION OF THE PERFORMANCE OF MULTI-GNSS ADVANCED ORBIT AND CLOCK AUGMENTATION – PRECISE POINT POSITIONING (MADOCA-PPP) IN JAPAN REGION

For users of Precise Point Positioning (PPP), Multi-GNSS Advanced Orbit and Clock Augmentation PPP signals provide corrective data. When using the PPP approach and/or PPP-Ambiguity Resolution (AR) method, the QZSS signal provides globally applicable error corrections on satellite orbit, clock offset, and code/phase biases. In addition, from FY2024, as a part of the MADOCA-PPP technology demonstration, wide-area ionospheric correction data will be provided for the Asia-Oceania region. A software estimator of precise satellite information developed by JAXA, Multi-GNSS Advanced Demonstration Tool for Orbit and Clock Analysis (MADOCA), allows u-blox CO99-ZED-F9P and MSJ 3008-GM4-QZS utilizing MADOCA-PPP to be used in GNSS applications that need sub-decimetre precision but don’t have to be expensive. Errors caused by positioning satellites are computed by using observation data from domestic and overseas GNSS monitoring station networks such as IGS and MIRAI, and obtained correction data is transmitted from QZSS signal to provide highly precise positioning augmentation services that can be used in the Asia-Oceania Region. Users may utilize the PPP technique for high-precision locating by employing a GNSS receiver that supports the QZSS signals. This paper describes an experiment carried out with the static method to combine GPS, GLONASS, and QZSS signals in the project site (ISHI, USUD and MIZU stations in Japan). This paper examines the GPS/GLONASS/QZSS obtainable accuracy. These obtained results indicate that integrating GPS system with GLONASS and QZSS is favoured for surveying applications. It appears that integrating GPS/GLONASS/QZSS (MADOCA precise ephemeris file) static measurements in the study area between 0–4 millimetres accuracy can be guaranteed on all occasions.

Multiband circularly-polarized stacked elliptical patch antenna with eye-shaped slot for GNSS applications

Abstract This paper introduces a tri-band stacked elliptical patch antenna featuring a right-handed circular polarized, designed to operate at the L2, L5, and L1 Global Navigation Satellite System bands. Initially, an elliptic patch is constructed and fed by a probe feed to generate TM110 and TM210 modes at resonance frequencies calculated using Mathieu functions. The probe position is precisely adjusted to excite the quasi-orthogonal mode of TM110 to generate circularly polarized (CP) waves at the L2 and L5 bands. Subsequently, an eye-shaped aperture is engraved into the elliptical patch to enhance the axial ratio (AR) beamwidth in the L2 and L5 bands and stimulate the orthogonal mode of TM210 to produce CP waves at the L1 band. Lastly, a stacked partially elliptical parasitic element is placed beneath the upper slotted elliptical patch to enhance the orthogonality of TM210 surface current versions and thus improve the AR beamwidth at the L1 band. The proposed antenna shows low reflection coefficient values at 1.12–1.33 (L2/L5), and 1.5–1.66 GHz (L1). The AR beamwidths are 133/213∘, 167/163∘, and 36/103∘ at two orthogonal cutplanes at L5, L2, and L1 bands, respectively. The antenna also has decent gains of 6–6.9 dBic across the three bands.

A new approach of multi-dimensional correlation as a separability measure of multiple outliers in GNSS applications

Abstract Detecting and identifying outliers/failures in GNSS measurements has garnered significant attention among researchers aiming to enhance the quality of GNSS positioning and navigation. This study delves into the analysis of the separability of multiple outliers when single, double, and triple outliers occur in single-point positioning (SPP) measurements. To achieve this, a novel method includes introducing a multi-dimensional correlation coefficient among test statistics. This coefficient functions as a measure of outliers separability and, in turn, assesses the possible impact of outliers on other measurements. This multi-dimensional correlation approach is based on a nested correlation ( ρ nested θ , φ ${\rho }_{\text{nested}}^{\theta ,\varphi }$ ) that explains the variations in test statistic values with and without common measurements in two pairs/combinations. The performance of the ρ nested θ , φ ${\rho }_{\text{nested}}^{\theta ,\varphi }$ is then compared with other two existing methods of multi-dimensional correlation namely the maximum ( ρ max θ , φ ${\rho }_{\mathrm{max}}^{\theta ,\varphi }$ ) and global ( ρ Global θ , φ ${\rho }_{\text{Global}}^{\theta ,\varphi }$ ) correlation. The results show that under the presence of two outliers and with and without common measurements in two pairs, the ρ nested θ ${\rho }_{\text{nested}}^{\theta }$ outperforms the, ρ max θ ${\rho }_{\mathrm{max}}^{\theta }$ and ρ Global θ ${\rho }_{\text{Global}}^{\theta }$ exhibiting a determination coefficient (R 2) value of approximately 0.95 and 0.62 respectively. The results furthermore reveal that for three outliers and with one, two, and noncommon measurements intersecting between two combinations, the values of R 2 are 0.62, 0.96, and 0.34. respectively. This means that the ρ nested θ , φ ${\rho }_{\text{nested}}^{\theta ,\varphi }$ can explain the variations in outlier test statistic values particularly in the case that common measurements appear in two pairs/combinations.

Geomagnetic Storm Variation of Vertical Total Electron Content (VTEC) Over Some Euro-African Stations

Geomagnetic storms are events which have physical effects on some ionospheric parameters that, to some extent,affects the state and dynamics of the ionosphere with important implications on GNSS applications. Here, the total electron content (TEC) of Brussels (50.80oN, 04.37oE), Madrid (40.43oN, 04.25oW) and Irkutsk (52.22oN, 104.32oE), which are all mid-latitude European stations are compared with Libreville (00.35oN, 09.67oE) and Lusaka (15.43oS, 28.32oE) which are equatorial and low-latitude stations respectively. This study is done over two geomagnetic storms that took place in the solstice period of 2004. Deviations of storm time VTEC from solar quiet (Sq) averages are calculated, analysed and presented. Similarities and differences of storm effects are observed in the European stations with enhancements and depressions. Diurnal solar quiet day variations showed high VTEC during the post-noon hours for all the stations. The VTEC deviations during storm time at Libreville lie within, for Lusaka it is. For the mid-latitude European stations, the deviations are lower such that is recorded at Brussels while is recorded for both Irkutsk and Madrid. Enhancement of VTEC during the daytime storm period is attributable to the super-fountain effect caused by the prompt penetration electric fields (PPEFs) into the ionosphere and magnetosphere while low VTEC at night-time is attributed to the process of recombination. Understanding the behaviour of the ionosphere during geomagnetic storms is important and necessary for a better understanding of the applications of GNSS.

A method for calculating real-time ZTD grid data in Chinese regions based on GNSS ZTD modified ERA5 grid products

The low spatial and temporal resolution and poor accuracy of real-time zenith tropospheric delay (ZTD) have always been one of the main constraints during the development of real-time GNSS applications. This paper presents a method to obtain real-time ZTD grid data in Chinese regions utilizing the ZTD-modified ERA5 grid products from GNSS stations. Initially, the original ZTD fitting function for vertical variation is improved. Then, the real-time ZTD grid data for the Chinese region (RZTDG) could be obtained by correcting the 7-day earlier ERA5 data through the real-time ZTD data from the GNSS stations. In this paper, we analyze the performance of the model under various weather conditions, and the results show that it still keeps a high accuracy even under variable weather conditions. ZTD data from 66 radiosonde stations in China in 2022 are used as reference values to evaluate the accuracy of the RZTDG. Experimental results show that the RMSE (2.3 cm) and MAE (1.8 cm) of the RZTDG are comparable to the ERA5 data of the day (RMSE: 2.4 cm, MAE: 1.8 cm) and significantly better than the accuracy of the HGPT2 (RMSE: 5.1 cm, MAE: 4.1 cm). Meanwhile, the Bias of RZTDG (0.1 cm) is much smaller than the Bias of HGPT2 (−0.9 cm) and the Bias of ERA5 (−0.8 cm), proving that the method in this paper has less deviation from the radiosonde ZTD data. Finally, the convergence times of the float PPP with and without tropospheric constraints are counted for 120 GNSS stations for DOY 11–13, DOY 101–103, and DOY 192–194 in 2022. The results show that the convergence time of the float PPP is reduced by 30% after constraining the ZTD using RZTDG.

Bayesian fault detection, identification, and adaptation for GNSS applications

Bayesian fault detection, identification, and adaptation for GNSS applications

A Compact Broadband Circularly Polarized Antenna with Novel Tilt Fences for GNSS Applications

A Compact Broadband Circularly Polarized Antenna with Novel Tilt Fences for GNSS Applications

Compact Dual-band CPW-fed Circularly Polarized Slot Antenna for GNSS Applications

Compact Dual-band CPW-fed Circularly Polarized Slot Antenna for GNSS Applications

Validation of GPS III transmit antenna calibrations

Accurate information about the satellite transmit antennas is essential for high-precision GNSS applications. Such metadata of the GPS III satellites were publicly made available by the manufacturer Lockheed Martin. They comprise phase center offsets (PCOs), phase patterns, and directivity patterns. These calibrations are validated with ground-based measurements of a global GPS tracking network and observations of a high-gain antenna. Phase center offsets and patterns are estimated from dual-frequency observations of a ground tracking network. The ionosphere-free L1/L2 z-PCOs show a 10 cm offset w.r.t. the manufacturer calibrations due to already known inconsistencies with the ITRF2020 scale fixed in the estimation. The standard deviation of the differences between estimated and calibrated z-PCOs is 2.7 cm. The estimated phase patterns have a 0.7 mm RMS consistency with the manufacturer calibrations after minimizing the raw patterns for nadir angles between 0° and 14°. The directivity patterns are validated with the effective isotropic radiated power (EIRP) measured with a 30 m high-gain antenna. The measured EIRP for the L1 and L2 band is affected by M-code transmission from a distinct antenna. When modeling the additional contribution of this antenna, the nadir-angle variation of the EIRP matches the calibrated directivity patterns with a precision of 0.1 dBW. Representative transmit power values of the main navigation antenna amount to 125 W, 30 W, and 85 W in the L1, L2, and L5 bands, while the L1 and L2 M-code signals are transmitted with about 30 W and 25 W, respectively.

Research on GNSS positioning and applications in Poland in 2015–2018

Research on GNSS positioning and applications in Poland in 2015–2018

A Fibonacci Series Motivated Circularly Polarized L-Band Slotted Antenna for GNSS Application

This paper proposes a co-planar waveguide-fed circularly polarized L-band antenna for GNSS Applications. The Fibonacci series inspired us to decide the physical dimensions of the radiating structure. The proposed antenna with the dimensions of 60 × 40 × 0.8 mm3 is fabricated by etching out several slots from the patch and ground plane as well. The circular polarization (CP) behavior is observed from different shaped slots in the ground plane as well as in radiating patches. The experimental and simulation results revealed good agreement over the entire operating frequency range.

Research on GNSS positioning and applications in Poland in 2019–2022

Research on GNSS positioning and applications in Poland in 2019–2022

DATA INTEGRITY AND QUALITY ANALYSIS OF LOW COST ZED-F9P U-BLOX GNSS RECEIVER

Thanks to the rapidly emerging low-cost dual-frequency GNSS receivers, a feasible alternative for geodetic-grade GNSS receivers became available for some GNSS applications. In this study, the performance of data integrity and quality of a low-cost ZED-F9P u-blox GNSS receiver was investigated by comparing it with a geodetic-grade GNSS receiver. Availability of the epoch and phase/code signal channels, signal-to-noise ratio (SNR), code multipath, and cycle slips were analyzed for the geodetic-grade and low-cost ZED-F9P u-blox GNSS receivers. One month’s data of GPS, GLONASS, and Galileo constellations were analysed using the RINEX files of the receivers. The results showed that the epoch availability of the geodetic-grade and u-blox GNSS receiver is comparable to each other, while the availability of phase/code signal channels of the geodetic-grade receiver is higher than the u-blox receiver. In terms of data quality, SNR values from both receivers are comparable, while the multipath level of the u-blox GNSS receiver is significantly higher than the geodetic-grade one. The results also showed that the number of cycle slips of the u-blox receiver is significantly higher than the geodetic-one.