East Components Research Articles

Spherical Elementary Current Systems Method Applied to Geomagnetic Field Modeling for the Adriatic

The aim of this work was to derive an accurate regional model of geomagnetic components on the Adriatic. Data of north, east and vertical geomagnetic components at repeat stations and ground survey sites enclosing the Adriatic Sea were used to obtain a geomagnetic model at 2010.5 epoch. The core field was estimated by use of the global Enhanced Magnetic Model, while the crustal field by a mathematical technique for expanding vector systems on a sphere into basis functions, known as spherical elementary current systems method. The results of this method were presented and compared to the crustal field estimations by the Enhanced Magnetic Model. The maps of isolines of the regional model are also presented.

Tightly Coupled Integration of GPS Ambiguity Fixed Precise Point Positioning and MEMS-INS through a Troposphere-Constrained Adaptive Kalman Filter.

Precise Point Positioning (PPP) makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF) combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD) operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC) algorithm is implemented by integrating PPP with inertial navigation system (INS) using an Extended Kalman filter (EKF). The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies of the height component are improved by 30.36%, 16.95% and 24.07% for three different convergence times, i.e., 60, 50 and 30 min, respectively. It shows that the ambiguity-fixed horizontal positioning accuracy has been significantly improved. When compared with the conventional PPP solution, it can be seen that position accuracies are improved by 19.51%, 61.11% and 23.53% for the north, east and height components, respectively, after one hour convergence through the troposphere constraint fixed PPP/INS with adaptive covariance model.

Experiments of absolute positioning using BEIDOU in Vietnam

We research on absolute positioning using Beidou pseudo-range measurements collected in Ho Chi Minh City. Positional accuracy achieved is 2.3m, 4.5m and 3.9m for the North, East and height components compared to (0.8, 0.9, 1.7) of GPS and (2.0, 1.9, 4.1) of GLONASS. This result shows that in Vietnam we can use only BEIDOU system for positioning and also opens the possibility of incorporating positioning satellite systems to improve accuracy.

Towards Reliable Velocities of Permanent GNSS Stations

Abstract In the modern geodesy the role of the permanent station is growing constantly. The proper treatment of the time series from such station lead to the determination of the reliable velocities. In this paper we focused on some pre-analysis as well as analysis issues, which have to be performed upon the time series of the North, East and Up components and showed the best, in our opinion, methods of determination of periodicities (by means of Singular Spectrum Analysis) and spatio-temporal correlations (Principal Component Analysis), that still exist in the time series despite modelling. Finally, the velocities of the selected European permanent stations with the associated errors determined following power-law assumption in the stochastic part is presented.

Multi-quadric collocation model of horizontal crustal movement

Abstract. To establish the horizontal crustal movement velocity field of the Chinese mainland, a Hardy multi-quadric fitting model and collocation are usually used. However, the kernel function, nodes, and smoothing factor are difficult to determine in the Hardy function interpolation. Furthermore, the covariance function of the stochastic signal must be carefully constructed in the collocation model, which is not trivial. In this paper, a new combined estimation method for establishing the velocity field, based on collocation and multi-quadric equation interpolation, is presented. The crustal movement estimation simultaneously takes into consideration an Euler vector as the crustal movement trend and the local distortions as the stochastic signals, and a kernel function of the multi-quadric fitting model substitutes for the covariance function of collocation. The velocities of a set of 1070 reference stations were obtained from the Crustal Movement Observation Network of China, and the corresponding velocity field was established using the new combined estimation method. A total of 85 reference stations were used as checkpoints, and the precision in the north and east component was 1.25 and 0.80 mm yr−1, respectively. The result obtained by the new method corresponds with the collocation method and multi-quadric interpolation without requiring the covariance equation for the signals.

The Influence of Zenith Tropospheric Delay on PPP-RTK

Abstract The PPP technique is more and more used in different GPS precise application. The PPP precision is related to many factors and the most important are: the number of satellites, the ambiguity resolution, the ability to model the ionospheric and tropospheric delays, solid earth and ocean tides, relativistic effects and antenna phase-center offsets and variations. The article is studying the effect of the zenith tropospheric delay (ZTD) using the GPT2 model and then computing in static mode the ZTD, which is than applied on PPP-RTK method. An analysis on dual frequency ionospheric–free phase combination (LC) and dual frequency ionospheric–free range combination (PC) was made in the first stage and then comparing the two solutions relative to the nominal position. The results revealed the fact that by using the ZTD determined in static mode in the detriment of ZTD from GPT2 model, the results are improving on North, East and Up position components. Also lower RMS was obtain when we used the ZTD from static mode comparative to the GPT2 model.

Regional Geomagnetic Field Model for Croatia at 2009.5

Geomagnetic data of north, east, and vertical components at Croatian repeat stations and ground survey sites, as well as European geomagnetic observatories and repeat stations, were used to obtain a regional geomagnetic model over Croatia at 2009.5 epoch. Different models were derived, depending on input data, and three modelling techniques were used: Taylor Polynomial, Adjusted Spherical Harmonic Analysis, and Spherical Harmonic Analysis. It was derived that the most accurate model over Croatia was the one when only Croatian data were used, and by using the Adjusted Spherical Harmonic Analysis. Based on Croatian repeat stations’ data in the interval 2007.5–2010.5, and a global Enhanced Magnetic Model, it was possible to estimate the crustal field at those sites. It was also done by taking into account the empirical adjustment for long-term external field variations. The higher crustal field values were found at those stations which are on or close to the Adriatic anomaly.

PPP/INS tightly coupled navigation using adaptive federated filter

Integration of the global positioning system (GPS) with inertial navigation system (INS) has been very intensively studied and widely applied in recent years. Conventional GPS/INS integrated systems that receive pseudorange and Doppler observations can only attain meter-scale accuracy. An INS has also been integrated with double-differenced GPS measurements that remove GPS errors, although this increases system cost. Following the availability of real-time precise orbit and clock products, a precise point positioning PPP/INS tightly coupled navigation system is presented here. Because various types of measurements such as pseudorange, carrier phase and Doppler are available, an adaptive federated filter method is proposed and applied to the PPP/INS integrated system to improve filter efficiency and adaptivity. Provided that the federated local filter and the adaptive filter are equivalent in form, an information allocation factor in the federated filter is constructed based on the adaptive filter factor. Simulation analyses for different INS grades show that the tactical grade INS can provide higher initial value accuracy for PPP. An experiment was performed to validate the new algorithm, and the results indicate that the INS can improve PPP accuracy, especially under challenging positioning conditions. PPP solution accuracy in the east, north and down components can improve by 45, 47 and 24 %, respectively, during partial GPS satellite blockages. The resolution accuracy of the proposed adaptive federated filter is similar to that of a centralized Kalman filter. The proposed method can also realize parallel filter computing and remove the influence of dynamic model errors.

Reference frame access under the effects of great earthquakes: a least squares collocation approach for non-secular post-seismic evolution

The 2010, (Mw 8.8) Maule, Chile, earthquake produced large co-seismic displacements and non-secular, post-seismic deformation, within latitudes 28\(^{\circ }\)S–40\(^{\circ }\)S extending from the Pacific to the Atlantic oceans. Although these effects are easily resolvable by fitting geodetic extended trajectory models (ETM) to continuous GPS (CGPS) time series, the co- and post-seismic deformation cannot be determined at locations without CGPS (e.g., on passive geodetic benchmarks). To estimate the trajectories of passive geodetic benchmarks, we used CGPS time series to fit an ETM that includes the secular South American plate motion and plate boundary deformation, the co-seismic discontinuity, and the non-secular, logarithmic post-seismic transient produced by the earthquake in the Posiciones Geodesicas Argentinas 2007 (POSGAR07) reference frame (RF). We then used least squares collocation (LSC) to model both the background secular inter-seismic and the non-secular post-seismic components of the ETM at the locations without CGPS. We tested the LSC modeled trajectories using campaign and CGPS data that was not used to generate the model and found standard deviations (95 % confidence level) for position estimates for the north and east components of 3.8 and 5.5 mm, respectively, indicating that the model predicts the post-seismic deformation field very well. Finally, we added the co-seismic displacement field, estimated using an elastic finite element model. The final, trajectory model allows accessing the POSGAR07 RF using post-Maule earthquake coordinates within 5 cm for \(\sim \)91 % of the passive test benchmarks.

Seasonal Hydrological Loading in Southern Tibet Detected by Joint Analysis of GPS and GRACE.

In southern Tibet, ongoing vertical and horizontal motions due to the collision between India and Eurasia are monitored by large numbers of global positioning system (GPS) continuous and campaign sites installed in the past decade. Displacements measured by GPS usually include tectonic deformation as well as non-tectonic, time-dependent signals. To estimate the regional long-term tectonic deformation using GPS more precisely, seasonal elastic deformation signals associated with surface loading must be removed from the observations. In this study, we focus on seasonal variation in vertical and horizontal motions of southern Tibet by performing a joint analysis of GRACE (Gravity Recovery and Climate Experiment) and GPS data, not only using continuous sites but also GPS campaign-mode sites. We found that the GPS-observed and GRACE-modeled seasonal oscillations are in good agreements, and a seasonal displacement model demonstrates that the main reason for seasonal variations in southern Tibet is from the summer monsoon and its precipitation. The biggest loading appears from July to August in the summer season. Vertical deformations observed by GPS and modeled by GRACE are two to three times larger than horizontal oscillations, and the north components demonstrate larger amplitudes than the east components. We corrected the GPS position time series using the GRACE-modeled seasonal variations, which gives significant reductions in the misfit and weighted root-mean-squares (WRMS). Misfit ( divided by degree of freedom) reductions for campaign sites range between 20% and 56% for the vertical component, and are much smaller for the horizontal components. Moreover, time series of continuous GPS (cGPS) sites near the 2015 Nepal earthquakes must be corrected using appropriate models of seasonal loading for analyzing postseismic deformation to avoid biasing estimates of the postseismic relaxation.

Tectonic effect for establishing a semi-dynamic datum in Southwest Taiwan

To accommodate the effects of crustal deformation in the current national static geodetic datum (Taiwan Geodetic Datum 1997 (TWD97)) in SW Taiwan, 221 campaign-mode global positioning system (GPS) stations from 2002 to 2010 were used in this study to generate a surface horizontal velocity model for establishing a semi-dynamic datum in SW Taiwan. An interpolation method, Kriging, and a tectonic block model, DEFNODE, were used to construct the surface horizontal velocity model. Forty-four continuous GPS stations were used to examine the performance of the semi-dynamic datum through exterior validation. The average values of the residual errors obtained using the Kriging method for the north and east components are ±1.9 and ±2.2 mm/year, respectively, whereas those obtained using the block model are ±2.0 and ±2.9 mm/year, respectively. The distribution of residuals greater than 5 mm/year for both models generally corresponds to a high strain rate area derived using the horizontal velocity field. In addition, these residuals may result from deep-seated landslide and active folding or mud diapir in a mudstone area. Similar exterior checking results obtained using the Kriging interpolation method and block model for SW Taiwan indicate a high station density and a relatively satisfactory station spatial coverage. However, the block model is superior to the Kriging method due to the consideration of characteristics of the geological structure in the block model. In addition, result from traditional coordinate transformation was used to compare with the semi-dynamic datum. The results indicate that a semi-dynamic datum is a feasible solution for maintaining the accuracy of TWD97 at an appropriate level over time in Taiwan.

Denoising effect of multiscale multiway analysis on high-rate GPS observations

In general, high-rate GPS data sets are subject to common mode error (CME), multipath error, and high-frequency random noise, which adversely affect the GPS positioning accuracy. In order to improve the precision and reliability of GPS positioning, a multiscale multiway principal component analysis (MSMPCA) denoising method is introduced here. The 1-Hz GPS coordinate time series at ten stations from the California Real Time GPS Network are employed to assess the performance of MSMPCA. Its results are compared with those of the classical denoising methods, including wavelet denoising, PCA, multiway PCA, and multiscale PCA. The results indicate that MSMPCA is able to eliminate not only high-frequency random noise but also low-frequency errors and CME. Furthermore, quantitative analysis shows that MSMPCA is more accurate than the classical denoising methods. Spectral analysis shows that a combination of white plus flicker noise is considered to be the adequate model for the noise characteristics of all three components. Both white and power-law noise amplitudes are smallest in the north component and largest in the vertical component. MSMPCA decreases the mean amplitudes of white noise from 1.3 to 0.0, 0.9 to 0.0, and 2.8 to 0.1 mm in north, east, and vertical components, and those of power-law noise from 4.6 to 1.2, 3.9 to 1.1, and 19.9 to 8.4 mm, respectively. MSMPCA is a promising alternative for removing noise of various frequencies (0.00025---0.5 Hz) from high-rate GPS signals.

Causes and characteristics of reverse bird migration: an analysis based on radar, radio tracking and ringing at Falsterbo, Sweden

That birds migrate in the reverse direction of the expected is a phenomenon of regular occurrence which has been observed at many sites. Here we use three different methods; tracking radar, radiotelemetry and ringing, to characterize the flights of these reverse migrants and investigate possible causes of reverse migration of nocturnally migrating passerines during autumn migration at Falsterbo peninsula, Sweden. Using these different methods we investigated both internal factors, such as age and fuel load, and external factors such as weather variables, competition and predation risk. Birds flying in the reverse direction were more likely to be lean and to be juveniles. Reverse migration was also more common with overcast skies and winds with north and east components. We did not find any effect of temperature, visibility, number of migrating sparrowhawks, or the total number of ringed birds at the site on the day of departure. We found that reverse migration is characterized by slower flight speeds (airspeed) at high altitudes and that it takes place later in the night than forward migration.

Estimation of effect of unequal secular variation on geomagnetic data reduction

The geomagnetic field components are periodically measured at repeat stations. The main objective of the repeat stations is to provide data for tracing the secular variation of the geomagnetic field components. Secular variation at the repeat station is generally different from that at geomagnetic observatory used in the data reduction. The effect of the secular variation differences on geomagnetic data reduction was estimated for the regions of Europe, North America (below 60°N) and Australia, respectively, during the period of 2000-2010. These estimations were obtained by using the monthly mean values of north, east and vertical components of geomagnetic field, recorded at geomagnetic observatories. The effects were calculated by using observatories pairs, with distances from 350 km (in Europe) to 3100 km (in North America and Australia). The maximal effects were found to be the smallest in east component in Europe and North America, and vertical component in Australia; the effects increase with time from a central reduction epoch and they are not constant during mentioned eleven years; they were less than 1 nT only in Europe, for distances between the observatories up to 1000 km in all three components and for periods spanning ±1 month from a central epoch. It was found that their year to year variability is mostly due to the non-eliminated external field residuals in the observatories monthly means; their effect is up to 3 nT for ±3 months from a central epoch. Further, the real effects were compared to those modeled by IGRF-12 model. The maximal differences between the real and the modeled values are below 4.5 nT in all three components, for ±3 months from a central epoch.

Real-time kinematic positioning over long baselines using triple-frequency BeiDou signals

The BeiDou system is the first global navigation satellite system in which all satellites transmit triple-frequency signals that can provide the positioning, navigation, and timing independently. A benefit of triple-frequency signals is that more useful combinations can be formed, including some extrawide-lane combinations whose ambiguities can generally be instantaneously fixed without distance restriction, although the narrow-lane ambiguity resolution (NL AR) still depends on the interreceiver distance or requires a long time to achieve. In this paper, we synthetically study decimeter and centimeter kinematic positioning using BeiDou triple-frequency signals. It starts with AR of two extrawide-lane signals based on the ionosphere-free or ionosphere-reduced geometry-free model. For decimeter positioning, one can immediately use two ambiguity-fixed extrawide-lane observations without pursuing NL AR. To achieve higher accuracy, NL AR is the necessary next step. Despite the fact that long-baseline NL AR is still challenging, some NL ambiguities can indeed be fixed with high reliability. Partial AR for NL signals is acceptable, because as long as some ambiguities for NL signals are fixed, positioning accuracy will be certainly improved.With accumulation of observations, more and more NL ambiguities are fixed and the positioning accuracy continues to improve. An efficient Kalman-filtering system is established to implement the whole process. The formulated system is flexible, since the additional constraints can be easily applied to enhance the model's strength. Numerical results from a set of real triple-frequency BeiDou data on a 50 km baseline show that decimeter positioning is achievable instantaneously.With only five data epochs, 84% of NL ambiguities can be fixed so that the real-time kinematic accuracies are 4.5, 2.5, and 16 cm for north, east, and height components (respectively), while with 10 data epochs more than 90% of NL ambiguities are fixed, and the real-time kinematic solutions are improved to centimeter level for all three coordinate components.

A global empirical model for estimating zenith tropospheric delay

Tropospheric delay acts as a systematic error source in the Global Navigation Satellite Systems (GNSS) positioning. Empirical models UNB3, UNB3m, UNB4 and EGNOS have been developed for use in Satellite-Based Augmentation Systems (SBAS). Model performance, however, is limited due to the low spatial resolution of the look-up tables for meteorological parameters. A new design has been established in this study for improving performance of the tropospheric delay model by more effectively eliminating the error produced by tropospheric delay. The spatiotemporal characteristics of the Zenith Tropospheric Delay (ZTD) were analyzed with findings that ZTD exhibits different annual variations at different locations and decreases exponentially with height increasing. Spherical harmonics are utilized based on the findings to fit the annual mean and amplitude of the ZTD on a global scale and the exponential function is utilized for height corrections, yielding the ZTrop model. On a global scale, the ZTrop features an average deviation of -1.0 cm and Root Mean Square (RMS) of 4.7 cm compared with the International GNSS Service (IGS) ZTD products, an average deviation of 0.0 cm and RMS of 4.5 cm compared with the Global Geodetic Observing System (GGOS) ZTD data, and an average deviation of -1.3 cm and RMS of 5.2 cm compared with the ZTD data from the Constellation Observing System of Meteorology, Ionosphere, and Climate (COSMIC). The RMS of the ZTrop model is 14.5% smaller than that of UNB3, 6.0% smaller than that of UNB3m, 16% smaller than that of UNB4, 14.5% smaller than that of EGNOS and equivalent to the sophisticated GPT2+Saas model in comparison with the IGS ZTD products. The ZTrop, UNB3m and GPT2+Saas models are finally evaluated in GPS-based Precise Point Positioning (PPP), as the models act to aid in obtaining PPP position error less than 1.5 cm in north and east components and relative large error (>5 cm) in up component with respect to the random walk approach.

Data reduction of Croatian geomagnetic repeat stations surveys by using the spherical elementary current systems method

The geomagnetic declination, inclination and total field data surveyed at the Croatian Geomagnetic Repeat Stations Network were reduced to 2008.5, 2009.5 and 2010.5 epochs by a well-known observatory-based and a proposed method, in instances when an influence of the differences of secular variations at a repeat station and at an observatory were not taken into account. The motivation came from distances and distribution of the nearby geomagnetic observatories. A technique for expanding vector systems on a sphere into basis functions, known as the Spherical Elementary Current System (SECS) method, was applied to obtain separation of the geomagnetic field variations into external and internal parts, over Croatia and surrounding countries. The aim of this work is to propose the SECS method for determination of the annual mean values of north, east and vertical components of Earth’s magnetic field at the Croatian repeat stations. The results of the SECS method were compared to an observatory-based method which assumes that the variations of components about their annual mean values at a repeat station are equal to those at a particular nearby reference observatory. For reducing a repeat station data by this simple method the Furstenfeldbruck, Grocka and Tihany observatories were used, while for the SECS method additional three observatories were employed. The reduction methods were found comparable, while in the majority of instances the SECS method demonstrated smaller standard deviations of the components’ annual means. Besides, the annual mean values of the vertical component had the highest accuracies for both methods. The results indicate that the SECS method can be an acceptable method for data reduction to annual mean values.

On the significance of periodic signals in noise analysis of GPS station coordinates time series

Each of the GPS-derived time series consists of the deterministic (functional) and stochastic part. We propose that the deterministic part includes all periodicities from 1st to 9th harmonics of residual Chandler, tropical and draconitic periods and compare it with commonly used calculations of the annual and semi-annual tropical curve. Then, we address the issues of whether all residual periodicities, as proposed here, need to be taken into consideration when performing noise analysis. We use the position time series from 180 International GNSS Service stations obtained at the Jet Propulsion Laboratory using the GIPSY-OASIS software in a Precise Point Positioning mode. The longest series has 22.1 years of GPS daily solutions. The spectral indices range from ---0.12 to ---0.92, while the median values of global spectral indices are equal to: ---0.41 ? 0.15, ---0.38 ? 0.12 and ---0.33 ? 0.18 for North, East and Up components, respectively. All non-modelled geophysical processes or non-included artificial effects in time series lead to an underestimation of errors of velocities, but also to changes in the velocity values themselves. The proposed assumption of seasonals subtraction caused the Akaike information criterion values to show a decrease in the median value of 30 %, which in fact means that all the seasonals mentioned here must be taken into account when analyzing noises. Finally, we noticed that there are some of the GPS stations that improved their velocity uncertainty even of 56 %.

Precise Point Positioning using the BeiDou Navigation Satellite System in South Korea

Global Positioning System (GPS) Precise Point Positioning (PPP) has been extensively used for geodetic applications. Since December 2012, BeiDou navigation satellite system has provided regional positioning, navigation and timing (PNT) services over the Asia-Pacific region. Recently, many studies on BeiDou system have been conducted, particularly in the area of precise orbit determination and precise positioning. In this paper PPP method based on BeiDou observations are presented. GPS and BeiDou data obtained from Mokpo (MKPO) station are processed using the Korea Astronomy and Space Science Institute Global Navigation Satellite System (GNSS) PPP software. The positions are derived from the GPS PPP, BeiDou B 1 / B 2 PPP and BeiDou B 1 /B 3 PPP, respectively. The position errors on BeiDou PPP show a mean bias < 2 cm in the east and north components and approximately 3 cm in the vertical component. It indicates that BeiDou PPP is ready for the precise positioning applications in the Asia-Pacific region. In addition, BeiDou tropospheric zenith total delay (ZTD) is compared to GPS ZTD at MKPO station. The mean value of their difference is approximately 0.52 cm.

Erratum to: Influence of different GPS receiver antenna calibration models on geodetic positioning

In the original publication, the last five sentences of the third paragraph under the section Results were incorrectly published. The corrected text is given below. ‘‘Specifically the update of the type mean robot calibration of the TRM29659.00/NONE caused a position offset of -3.9 mm in the east component and 5.8 mm in the up component. Note that its type mean calibration in the igs08.atx is based on 18 individual calibrations compared to 12 in the igs05.atx, hence the importance of including RMS values in the IGS antenna calibration files.’’