Papers by Krzysztof Sośnica
Geodesy and Cartography, 2019
Global Geodetic Observing System (GGOS) was established in 2003 by the International Association ... more Global Geodetic Observing System (GGOS) was established in 2003 by the International Association of Geodesy (IAG) with the main goal to deepen understanding of the dynamic Earth system by quantifying human-induced Earth’s changes in space and time. GGOS allows not only for advancing Earth Science, including solid Earth, oceans, ice, atmosphere, but also for better understanding processes between different constituents forming the system Earth, and most importantly, for helping authorities to make intelligent societal decisions. GGOS comprises different components to provide the geodetic infrastructure necessary for monitoring the Earth system and global changes. The infrastructure spreads from the global scale, through regional, to national scales. This contribution describes the GGOS structure, components, and goals with the main focus on GGOS activities in Poland, including both the development of the geodetic observing infrastructure as well as advances in processing geodetic obs...
In the recent years the meaning of the airborne las r scanning as the technique for obtaining pre... more In the recent years the meaning of the airborne las r scanning as the technique for obtaining precise data of terrain has grown. One of the priority result, which can de rived from ALS data is Digital Terrain Model. Filte ring is the first step in processing the airborne laser scanning data . This process is based on elimination of all point s which were reflected by objects which do not represent the phy sical surface of the ground. It means that in the 3 D point cloud all construction, vegetation, engineering objects shoul d be eliminated, when naturally formed elements of land should remain intact. The problem which may come across du ring the filtering process is huge datasets of airb orne laser scanning. This makes the need to seek fast and effe ctive filtering algorithms. This paper presents a m ethod of the filtering based on discrete fast wavelet transform. The studies and practical experiences show that th e method is very effective and allows the filtering of one million p...
Earth, Planets and Space
The number of satellites equipped with retroreflectors dedicated to Satellite Laser Ranging (SLR)... more The number of satellites equipped with retroreflectors dedicated to Satellite Laser Ranging (SLR) increases simultaneously with the development and invention of the spherical geodetic satellites, low Earth orbiters (LEOs), Galileo and other components of the Global Navigational Satellite System (GNSS). SLR and GNSS techniques onboard LEO and GNSS satellites create the possibility of widening the use of SLR observations for deriving SLR station coordinates, which up to now have been typically based on spherical geodetic satellites. We determine SLR station coordinates based on integrated SLR observations to LEOs, spherical geodetic, and GNSS satellites orbiting the Earth at different altitudes, from 330 to 26,210 km. The combination of eight LEOs, LAGEOS-1/2, LARES, and 13 Galileo satellites increased the number of 7-day SLR solutions from 10–20% to even 50%. We discuss the issues of handling of range biases in multi-satellite combinations and the proper solution constraining and wei...
GPS Solutions
Three main effects from general relativity (GR) may change the geometry and orientation of artifi... more Three main effects from general relativity (GR) may change the geometry and orientation of artificial earth satellite orbits, i.e., the Schwarzschild, Lense–Thirring, and De Sitter effects. So far, the verification of GR effects was mainly based on the observations of changes in the orientation of satellite orbital planes. We directly observe changes of the satellite orbit geometry caused by GR represented by the semimajor axis and eccentricity. We measure the variations of orbit size and shape of GPS, GLONASS, and Galileo satellites in circular and eccentric orbits and compare the results to the theoretical effects using three years of real GNSS data. We derive a solution that assumes the GR to be true, and a second solution, in which the post-Newtonian parameters are estimated, thus, allowing satellites to find their best spacetime curvature. For eccentric Galileo, GR changes the orbital shape and size in perigee in such a way that the orbit becomes smaller but more circular. In t...
Remote Sensing
The Earth’s time-variable gravity field is of great significance to study mass change within the ... more The Earth’s time-variable gravity field is of great significance to study mass change within the Earth’s system. Since 2002, the NASA-DLR Gravity Recovery and Climate Experiment (GRACE) and its successor GRACE follow-on mission provide observations of monthly changes in the Earth gravity field with unprecedented accuracy and resolution by employing low-low satellite-to-satellite tracking (LLSST) measurements. In addition to LLSST, monthly gravity field models can be acquired from satellite laser ranging (SLR) and high-low satellite-to-satellite tracking (HLSST). The monthly gravity field solutions HLSST+SLR were derived by combining HLSST observations of low earth orbiting (LEO) satellites with SLR observations of geodetic satellites. Bandpass filtering was applied to the harmonic coefficients of HLSST+SLR solutions to reduce noise. In this study, we analyzed the performance of the monthly HLSST+SLR solutions in the spectral and spatial domains. The results show that: (1) the accura...
<p>Variations in the Earth's rotation can be examined in the low-fr... more <p>Variations in the Earth's rotation can be examined in the low-frequency and high-frequency temporal scales. The low-frequency variations are dominated by the annual and Chandler wobbles, while the high-frequency variations are primarily caused by tidal effects and mass redistributions within the system Earth. Depending on the purpose, the Earth Rotation Parameters (ERPs) can be estimated in different time resolutions using space-geodetic techniques, especially using GNSS. However, the residual signals between different space geodetic techniques or satellite constellations indicate system-specific differences, which have to be correctly identified.</p><p>This research provides the daily, and sub-daily series of Earth Rotation Parameters (ERPs) estimated using GPS, GLONASS, and Galileo observations. We test different sampling intervals of estimated ERPs from 1h to 24h. The GNSS-based sub-daily estimates have been compared with the external models of variations in ERPs induced by the ocean tides from the IERS 2010 Conventions, a new model by Desai-Sibois, and the VLBI-based model by Gipson.</p><p>Any system-specific ERPs are affected by the orbital and draconitic signals. The orbital signals are visible in all system-specific ERPs at the periods that arise from the resonance between the Earth's rotation and the satellite revolution period, e.g., 8.87h, 34.22h, 3.4 days, 10 days for Galileo; 7.66h, 21.29h, 3.9 days, 7.9 days for GLONASS; 7.98h (S3 tidal term), 11.97h (S2 tidal term), 23.93h (S1 tidal term) for GPS. In the Galileo and GLONASS solutions, the artificial non-tidal signals' amplitudes can reach up to 30 µas. The GPS-derived sub-daily ERPs suffer from the overlapping periods of the diurnal and semidiurnal tidal terms and the harmonics of the GPS revolution period. After recovery of 38 sub-daily tidal terms, the Galileo-based model is more consistent with the external models than the GPS-based model, especially in the prograde diurnal band. The results confirmed that the Desai–Sibois model is more consistent with GNSS observations than the currently recommended model by the IERS 2010 Conventions. Moreover, GPS-based length-of-day (LoD) is systematically biased with respect to the IERS-C04-14 values with a mean offset of −22.4 µs/day, because of the deep resonance 2:1 between the satellite revolution period and the Earth rotation. The Galileo-based and GLONASS-based solutions are almost entirely free of this issue. Against the individual system-specific solutions, the multi-GNSS solution is not affected by most of the system-specific artifacts. Thus, multi-GNSS solutions are clearly beneficial for the estimation of both daily and sub-daily ERPs.</p>
Geophysical Journal International
SUMMARY We recompute the 26-yr weekly Geocentre Motion (GCM) time-series from 1994 to 2020 throug... more SUMMARY We recompute the 26-yr weekly Geocentre Motion (GCM) time-series from 1994 to 2020 through the network shift approach using Satellite Laser Ranging (SLR) observations to LAGEOS1/2. Then the Singular Spectrum Analysis (SSA) is applied for the first time to separate and investigate the geophysical signals from the GCM time-series. The Principal Components (PCs) of the embedded covariance matrix of SSA from the GCM time-series are determined based on the w-correlation criterion and two PCs with large w-correlation are regarded as one periodic signal pair. The results indicate that the annual signal in all three coordinate components and semi-annual signal in both X and Z components are detected. The annual signal from this study agrees well in both amplitude and phase with those derived by the Astronomical Institute of the University of Bern and the Center for Space Research, especially for the Y and Z components. Besides, the other periodic signals with the periods of (1043.6,...
<p&amp... more <p>Recent studies on troposphere delay in Satellite Laser Ranging (SLR) show that the compliance of horizontal gradients of troposphere delay reduces the observation residuals, as well as improves the consistency between SLR results and other space geodetic techniques, all of which are essential for the realization of the terrestrial reference frame. In this work, we examine 3 novel approaches of troposphere delay modeling in SLR, with respect to the standard Mendes-Pavlis approach. We test Potsdam Mapping Function (PMF) with mapping function coefficients and linear horizontal gradients which are based on ERA5 reanalysis provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) model with improved time and spatial resolution in comparison to ERA-Interim reanalysis. We also test a solution based on Vienna Mapping Function 3 for optical observations (VMF3o) which considers the separation of the mapping functions for hydrostatic and non-hydrostatic delays and horizontal gradients. Eventually, we test a solution based on Mendes – Pavlis model with a parameterized model for horizontal gradients based on the 16-year time series of horizontal gradients from PMF. To conduct this experiment, we use SLR observations to passive geodetic satellites LAGEOS-1 and LAGEOS-2. From differences of residual standard deviations for all proposed solutions, we observe an improvement of the SLR observation residuals, for low elevation angles above 10% and improvement of the consistency between estimated pole coordinates and the combined solution IERS-14-C04 series with respect to the currently recommended solutions that neglect the horizontal gradients in SLR solutions.</p>
<p>Numerous... more <p>Numerous active low Earth orbiters (LEOs) and Global Navigation Satellite System (GNSS) satellites, including the Galileo constellation, are equipped with laser retroreflectors used for Satellite Laser Ranging (SLR). Moreover, most of LEOs are equipped with GNSS receivers for precise orbit determination. SLR measurements to LEOs, GNSS, and geodetic satellites vary in terms of the number of registered normal points (NPs) or registered satellite passes. In 2016-2018, SLR measurements to LEOs constituted 81% of all NPs and 59% of all registered satellite passes, whereas 10% of NPs and 30% of satellite passes, respectively, were assigned to GNSS. The remaining SLR measurements were completed by geodetic satellites, including LAGEOS-1/2, and LARES-1.</p><p>In this study, we show that the SLR observations to Galileo, passive geodetic and active LEO satellites together with precise GNSS-based orbits of LEOs and Galileo, can be used for the determination of global geodetic parameters, such as geocenter coordinates (GCC) and Earth rotation parameters (ERPs), i.e. pole coordinates, and length-of-day parameter.</p><p>GCC are typically determined using SLR observations to passive geodetic satellites, such as LAGEOS-1/2. Also, the SLR observations to LAGEOS-1/2 together with GNSS and Very Long Baseline Interferometry data are used for the determination of ERPs. Here, we use SLR observations to Galileo, LAGEOS-1/2, LARES-1, Sentinel-3A, SWARM-A/B/C, TerraSAR-X, Jason-2, GRACE-A/B satellites to investigate whether they can be applied for the reference frame realization and for deriving high-quality global geodetic parameters.</p><p>We present various types of solutions to investigate the best solution set-up. The studied solutions differ in terms of solution lengths, the combination of different sets of satellites and the relative weights for the variance scaling factors of technique and satellite-specific normal equations. We compare our results with the standard LAGEOS-based solutions, the combined EOP-14-C04 products and show the consistency of the results.</p>
Pure and Applied Geophysics
The goal of this paper is to determine and analyze the common geocenter signal from the geocenter... more The goal of this paper is to determine and analyze the common geocenter signal from the geocenter coordinates based on four independent techniques: Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), Global Navigation Satellite System (GNSS), Gravity Recovery And Climate Experiment with the ocean bottom pressure model, and Satellite Laser Ranging, and to analyze the residuals as the differences between these geocenter coordinates and their common signal. Another objective of this paper is to compute variable amplitudes and phases of the annual and semi-annual oscillations in the geocenter coordinates of these techniques by the combination of the Fourier Transform Band Pass Filter (FTBPF) with the Hilbert Transform (FTBPF + HT) and to compare their mean values with those obtained by other authors. It was assumed that the geocenter time series of individual techniques consist of the common signal of geocenter motion, systematic errors resulting from orbital mode...
Remote Sensing
Sentinel-3A/3B (S3A/B) satellites are equipped with a number of precise instruments dedicated to ... more Sentinel-3A/3B (S3A/B) satellites are equipped with a number of precise instruments dedicated to the measurement of surface topography, sea and land surface temperatures and ocean and land surface color. The high-precision orbit is guaranteed by three instruments: Global Positioning System (GPS) receiver, laser retroreflector dedicated to Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) antenna. In this article, we check the possibility of using SLR observations and GPS-based reduced-dynamic orbits of active S3A/B satellites for the determination of global geodetic parameters, such as geocenter motion, Earth rotation parameters (ERPs) and the realization of the terrestrial reference frame, based on data from 2016-2018. The calculation process was preceded with the estimation of SLR site range biases, different network constraining tests and a different number of orbital arcs in the analyzed solutions. The repeatability of SL...
Journal of Surveying Engineering
AbstractThe Gauss–Helmert observational model is derived in this paper for total station position... more AbstractThe Gauss–Helmert observational model is derived in this paper for total station positioning directly in geocentric reference frame including Global Navigation Satellite Systems (GNSS) meas...
GPS Solutions
The recent development of the Galileo space segment and the accompanying support of the Internati... more The recent development of the Galileo space segment and the accompanying support of the International GNSS Service (IGS) allows for worldwide Galileo-only positioning. In this study, different techniques of dual-frequency absolute positioning using the fully serviceable Galileo constellation are evaluated for the first time and compared to the performance of GPS positioning. The daily static positioning based on the broadcast ephemeris using Galileo pseudoranges is significantly more accurate than the corresponding GPS solutions, obtaining the accuracy of a few decimeters. In the kinematic mode, the accuracy is better than 10 m and 20 m for the horizontal and vertical components, respectively, which is comparable to that of GPS. Precise absolute positioning using pseudorange and carrier phase Galileo observations combined with IGS Real-Time Service (RTS) or Multi-GNSS Experiment products is not yet as good as the corresponding GPS solutions. In the static mode, the root mean squared error (RMSE) between estimated and reference coordinates does not exceed 0.05 m and 0.06 m for the horizontal and vertical components, respectively. In the kinematic mode, the respective accuracies are better than 0.17 m and 0.21 m. Moreover, we show that both GPS and Galileo pseudorange solutions benefit from the RTS when compared to the broadcast solutions with the improvement in the accuracy between 10 and 59%. Remarkable results are achieved for Galileo Precise Point Positioning (PPP) solutions based on the broadcast ephemeris. In the static mode, the RMSE is 0.07 and 0.10 m for the horizontal and vertical components which is three and two times better, respectively, then the corresponding solutions based on GPS.
Journal of Geodesy
Satellite laser ranging (SLR) to low Earth orbiters (LEOs) provides optical distance measurements... more Satellite laser ranging (SLR) to low Earth orbiters (LEOs) provides optical distance measurements with mm-to cm-level precision. SLR residuals, i.e., differences between measured and modeled ranges, serve as a common figure of merit for the quality assessment of orbits derived by radiometric tracking techniques. We discuss relevant processing standards for the modeling of SLR observations and highlight the importance of line-of-sight dependent range corrections for the various types of laser retroreflector ararys (LRAs). A 1-3 cm consistency of SLR observations and GPSbased precise orbits is demonstrated for a wide range of past and present LEO missions supported by the International Laser Ranging Service (ILRS). A parameter estimation approach is presented to investigate systematic orbit errors and it is shown that SLR validation of LEO satellites is not only able to detect radial but also along-track and cross-track offsets. SLR residual statistics clearly depend on the employed precise orbit determination technique (kinematic vs. reduced-dynamic, float vs. fixed ambiguities) but also reveal pronounced differences in the ILRS station performance. Using the residuals-based parameter estimation approach, corrections to ILRS station coordinates, range bi
Journal of Geodesy
Quality control systems for satellite laser ranging (SLR) observations have been developed at a n... more Quality control systems for satellite laser ranging (SLR) observations have been developed at a number of analysis institutes worldwide, using various software packages of precise orbit determination and data analysis. Satellite laser range observations, primarily from the two LAGEOS satellites but also from other satellites in low-Earth orbits and up to GNSS altitude, are being processed on a sub-daily to weekly basis. The generated quality control reports are widely used to detect various kinds of problems and quickly provide anomalous information to laser ranging stations. They have been effective in shortening the time to return to normal operations when anomalous data are detected and in quantifying the performance of laser ranging stations. Consequently, a rapid feedback loop has now been incorporated in the modern SLR operation.
Remote Sensing
The combination of Global Navigation Satellite Systems (GNSS) may improve the accuracy and precis... more The combination of Global Navigation Satellite Systems (GNSS) may improve the accuracy and precision of estimated coordinates, as well as the convergence time of Precise Point Positioning (PPP) solutions. The key conditions are the correct functional model and the proper weighting of observations, for which different characteristics of multi-GNSS signals should be taken into account. In post-processing applications, the optimum stochastic model can be obtained through the analysis of post-fit residuals, but for real-time applications the stochastic model has to be defined in advanced. We propose five different weighting schemes for the GPS + GLONASS + Galileo + BeiDou combination, including two schemes with no intra-system differences, and three schemes that are based on signal noise and/or quality of satellite orbits. We perform GPS-only and five multi-GNSS solutions representing each weighting scheme. We analyze formal errors of coordinates, coordinate repeatability, and solution convergence time. We found that improper or equal weighting may improve formal errors but decreases coordinate repeatability when compared to the GPS-only solution. Intra-system weighting based on satellite orbit quality allows for a reduction of formal errors by 40%, for shortening convergence time by 40% and 47% for horizontal and vertical components, respectively, as well as for improving coordinate repeatability by 6%.
Advances in Space Research
Abstract Ambiguity fixing to integer numbers of the phase measurements has been proven to amelior... more Abstract Ambiguity fixing to integer numbers of the phase measurements has been proven to ameliorate the accuracy of GNSS data processing. Until now there are two strategies to achieve ambiguity resolution; by forming double differences and by using undifferenced phase measurements. In this article, the potentiality of using the latter method for fixing the phase ambiguities for the Galileo system combined with GPS measurements in a Multi-GNSS solution is proved. The integer property of the Galileo phase clocks is demonstrated. GPS and Galileo phase fixed orbit and “integer” clock products are compared to the float solutions. Both orbit overlaps and orbit validation using satellite laser ranging (SLR) validation methods showed that there is an improvement mainly in the normal and the along track direction.
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Papers by Krzysztof Sośnica