GPS Solutions Research Articles

New estimation of Nile Delta subsidence rates from InSAR and GPS analysis

Increase of water level in most of the world’s oceans and seas, including the Mediterranean, due to global warming may have a serious impact on the Nile Delta. The Nile Delta is considered as one of the most important regions in Egypt as more than 50% of the Egyptians are living there. To study the thread of a potentially sinking and flooding of the Nile Delta, here, we estimate present vertical motion by use of the Persistent Scatterer InSAR (PSI) analysis in addition to the available GPS stations in the Nile Delta. The subsidence rate of the Nile Delta is estimated by applying the PSI processing for all archived Envisat SAR data from the descending tracks 207 and 436. From these tracks, 36 and 37 SAR scenes were collected, respectively. Moreover, the results of a time series analysis for six GPS permanent stations in the Nile Delta were used to validate the estimated subsidence rates from PSI analysis. The PSI and GPS solutions show that the estimated ground deformation is strongly localized at the big cities. From time series for selected PS pixels from Cairo, Tanta, Mahala, Mansoura, Damietta, and Port Said, the estimated subsidence rates from Envisat scenes are around − 6.4 ± 0.4 mm/year, − 4.0 ± 0.6 mm/year, − 4.8 ± 1.0 mm/year, − 10.0 ± 1.2 mm/year, − 10.3 ± 1.6 mm/year, and − 4.9 ± 1.6 mm/year, respectively. The localization of subsidence rates at big cities implies that the detected signals may be due to human activities, such as ground water pumping, and that the Delta as a whole presently is not subsiding.

Integrated Orbit Determination of FengYun‐3C, BDS, and GPS Satellites

AbstractAiming at weather forecast and global climate research, the satellite FengYun‐3C (FY‐3C), as the new generation of China's weather satellites, was launched in 2013. It carries the Global Navigation Satellite Systems Occultation Sounder instrument, a BDS + GPS receiver, to fulfill the demand of orbit determination and occultation. In this contribution, we develop an integrated orbit determination of FY‐3C, BDS, and GPS satellites by joint processing of onboard FY‐3C and ground data during 2013–2017. Four processing schemes, BDS, GPS, BDS + GPS, and BDS (without Geostationary Earth Orbit [GEO]) + GPS, are designed to investigate the capability of BDS for the integrated precise orbit determination and the benefit of BDS and GPS fusion. Regional and global networks are also employed to analyze the influence of station distribution on the orbit determination. The results show that with a regional network, both BDS and GPS orbits present a significant improvement after including FY‐3C data. For the BDS + GPS one‐step solution, GPS orbits are improved by 20% compared with the two‐step solution, while the improvement can reach 42%, 27%, and 27% for BDS GEO, Inclined Geosynchronous Satellite Orbit, and Medium Earth Orbit, respectively. The precision improvement of FY‐3C is respectively 26%, 44%, and 30% in along, cross, and radial components. For a global network, the orbit precision of the BDS + GPS solution is improved by 4% for GPS and 5%, 16%, and 19% for BDS GEO, Inclined Geosynchronous Satellite Orbit, and Medium Earth Orbit, respectively. For FY‐3C, the orbit improvement can reach 7%. The validation with satellite laser ranging also demonstrates the benefit of the integrated orbit determination. Such a high‐quality orbit will potentially benefit meteorological studies and applications.

A high strength green nanocomposites based on wood veneer nanocrystalline cellulose and epoxy resin polymer

This study was conducted to utilize natural thin wood veneers, nanocrystalline cellulose (NCC) and epoxy resin to produce new bionanocomposites. The thin wood veneers were used as the basic structure element in the nanocomposites. The NCC was obtained from the chemically hydrolyzed sawdust with diameter of ~10-20 nm. In this study, NCC was mixed with 3-glycidyloxypropyltrimethoxysilane (GPS) before being dispersed homogeneously into the epoxy resin and thin veneer. The GPS which act as the coupling agent enhanced the interfacial adhesion between NCC and epoxy resin polymer. The Fourier Transform Infrared Spectroscopy (FTIR) results showed that NCC was successfully treated with GPS. The finding showed that the optimum value of GPS solution required to functionalize NCC was 0.5 wt/wt %. The results on tensile strength tests on the green nanocomposites also showed that the strength improved upon the incorporation of treated NCC into epoxy resin and thin veneer. By incorporating treated NCC (0.1%) into the thin wood veneer/epoxy resin polymer based nanocomposites, the maximum increment value of tensile strength was found to have a 23% improvement compared to the control sample without NCC. The enhancement in the strength properties was expected as NCC possessed high surface-to-volume and aspect ratio characteristics. Through this study new high strength green nanocomposites have been successfully developed.

Influence of subdaily model for polar motion on the estimated GPS satellite orbits

In this contribution, it is shown that GPS orbits are able to absorb some diurnal signals in polar motion. The arising implications for the influence of the subdaily pole model on GPS solutions are discussed. Two signals in polar motion can be absorbed by GPS orbits: a retrograde signal with a period of a sidereal day (23 h 56 min 4 s) and a prograde signal with a period matching the revolution period of the GPS satellites in the terrestrial reference frame (23 h 55 min 56 s). We show that the retrograde signal contributes to the absolute orientation of the orbital planes in space and the prograde signal, due to coincidence of its period with the period of revolution of the GPS satellites, contributes to the position of the geocenter for each individual satellite. It is known from previous studies that there are systematic differences between orbital parameters from GPS solutions computed with different subdaily pole models. We show in this paper that this behavior can be explained by the absorption effects in 1-day GPS orbits. Diurnal signals cannot be spectrally separated over a time interval of 1 day. Adjustment of any diurnal prograde or retrograde signal to a subdaily pole time series given by a subdaily model over 24 h will lead to an estimated signal with a nonzero amplitude. Thus, any subdaily pole model used in the processing of space geodetic observations contains a part which corresponds numerically to the discussed prograde signal and a part which corresponds to the retrograde diurnal signal. Different pole models show different amplitudes of the diurnal signals which will be absorbed by the orbits. As a result, GPS orbits computed with different subdaily pole models have systematically different orientation and position in space. Using 1-day GPS solutions over a time span of 13 years (1994–2007), we show that the systematic variations in orbit position and orientation caused by individual tidal terms in polar motion can be well predicted and explained by the suggested mechanism.

Performance of GPS and GPS/SINS navigation in the CE-5T1 skip re-entry mission

A CE-5T1 spacecraft completed a high-speed skip re-entry to the earth after a circumlunar flight on October 31, 2014. In addition to the strapdown inertial navigation system (SINS), a lightweight GPS receiver with rapid acquisition was developed as a navigation sensor in the re-entry capsule. The GPS receiver effectively solved the poor accuracy problem of long-term navigation using only the SINS. In contrast to ground users and low-earth-orbit spacecraft, numerous factors, including high altitude and kinetic characteristics in high-speed skip re-entry, are important for GPS positioning feasibility and were presented in accordance with the flight data. GPS solutions started at nearly 4900 km orbital altitude during the phases of re-entry process. These solutions were combined by an inertial measurement unit in a loosely coupled integrated navigation method and SINS navigation initialization. A simplified GPS/SINS navigation filter for limited resources was effectively developed and implemented on board for spacecraft application. Flight data estimation analyses, including trajectory, attitude, position distribution of GPS satellite, and navigation accuracy, were presented. The estimated accuracy of position was better than 42 m, and the accuracy of velocity was better than 0.1 m/s.

Crustal structure of the southeastern Tibetan Plateau from gravity data: New evidence for clockwise movement of the Chuan–Dian rhombic block

The crustal deformation beneath the Chuan–Dian rhombic block (CDB) and surrounding regions has been studied in geological and geodetic methods, and provide important insights into the kinematics and dynamics about the clockwise movement of this tectonic block. In this work, we present images of the normalized full gradient (NFG) of the Bouguer gravity anomalies from five gravity profiles across the boundary faults of the CDB measured in recent years, and investigate the distribution characteristics of the crustal anomalous bodies along the profiles. Firstly, an anomalous body with eastward dipping exist beneath the Xianshuihe fault, suggesting that crustal mass move to east. Secondly, near the Xiaojiang fault, two anomalous bodies dip westward with depth increasing. The inferred movement direction of the north one is from west to east, and the south one is from east to west. Thirdly, anomalous bodies on the northeast and southwest sides of the Red River fault suggest the directions of crustal movement is from northeast to southwest. These results are also consistent with GPS solutions, and provide gravity evidence for crustal deformation of the CDB with clockwise rotation.

Statistical significance of trends in Zenith Wet Delay from re-processed GPS solutions

Long series of Zenith Wet Delay (ZWD) obtained as part of a homogeneous re-processing of Global Positioning System solutions constitute a reliable set of data to be assimilated into climate models. The correct stochastic properties, i.e. the noise model of these data, have to be identified to assess the real value of ZWD trend uncertainties since assuming an inappropriate noise model may lead to over- or underestimated error bounds leading to statistically insignificant trends. We present the ZWD time series for 1995–2017 for 120 selected globally distributed stations. The deterministic model in the form of a trend and significant seasonal signals were removed prior to the noise analysis. We examined different stochastic models and compared them to widely assumed white noise (WN). A combination of the autoregressive process of first-order plus WN (AR(1) + WN) was proven to be the preferred stochastic representation of the ZWD time series over the generally assumed white-noise-only approach. We found that for 103 out of 120 considered stations, the AR(1) process contributed to the AR(1) + WN model in more than 50% with noise amplitudes between 9 and 68 mm. As soon as the AR(1) + WN model was employed, 43 trend estimates became statistically insignificant, compared to 5 insignificant trend estimates for a white-noise-only model. We also found that the ZWD trend uncertainty may be underestimated by 5–14 times with median value of 8 using the white-noise-only assumption. Therefore, we recommend that AR(1) + WN model is employed before tropospheric trends are to be determined with the greatest reliability.

INTEGRITY ANALYSIS OF REAL-TIME PPP TECHNIQUE WITH IGS-RTS SERVICE FOR MARITIME NAVIGATION

Abstract. Open sea and inland waterways are the most widely used mode for transporting goods worldwide. It is the International Maritime Organization (IMO) that defines the requirements for position fixing equipment for a worldwide radio-navigation system, in terms of accuracy, integrity, continuity, availability and coverage for the various phases of navigation. Satellite positioning systems can contribute to meet these requirements, as well as optimize marine transportation. Marine navigation usually consists of three major phases identified as Ocean/Coastal/Port approach/Inland waterway, in port navigation and automatic docking with alert limit ranges from 25 m to 0.25 m. GPS positioning is widely used for many applications and is currently recognized by IMO for a future maritime navigation. With the advancement in autonomous GPS positioning techniques such as Precise Point Positioning (PPP) and with the advent of new real-time GNSS correction services such as IGS-Real-Time-Service (RTS), it is necessary to investigate the integrity of the PPP-based positioning technique along with IGS-RTS service in terms of availability and reliability for safe navigation in maritime application. This paper monitors the integrity of an autonomous real-time PPP-based GPS positioning system using the IGS real-time service (RTS) for maritime applications that require minimum availability of integrity of 99.8 % to fulfil the IMO integrity standards. To examine the integrity of the real-time IGS-RTS PPP-based technique for maritime applications, kinematic data from a dual frequency GPS receiver is collected onboard a vessel and investigated with the real-time IGS-RTS PPP-based GPS positioning technique. It is shown that the availability of integrity of the real-time IGS-RTS PPP-based GPS solution is 100 % for all navigation phases and therefore fulfil the IMO integrity standards (99.8 % availability) immediately (after 1 second), after 2 minutes and after 42 minutes of convergence time for Ocean/Coastal/Port approach/Inland waterway, in port navigation and automatic docking, respectively. Moreover, the misleading information is about 2 % for all navigation phases that is considered less safe is not in immediate danger because the horizontal position error is less than the navigation alert limits.

Development of a self-driving car that can handle the adverse weather

Lane and road recognition are essential for self-driving where GPS solution is inaccurate due to the signal block or multipath in an urban environment. Vision based lane or road recognition algorithms have been studied extensively, but they are not robust to changes in weather or illumination due to the characteristic of the sensor. Lidar is a sensor for measuring distance, but it also contains intensity information. The road mark on the road is made to look good with headlight at night by using a special paint with good reflection on the light. With this feature, road marking can be detected with lidar even in the case of changes in illumination due to the rain or shadow. In this paper, we propose equipping autonomous cars with sensor fusion algorithms intended to operate in a different weather conditions. The proposed algorithm was applied to the self-driving car EureCar (KAIST) in order to test its feasibility for real-time use.

Comparison of observed and modeled seasonal crustal vertical displacements derived from multi‐institution GPS and GRACE solutions

AbstractEleven GPS crustal vertical displacement (CVD) solutions for 110 IGS08/IGS14 core stations provided by the International Global Navigation Satellite Systems Service Analysis Centers are compared with seven Gravity Recovery and Climate Experiment (GRACE)‐modeled CVD solutions. The results of the internal comparison of the GPS solutions from multiple institutions imply large uncertainty in the GPS postprocessing. There is also evidence that GRACE solutions from both different institutions and different processing approaches (mascon and traditional spherical harmonic coefficients) show similar results, suggesting that GRACE can provide CVD results of good internal consistency. When the uncertainty of the GPS data is accounted for, the GRACE data can explain as much as 50% of the actual signals and more than 80% of the GPS annual signals. Our study strongly indicates that GRACE data have great potential to correct the nontidal loading in GPS time series.

Geometry of GPS dilution of precision: revisited

We revisit the geometric interpretation of GPS dilution of precision (DOP) factors giving emphasis on the geometric impact of the receiver clock parameter on the conventional GPS positioning solution. The comparison is made between the solutions with and without an estimated receiver clock parameter, i.e., conventional GPS versus pure trilateration solution. The generalized form of the DOP factors is also presented for observation redundancy greater than zero. The DOP factor equations are established as functions of triangle surfaces and tetrahedron volumes formed by the receiver-satellite unit vectors or by these vectors between themselves. To facilitate the comparison of the solutions with and without a receiver clock parameter, the average of receiver-satellite unit vectors is introduced to interpret the DOP factors geometrically. The geometry of satellite outage is also revisited from a geometric point of view. Finally, the geometric interpretation of receiver clock constrains within a positioning solution is also investigated.

Integrated Precipitable Water from GPS Observations and CIMEL Sunphotometer Measurements at CGO Belsk

AbstractThis paper describes results of integrated precipitable water co-located measurements from two techniques: GPS solution and CIMEL-318 sunphotometer. Integrated Precipitable Water (IPW) is an important meteorological parameter and is derived from GPS tropospheric solutions for GPS station at Central Geophysical Observatory (CGO), Polish Academy of Sciences (PAS), Belsk and compared with sunphotometer (CIMEL-318 device by Cimel Electronique) data provided by Aerosol Robotic Network (AERONET). Two dedicated and independent GPS solutions: network solution in the sub-network of European Permanent Network (EPN) and precise point positioning solution have been made to obtain tropospheric delays. The quality of dedicated tropospheric solutions has been verified by comparison with EPN tropospheric combined product. Several IPW comparisons and analyses revealed systematic difference between techniques (difference RMS is over 1 mm). IPW bias changes with season: annual close to 1 mm IPW (and semi-annual term also present). IPW bias is a function of atmospheric temperature. Probable cause of this systematic deficiency in solar photometry as IPW retrieval technique is a change of optical filter characteristics in CIMEL.

Validating the efficacy of GPS tracking vehicle movement for driving behaviour assessment

Vehicle movement trajectory recorded by GPS maps the vehicle’s lane position in time sequence, therefore theoretically can be used to assess driving behaviour. However, the data quality level which can be achieved for vehicle movement tracking by different GPS receivers and positioning techniques hasn’t been fully explored and documented. This study systematically validated the efficacy of GPS recording vehicle movement using different types of receivers and positioning techniques. The receivers include both recreational and professional devices; the positioning techniques refer to Single Point Positioning (SPP), Differential GPS (DGPS) and Real-time kinematic (RTK) solutions. The field trials tested the positioning accuracy as well as the quality of trajectory tracking by comparing the recorded positions to benchmarks. The study findings indicate that vehicle movement trajectories recorded by recreational-grade GPS receivers can only match other spatial information at low resolution, which is limited to the assessment of wayfinding and navigation behaviour. In contrast, the SPP, DGPS and RTK techniques undertaken by professional receivers can raise horizontal accuracy to the metre, decimetre, and centimetre level respectively. For under open sky road driving, the RTK solution generated accurate and precise vehicle movement trajectories sufficient for extracting vehicle lane position, speed, acceleration/deceleration, so as to detect detailed driving events and quantitatively assess individual driver behaviour. This paper serves as a critical reference for other researchers on the different types of GPS receivers and solutions prior to engaging a GPS in their studies.

GPS AND GLONASS COMBINED STATIC PRECISE POINT POSITIONING (PPP)

Abstract. With the rapid development of multi-constellation Global Navigation Satellite Systems (GNSSs), satellite navigation is undergoing drastic changes. Presently, more than 70 satellites are already available and nearly 120 more satellites will be available in the coming years after the achievement of complete constellation for all four systems- GPS, GLONASS, Galileo and BeiDou. The significant improvement in terms of satellite visibility, spatial geometry, dilution of precision and accuracy demands the utilization of combining multi-GNSS for Precise Point Positioning (PPP), especially in constrained environments. Currently, PPP is performed based on the processing of only GPS observations. Static and kinematic PPP solutions based on the processing of only GPS observations is limited by the satellite visibility, which is often insufficient for the mountainous and open pit mines areas. One of the easiest options available to enhance the positioning reliability is to integrate GPS and GLONASS observations. This research investigates the efficacy of combining GPS and GLONASS observations for achieving static PPP solution and its sensitivity to different processing methodology. Two static PPP solutions, namely standalone GPS and combined GPS-GLONASS solutions are compared. The datasets are processed using the open source GNSS processing environment gLAB 2.2.7 as well as magicGNSS software package. The results reveal that the addition of GLONASS observations improves the static positioning accuracy in comparison with the standalone GPS point positioning. Further, results show that there is an improvement in the three dimensional positioning accuracy. It is also shown that the addition of GLONASS constellation improves the total number of visible satellites by more than 60% which leads to the improvement of satellite geometry represented by Position Dilution of Precision (PDOP) by more than 30%.

GPS AND GLONASS COMBINED STATIC PRECISE POINT POSITIONING (PPP)

With the rapid development of multi-constellation Global Navigation Satellite Systems (GNSSs), satellite navigation is undergoing drastic changes. Presently, more than 70 satellites are already available and nearly 120 more satellites will be available in the coming years after the achievement of complete constellation for all four systems- GPS, GLONASS, Galileo and BeiDou. The significant improvement in terms of satellite visibility, spatial geometry, dilution of precision and accuracy demands the utilization of combining multi-GNSS for Precise Point Positioning (PPP), especially in constrained environments. Currently, PPP is performed based on the processing of only GPS observations. Static and kinematic PPP solutions based on the processing of only GPS observations is limited by the satellite visibility, which is often insufficient for the mountainous and open pit mines areas. One of the easiest options available to enhance the positioning reliability is to integrate GPS and GLONASS observations. This research investigates the efficacy of combining GPS and GLONASS observations for achieving static PPP solution and its sensitivity to different processing methodology. Two static PPP solutions, namely standalone GPS and combined GPS-GLONASS solutions are compared. The datasets are processed using the open source GNSS processing environment <i>gLAB</i> 2.2.7 as well as <i>magicGNSS</i> software package. The results reveal that the addition of GLONASS observations improves the static positioning accuracy in comparison with the standalone GPS point positioning. Further, results show that there is an improvement in the three dimensional positioning accuracy. It is also shown that the addition of GLONASS constellation improves the total number of visible satellites by more than 60% which leads to the improvement of satellite geometry represented by Position Dilution of Precision (PDOP) by more than 30%.

CO-GPS: Energy Efficient GPS Sensing with Cloud Offloading

Location is a fundamental service for mobile computing. Typical GPS receivers, although widely available for navigation purposes, may consume too much energy to be useful for many applications. Observing that in many sensing scenarios, the location information can be post-processed when the data is uploaded to a server, we design a cloud-offloaded GPS (CO-GPS) solution that allows a sensing device to aggressively duty-cycle its GPS receiver and log just enough raw GPS signal for post-processing. Leveraging publicly available information such as GNSS satellite ephemeris and an Earth elevation database, a cloud service can derive good quality GPS locations from a few milliseconds of raw data. Using our design of a portable sensing device platform called CLEON, we evaluate the accuracy and efficiency of the solution. Compared to more than 30 seconds of heavy signal processing on standalone GPS receivers, we can achieve three orders of magnitude lower energy consumption per location tagging.

Precise Point Positioning Using Triple GNSS Constellations in Various Modes.

This paper introduces a new dual-frequency precise point positioning (PPP) model, which combines the observations from three different global navigation satellite system (GNSS) constellations, namely GPS, Galileo, and BeiDou. Combining measurements from different GNSS systems introduces additional biases, including inter-system bias and hardware delays, which require rigorous modelling. Our model is based on the un-differenced and between-satellite single-difference (BSSD) linear combinations. BSSD linear combination cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver oscillator. Forming the BSSD linear combination requires a reference satellite, which can be selected from any of the GPS, Galileo, and BeiDou systems. In this paper three BSSD scenarios are tested; each considers a reference satellite from a different GNSS constellation. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS, Galileo, and BeiDou PPP solution and to handle the newly introduced biases. A total of four data sets collected at four different IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) network are used to correct the GPS, Galileo, and BeiDou measurements in the post-processing PPP mode. A real-time PPP solution is also obtained, which is referred to as RT-PPP in the sequel, through the use of the IGS real-time service (RTS) for satellite orbit and clock corrections. However, only GPS and Galileo observations are used for the RT-PPP solution, as the RTS-IGS satellite products are not presently available for BeiDou system. All post-processed and real-time PPP solutions are compared with the traditional un-differenced GPS-only counterparts. It is shown that combining the GPS, Galileo, and BeiDou observations in the post-processing mode improves the PPP convergence time by 25% compared with the GPS-only counterpart, regardless of the linear combination used. The use of BSSD linear combination improves the precision of the estimated positioning parameters by about 25% in comparison with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 minutes for the BSSD model, which represents about 50% reduction, in comparison with the GPS-only PPP solution. The GNSS RT-PPP solution, on the other hand, shows a similar convergence time and precision to the GPS-only counterpart.

An assessment of static precise point positioning using GPS only, GLONASS only, and GPS plus GLONASS

The aim of this paper is to look into the achievable repeatability and accuracy from Precise Point Positioning (PPP) daily solutions when using GPS only (PPP GPS), GLONASS only (PPP GLO), and GPS plus GLONASS (PPP GPS+GLO) for static positioning. As part of the assessment, a comparison with Global Double Difference (DD) GPS daily solutions is presented. It is shown, therefore, that all of the PPP daily solutions can achieve millimetric level repeatability, similar to the global DD GPS solutions. Furthermore, the mean of the biases between the PPP daily solutions and the global DD GPS daily solutions are constellation type dependent, while an improvement is found in the vertical component for PPP GPS+GLO over PPP GLO, as the latter may be more affected by any imperfections in the models for GLONASS antenna phase centre variations. It is concluded that PPP GLO daily solutions have the ability to be used as independent solutions to PPP GPS daily solutions for static positioning, and as an alternative to PPP GPS+GLO or global DD GPS daily solutions.

Distributed monitoring system for voltage dip classification over distribution grid

Abstract The installation of Power Quality (PQ) meters is becoming mandatory in many countries to face the problems introduced by the increasing number of renewable energy sources with intermittent generation. Unfortunately, the current situation is unbalanced: PQ meters are installed on High Voltage (HV) transmission lines and sometimes on Medium Voltage (MV) lines, while the highest number of renewable generators is connected to Low Voltage (LV) grid. In this paper, a novel measurement system for the analysis of voltage dips is proposed. If compared with existing similar systems, the proposed distributed measuring system has the following new characteristics: it is composed of a network of PQ meters on HV, MV and also on LV lines; it uses a heterogeneous communication infrastructure to interconnect meters; it has a cost-effective network-based time synchronization instead of costly GPS solutions; it implements a distributed algorithm to determine the origin of PQ problems. This novel approach overcomes scalability issue, which currently is limiting a larger penetration of PQ systems. The proposed distributed system for monitoring of voltage dips has been deployed in a real distribution grid in Italy. The paper reports analyses on data collected during an entire year. Voltage dips have been correlated and analyzed thanks to the time synchronization of the system.

Investigation of long-range dependencies in the stochastic part of daily GPS solutions

The long-range dependence (LRD) of the stochastic part of GPS-derived topocentric coordinates change (North, East, Up) results with relatively high autocorrelation values with a focus on self-similarity. One of the reasons for such self-similarity in the GPS time series are noises that are commonly recognised to prevail in the form of the flicker noise model. To prove the self-similarity of the stochastic part of GPS time series we used more than 130 ASG-EUPOS (active geodetic network EUPOS) stations from an area of Poland with a 5-year span of the daily topocentric coordinate changes. The deterministic part of time series was removed by means of the least-squares (LS) method, median absolute deviation (MAD) criterion and the sequential t-test algorithm, respectively. Then the self-similarity of the residue was proved by the results of the Ljung–Box test, whose values close to zero showed the dependence of the stochastic part of the GPS time series. The residue was analysed by means of the rescaled range (R/S) method with the H (Hurst) parameter and the detrended fluctuation analysis (DFA) with the scaling exponent α. Both H and α values ranged within assumed LRD limits of 0.5 and 1. This analysis was followed by noise investigation with a maximum likelihood estimation (MLE). The white plus the power-law noise models were assumed a priori, which gave us a spectral indices κ between − 0.4 and − 1.2 for all of the time series. It proved that fractional white noise outweighs other types of noises in GPS time series. Authors found here, that the LRD methods by omitting the noise amplitude data led to an underestimation of H values and their misinterpretation. The larger the omitted amplitude is, the greater the difference between the noise characters estimated with R/S values in comparison to the reference values of κ are. Some of these differences exceed even the value of 0.6, which may result in the estimation of false noise character in GPS data thus eliciting wrong conclusions.