Pawel Wielgosz

Regional Ionosphere Mapping with Kriging and Multiquadric Methods

This paper demonstrates the concept and practical examples of instantaneous mapping of regional ionosphere, based on GPS observations from the State of Ohio continuously operating reference stations (CORS) network. Interpolation/prediction techniques, such as kriging (KR) and the Multiquadric Model (MQ), which are suitable for handling multi-scale phenomena and unevenly distributed data, were used to create total electron content (TEC) maps. Their computational efficiency (especially the MQ technique) and the ability to handle undersampled data (especially kriging) are particularly attractive. Presented here are the preliminary results based on GPS observations collected at five Ohio CORS stations (~100 km sta-tion separation and 1-second sampling rate). Dual frequency carrier phase and code GPS observations were used. A zero-difference approach was used for absolute TEC recovery. The quality of the ionosphere rep-resentation was tested by comparison to the International GPS Service (IGS) Global Ionosphere Maps (GIMs), which were used as a reference.

Accounting for Galileo–GPS inter-system biases in precise satellite positioning

Availability of two overlapping frequencies L1/E1 and L5/E5a of the signals transmitted by GPS and Galileo systems offers the possibility of tightly combining observations from both systems in a single observational model. A tightly combined observational model assumes a single reference satellite for all observations from both Galileo and GPS systems. However, when inter-system double-differenced observations are created, receiver inter-system bias is introduced. This study presents the results and the methodology for estimation and accounting for phase and code GPS-Galileo inter-system bias in precise relative positioning. The research investigates the size and temporal stability of the estimated bias for different receiver pairs as well as examines the influence of accounting for the inter-system bias on the user position solution. The obtained numerical results are based on four experiments carried out at different locations and time periods using both real and simulated GNSS data.

Troposphere modeling for precise GPS rapid static positioning in mountainous areas

In global navigation satellite system precise positioning, double differencing of the observations is the common approach that allows for significant reduction of correlated atmospheric effects. However, with growing distance between the receivers, tropospheric errors decorrelate causing large residual errors affecting the carrier phase ambiguity resolution and positioning quality. This is especially true in the case of height differences between the receivers. In addition, the accuracy achieved by using standard atmosphere models is usually unsatisfactory when the tropospheric conditions at the receiver locations are significantly different from the standard atmosphere. This paper presents an evaluation of three different approaches to troposphere modeling: (a) neglecting the troposphere, (b) using a standard atmosphere model, and (c) estimating tropospheric delays at the reference station network and providing interpolated tropospheric corrections to the user. All these solutions were repeated with various constraints imposed on the tropospheric delays in the least-squares adjustment. The quality of each solution was evaluated by analyzing the residual height errors calculated by comparing the estimated results to the reference coordinates. Several permanent GPS stations of the EUPOS (European Position Determination System) active geodetic network located in the Carpathian Mountains were selected as a test reference network. The distances between the reference stations ranged from 64 to 122 km. KRAW station served as a simulated user receiver located inside the reference network. The user receiver ellipsoidal height is 267 m and the reference station heights range from 277 to 647 m. The results show that regardless of station height differences, it is recommended to model the tropospheric delays at the reference stations and interpolate them to the user receiver location. The most noticeable influence of the residual (unmodeled) tropospheric errors is observed in the station height component. In many cases, mismodeling of the troposphere disrupts ambiguity resolution and, therefore, prevents the user from obtaining an accurate position.

On Constraining Zenith Tropospheric Delays in Processing of Local GPS Networks with Bernese Software

Abstract The aim of this research was to develop the best strategy for the mitigation of the tropospheric delays in processing of precise local GPS networks. With the requirement of sub-centimetre accuracy and the availability of precise IGS products, one of the ultimate accuracy limiting factors in GPS positioning is the tropospheric delay. This is especially true for the accuracy of the height component. In many precise GPS applications, e.g. ground deformation and displacement analyses, volcano monitoring, the vertical accuracy is of crucial importance. Several processing strategies for the troposphere modelling available in the Bernese software were applied and tested. The results from our research show that in the case of small networks (with baselines <10 km and point height differences < 100m)the best strategy is to use of a troposphere model in order to derive zenith tropospheric delays that are fixed in the adjustment. This allows to achieve mm-level accuracies of both horizontal and vertical coordinates. The estimation of the tropospheric delays from the GPS data does not provide satisfactory results, even in the case of a relative troposphere estimation.

Results of the application of tropospheric corrections from different troposphere models for precise GPS rapid static positioning

In many surveying applications, determination of accurate heights is of significant interest. The delay caused by the neutral atmosphere is one of the main factors limiting the accuracy of GPS positioning and affecting mainly the height coordinate component rather than horizontal ones. Estimation of the zenith total delay is a commonly used technique for accounting for the tropospheric delay in static positioning. However, in the rapid static positioning mode the estimation of the zenith total delay may fail, since for its reliable estimation longer observing sessions are required. In this paper, several troposphere modeling techniques were applied and tested with three processing scenarios: a single baseline solution with various height differences and a multi-baseline solution. In specific, we introduced external zenith total delays obtained from Modified Hopfield troposphere model with standard atmosphere parameters, UNB3m model, COAMPS numerical weather prediction model and zenith total delays interpolated from a reference network solution. The best results were obtained when tropospheric delays derived from the reference network were applied.

Observation of the ionospheric storm of October 11, 2008 using FORMOSAT-3/COSMIC data

The electron density profiles retrieved from the COSMIC radio occultation measurements were examined in order to estimate the possibility of its use as additional data source to study changes in electron density distribution occurred during ionospheric storms. The ionosphere behaviour during moderate geomagnetic storm which occurred on October 11, 2008 was analysed. The short-duration positive effect was revealed distinctly in GPS TEC and ionosonde measurements. For the European mid-latitude region it reached the factor of 2 or more relative to the undisturbed conditions. COSMIC data were analyzed and their validity was tested by comparison with ground-based measurements. It was shown the good agreement between independent measurements both in quiet and disturbed conditions. Analysis of COSMIC-derived electron density profiles revealed changes of the bottom-side and topside parts of the ionosphere.

High latitude TEC fluctuations and irregularity oval during geomagnetic storms

GPS measurements obtained by the global IGS network were used to study the occurrence of TEC fluctuations in the northern and southern high-latitude ionosphere during severe geomagnetic storms. In the northern hemisphere, GPS stations located higher than 55N Corrected Geomagnetic Latitude (CGL) at different longitudes were selected. In the southern hemisphere, Antarctic permanent GPS stations were used. Dual-frequency GPS measurements for individual satellite passes served as raw data. As a measure of fluctuation activity the rate of TEC (ROT) was used, and the fluctuation intensity was evaluated using the ROTI index. Using daily GPS measurements from all selected stations, images of the spatial and temporal behavior of TEC fluctuations were formed (in Corrected Geomagnetic Coordinates—CGC and geomagnetic local time—GLT). Similarly to the auroral oval, these images demonstrate an irregularity oval. The occurrence of the irregularity oval relates to the auroral oval, cusp and polar cap. During a storm, the intensity of TEC fluctuations essentially increased. The irregularity oval expands equatorward with an increase of magnetic activity. The study showed that the existing high-latitude GPS stations can provide a permanent monitoring tool for the irregularity oval in near real-time. In this paper, the features of the development of phase fluctuations at the geomagnetic conjugate points, and inter-hemispheric differences and similarities during winter and summer conditions, are discussed.

THE IMPACT OF THE IONOSPHERIC CORRECTION LATENCY ON LONG-BASELINE INSTANTANEOUS KINEMATIC GPS POSITIONING

Abstract The primary objective of this paper is to estimate the influence of the double-difference (DD) ionospheric corrections latency on the instantaneous (one-epoch) ambiguity resolution (AR) in longrange RTK under typical ionospheric conditions. The key to the success in integer AR rests mainly in the mitigation of the atmospheric errors, i.e., the ionospheric and tropospheric delays. Between these two, the former has the greatest influence on the AR, since both ambiguities and ionospheric delay are frequency-dependent. Instantaneous RTK is presently one of the most challenging topics in precise GPS applications. The research presented here addresses this topic through the development and testing of a multiple reference station approach implemented in the MPGPS™ (Multi Purpose GPS Processing Software) software. Atmospheric corrections are used in order to obtain a high quality RTK position over long distances. In our approach, DD ionospheric correction prediction derived from the previous correctly resolved epoch is applied. Yet, at the beginning of the session, a short initialization period is still required in order to produce the initial prediction. After the initialization the method is based on single epoch solution. This method assures a high success rate of the instantaneous AR for long baselines (over 100 km). Since the previous-epoch ionospheric delay is used, and instantaneous mode is applied in the algorithm, the proposed method is robust against cycle slips and data gaps, and still capable of producing centimetre-level RTK positions. The RTK solution was simulated in the post-processing mode. Namely, different DD ionospheric delay correction latencies were simulated in 10 s increments and sent to the (simulated) rover in order to test the AR performance. The AR results were compared and analyzed, and the performance of the RTK positioning was assessed based on the static true solution. Several hours of GPS data, collected by the State of Israel permanently tracking network, were processed. The analyses show that about 90 s latency may exist while the instantaneous ambiguities could still be resolved correctly. The numerical tests presented in this study show the centimetre-level positioning results for mobile receiver.

Selected properties of GPS and Galileo-IOV receiver intersystem biases in multi-GNSS data processing

Two overlapping frequencies—L1/E1 and L5/E5a—in GPS and Galileo systems support the creation of mixed double-differences in a tightly combined relative positioning model. On the other hand, a tightly combined model makes it necessary to take into account receiver intersystem bias, which is the difference in receiver hardware delays. This bias is present in both carrier-phase and pseudorange observations. Earlier research showed that using a priori knowledge of earlier-calibrated ISB to correct GNSS observations has significant impact on ambiguity resolution and, therefore, precise positioning results. In previous research concerning ISB estimation conducted by the authors, small oscillations in phase ISB time series were detected. This paper investigates this effect present in the GPS–Galileo-IOV ISB time series. In particular, ISB short-term temporal stability and its dependence on the number of Galileo satellites used in the ISB estimation was examined. In this contribution we investigate the amplitude and frequency of the detected ISB time series oscillations as well as their potential source. The presented results are based on real observational data collected on a zero baseline with the use of different sets of GNSS receivers.

Impact and implementation of higher-order ionospheric effects on precise GNSS applications

High precision Global Navigation Satellite Systems (GNSS) positioning and time transfer require correcting signal delays, in particular higher-order ionospheric (I2+) terms. We present a consolidated model to correct second- and third-order terms, geometric bending and differential STEC bending effects in GNSS data. The model has been implemented in an online service correcting observations from submitted RINEX files for I2+ effects. We performed GNSS data processing with and without including I2+ corrections, in order to investigate the impact of I2+ corrections on GNSS products. We selected three time periods representing different ionospheric conditions. We used GPS and GLONASS observations from a global network and two regional networks in Poland and Brazil. We estimated satellite orbits, satellite clock corrections, Earth rotation parameters, troposphere delays, horizontal gradients, and receiver positions using a global GNSS solution, Real-Time Kinematic (RTK) and Precise Point Positioning (PPP) techniques. The satellite-related products captured most of the impact of I2+ corrections, with the magnitude up to 2 cm for clock corrections, 1 cm for the along- and cross-track orbit components, and below 5 mm for the radial component. The impact of I2+ on troposphere products turned out to be insignificant in general. I2+ corrections had limited influence on the performance of ambiguity resolution and the reliability of RTK positioning. Finally, we found that I2+ corrections caused a systematic shift in the coordinate domain that was time- and region-dependent, and reached up to -11 mm for the North component of the Brazilian stations during the most active ionospheric conditions. .