Estimation of absolute GNSS satellite antenna group delay variations based on those of absolute receiver antenna group delays

GNSS satellite and receiving antennas exhibit group delay variations (GDV), which affect code pseudorange measurements. Like antenna phase center variations, which affect phase measurements, they are frequency-dependent and vary with the direction of the transmitted and received signal. GNSS code observations contain the combined contributions of satellite and receiver antennas. If absolute GDV are available for the receiver antennas, absolute satellite GDV can be determined. In 2019, an extensive set of absolute receiver antenna GDV was published and, thus, it became feasible to estimate absolute satellite antenna GDV based on terrestrial observations. We used the absolute GDV of four selected receiver antenna types and observation data of globally distributed reference stations that employ these antenna types to determine absolute GDV for the GPS, GLONASS, Galileo, BeiDou, and QZSS satellite antennas. Besides BeiDou-2 satellites whose GDV are known to reach up to 1.5 m peak-to-peak, the GPS satellites show the largest GDV at frequencies L1 and L5 with up to 0.3 and 0.4 m peak-to-peak, respectively. They also show the largest satellite-to-satellite variations within a constellation. The GDV of GLONASS-M satellites reach up to 25 cm at frequency G1; Galileo satellites exhibit the largest GDV at frequency E6 with up to 20 cm; BeiDou-3 satellites show the largest GDV of around 15 cm at frequencies B1-2 and B3. Frequencies L2 of GPS IIIA, E1 of Galileo FOC, and B2a/B2b of BeiDou-3 satellites are the least affected. Their variations are below 10 cm.

Estimation of station-dependent LRA correction parameters for the TOPEX/Poseidon mission

<p>Launched in 1992, the TOPEX/Poseidon (T/P) mission is one of the first major altimetry missions. It is the predecessor of the Jason satellites which orbit the Earth on a very similar orbit. The geodetic space technique SLR (Satellite Laser Ranging) provides observations of this mission by targeting the Laser Retroreflector Array (LRA) mounted on the spacecraft. The T/P LRA is extremely large and not optimally designed. It thus causes big variations in the LRA phase center. These variations are a significant limiting factor of the orbit accuracy which makes it essential to apply a measurement correction for precise orbit determination. Up to now, only tabulated LRA corrections are available which require an interpolation.</p><p>In this contribution, we present a new approach to determine station-dependent LRA corrections to improve the phase center variations. The approach is based on a continuous analytical correction function which only uses the observation azimuth and zenith angle in combination with four parameters. These parameters are computed within an estimation process for each observing SLR station. Therefore, uncorrected SLR residuals based on raw SLR normal point observations are used. The correction value is added to the SLR measurement and counteracts the LRA phase center variations.</p><p>The advantages of this method are the continuous functional, which is easy to implement in existing software packages, as well as the avoidance of an interpolation between tabulated values. Furthermore, the differences between orbits determined with and without the LRA correction will be presented. Station coordinate time series and orbit comparisons with external T/P orbits are investigated in order to prove the high quality of the obtained LRA corrections.</p>

Phase Center Corrections for BDS IGSO and MEO Satellites in IGb14 and IGSR3 Frame

As pre-launch antenna calibrations are not available for GPS and GLONASS satellites, the high correlation between the terrestrial scale and phase center offset (PCO) prevents a reliable estimation of the terrestrial scale with GNSS (Global Navigation Satellite System) technology. Fortunately, the ground calibrated PCO values for Galileo, BeiDou navigation satellite system (BDS), and QZSS have been released, making a reliable estimation of the terrestrial scale with GNSS possible. In the third reprocess (repro3) of International GNSS Service (IGS), the terrestrial scale derived with Galileo, has been used. To evaluate the consistency of the terrestrial scale derived from the BDS-released PCOs as well as Galileo-released ones, and to incorporate BDS into IGS repro3 as well as operational legacy analysis, the phase center variations (PCV) and PCO for BDS medium earth orbit (MEO) and inclined geostationary orbit (IGSO) satellites are estimated to be consistent with GPS/GLONASS antenna offsets in two frames, i.e., IGb14 and IGS R3, considering robot calibrations of the ground receiver antenna models for BDS released by Geo++. We observe that the average offset of Z-PCOs achieves +98.8 mm between BDS official released and the estimated PCOs in IGb14 frame for BDS-3 MEO satellites, whereas the average offset for Z-PCO is about +174.1 mm (about −1.27 ppb at the height of BDS MEO satellites) between the solutions in IGSR3 and IGb14 frame. The phase center solutions are evaluated with orbit boundary disclosures (OBD) as well as the global station coordinates. The orbit consistency benefits from the PCO/PCV estimates, particularly for BDS-2 MEO satellites, of which the 3D RMS (root mean square) OBD is reduced by 50%, whereas 3D OBD achieves about 90.0 mm for BDS-3 MEO satellites. Moreover, the scale bias between BDS-derived station coordinates and IGS legacy solutions in IGb14 frame is reduced from +0.446 ± 0.153 ppb to +0.012 ± 0.112 ppb using PCO/PCV estimates in IGb14, instead of the BDS official released values. Additionally, the residuals of the BDS-derived station heights (after the Helmert transformation) are slightly reduced from 9.65 to 8.62 mm. On the other hand, about +0.226 ± 0.175 ppb is observed between BDS-only coordinate solutions derived from PCO/PCV estimates in IGSR3 frame and the IGS repro3 initial combination. These results demonstrate that the scale inconsistency derived from BDS and Galileo released PCOs is about +1.854 ± 0.191 ppb, and a good consistency of PCO/PCC estimates for BDS in IGb14 and IGSR3 frame with other systems of GPS/ GLONASS antenna offsets is achieved.

Site Characterization and Multipath Maps Using Zernike Polynomials

<p>Receiver antenna calibration plays an important role in precise point positioning (PPP). The correct management of the phase center offset and variations (PCV) and multipath effects can drastically improve the estimation of tropospheric parameters and the stability of the position over short measurement sessions. Correction parameters, to compensate for PCV, are usually computed in laboratory on all the geodetic grade antennas, but they are not available for low-cost apparatus; multipath can be partially mitigated by a robot calibration on site but this is an expensive procedure that is rarely adopted. Multipath staking maps (MPS) using carrier phase observation residuals are a cheap and powerful tool to generate site-specific corrections, effective for reducing both near-field and far-field effects. These maps can be generated by gridding multiple residuals falling in a cell of a pre-determined size. In this work, we propose to compute a set of polynomial coefficients of a Zernike expansion from the residuals of a PPP uncombined least-squares adjustment performed by the open-source goGPS processing software; these coefficients can be later used to synthesize corrections of the observations for the next processing of the target station. In contrast with gridding techniques, this approach allows a to generate smoother corrections and allows a limited automatic extrapolation of the correction values in areas of the sky that were not covered by observations in the set of data used in the calibration phase. The results show that the technique is effective in the modelling of multipath and residual phase center variations allowing a drastic reduction of the undifferenced residuals. Zernike polynomials are a sequence of polynomials orthogonal on the unit disk, vastly used in optics but, to our knowledge, never considered for GNSS applications, their symmetric properties and the circular support area makes them an interesting object of investigation for other possible usages in GNSS processing.</p>

The Effect of TLS Radome on GNSS Precise Positioning

This article presents the results of a test carried out to check the usability of spherical TLS targets as GNSS antenna radomes (herein called TLS radomes). On different days, the survey was conducted using two GNSS antennas, one of them with a TLS radome. Measurements were made using 2 roof pillars on the rooftop as base-rover pillars with little obstruction. The measurements were carried out for approximately 1 hour in every scenario. The software used for data processing is MATLAB-based software and the raw data were processed using the double difference (DD) strategy to obtain optimal results. The results of the data processing indicated that the TLS radome has no significant influence on availability and accuracy of estimated position. The signals are slightly attenuated by the radome (1-2 dBHz) and the noise level is slightly increased but both effects are negligible for practical purposes. However, we found that the antenna should be calibrated with the TLS radome to clarify apparent minor phase center eccentricities (1-2 mm) and to reduce systematic effects with long periods (few minutes) and amplitudes up to about 5 mm which are likely due to phase center variations.

Potential of GPS Common Clock Single-differences for Deformation Monitoring

Global satellite navigation systems (GNSS) are a standard measurement device for deformation monitoring. In many applications, double-differences are used to reduce distance dependent systematic effects, as well as to eliminate the receiver and satellites clock errors. However, due to the navigation principle of one way ranging used in GPS, the geometry of the subsequent adjustment is weakened. As a result, the height component is generally determined three times less precisely than the horizontal coordinates. In addition, large correlations between the height and elevation dependent effects exist such as tropospheric refraction, mismodelled phase center variations, or multipath which restricts the attainable accuracy. However, for a kinematic analysis, i. e. for estimating high rate coordinate time series, the situation can be significantly improved if a common clock is connected to different GNSS receivers in a network or on a baseline. Consequently, between-station single-differences are sufficient to solve for the baseline coordinates. The positioning geometry is significantly improved which is reflected by a reduction of the standard deviation of kinematic heights by about a factor 3 underlining the benefits of this new approach. Real data from baselines at the Physikalisch-Technische Bundesanstalt campus at Braunschweig where receivers are connected over 290 m via an optical fiber link to a common clock was analysed.

SHORT STATIC GPS/GLONASS OBSERVATION PROCESSING IN THE CONTEXT OF ANTENNA PHASE CENTER VARIATION PROBLEM

So far, three methods have been developed to determine GNSS antenna phase center variations (PCV). For this reason, and because of some problems in introducing absolute models, there are presently three models of PCV receiver antennas (relative, absolute converted and absolute) and two satellite antennas (standard and absolute). Additionally, when simultaneously processing observations from different positioning systems (e.g. GPS and GLONASS), we can expect a further complication resulting from the different structure of signals and differences in satellite constellations. This paper aims at studying the height differences in short static GPS/GLONASS observation processing when different calibration models are used. The analysis was done using 3 days of GNSS data, collected with three different receivers and antennas, divided by half hour observation sessions. The results show that switching between relative and absolute PCV models may have a visible effect on height determination, particularly in high accuracy applications. The problem is especially important when mixed GPS/GLONASS observations are processed. The update of receiver antenna calibrations model from relative to absolute in our study (using LEIAT504GG, JAV_GRANT-G3T and TPSHIPER_PLUS antennas) induces a jump (depending on the measurement session) in the vertical component within to 1.3 cm (GPS-only solutions) or within 1.9 cm (GPS/GLONASS solutions).

Phase Errors Simulation Analysis for GNSS Antenna in Multipath Environment

High-precision GNSS application requires the exact phase center calibration of antenna. Various methods are published to determine the locations of the phase center. In the outfield, when the phase errors that arose by multipath exceed the phase center variations (PCV) tolerance, the calibration values may be not useful. The objective of this paper is thus to evaluate the phase errors that arose by multipath signals. An improved model of antenna receiving signal is presented. The model consists of three main components: (1) an antenna model created by combination of right hand circular polarization (RHCP) and left hand circular polarization (LHCP), (2) a multipath signals model including amplitude, phase, and polarization, and (3) a ground reflection model applying to circular polarization signals. Based on the model, two kinds of novel up-to-down(U/D)ratios are presented. The performance of the model is assessed against the impact of up-to-down ratio of antenna on phase errors.

Determinação dos coeficientes dos harmônicos esféricos para o cálculo dos parâmetros pcv e pco utilizando dados de programas comerciais de calibração

Erros provenientes do centro de fase da antena, conhecidos como PCV - Phase Center Variations - são considerados agentes limitadores da acurácia do posicionamento relativo GNSS e do Posicionamento por Ponto Preciso (PPP). As PCVs dependem da direção do sinal do satélite e podem ser modeladas por parâmetros determinados por calibração de antenas em que são utilizados programas específicos, como por exemplo Wasoft/Kalib. Alguns autores afirmam que os programas aplicam funções harmônicas esféricas para a modelagem dos parâmetros PCV, mas não informam quais coeficientes são adotados para que a modelagem seja alcançada. Nesta pesquisa, são utilizados os parâmetros PCV de calibração determinados pelo programa comercial WaSoft/Kalib para a antena LEIAX 1202GG. O objetivo principal é calcular os coeficientes a nm e b nm da expansão em funções harmônicas esféricas. Os coeficientes são utilizados para determinar novos parâmetros PCV e PCO que são comparados aos parâmetros obtidos pelo programa comercial Wasoft/Kalib. Os novos parâmetros e os parâmetros calibrados são utilizados para determinar as coordenadas geodésicas de dois pontos com o objetivo de serem comparadas. Foram realizados testes para duas linhas de base diferentes e os resultados confirmam diferenças submilimétricas para as PCVs e milimétricas para a componente vertical do vetor PCO.