Jacek Paziewski

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.

Precise GNSS single epoch positioning with multiple receiver configuration for medium-length baselines: methodology and performance analysis

The configuration of multiple GNSS antennas and receivers on a common moving platform is widely used for attitude determination. This rigid configuration with nearby antennas can form several constraints, which can be used in order to improve the accuracy of the solution. In particular, known baseline length, relationships between ambiguities on different baselines as well as similar tropospheric and ionospheric delays can be applied in the relative positioning model. The objective of the presented research was to develop a method for taking advantage of the abovementioned constraints in order to improve the ambiguity resolution and consequently the performance of the precise GNSS positioning. This study is based on the processing of medium length baselines up to 70 km length in the instantaneous mode. The results show clear improvement in ambiguity resolution domain in comparison to the commonly used ionosphere-weighted troposphere-estimated geometry based model.

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.

Study on reliable GNSS positioning with intense TEC fluctuations at high latitudes

The study presents the influence of strong total electron content (TEC) fluctuations occurring at high latitudes on rapid static positioning. The authors propose an algorithm mitigating the impact of dynamic temporal changes in electron content using the rate of TEC corrections. It consists of modifying the observations using the measured rate of TEC variations and hence allows reducing the number of parameters to one ionospheric delay of a reference epoch per satellite and per session. An analysis was carried out for a typical quiet day in solar minimum on September 6, 2009 and a disturbed day during high solar activity on March 17, 2013. For a standard geometry-based relative model with weighted ionosphere and troposphere, the results confirmed the dramatic drop of ambiguity resolution efficiency during a violent space weather event. The results obtained for the new algorithm, however, demonstrate its wide applicability and a 10-fold improvement in ambiguity success rate during the disturbed day.

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. .

On the Applicability of Galileo FOC Satellites with Incorrect Highly Eccentric Orbits: An Evaluation of Instantaneous Medium-Range Positioning

This study addresses the potential contribution of the first pair of Galileo FOC satellites sent into incorrect highly eccentric orbits for geodetic and surveying applications. We began with an analysis of the carrier to noise density ratio and the stochastic properties of GNSS measurements. The investigations revealed that the signal power of E14 & E18 satellites is higher than for regular Galileo satellites, what is related to their lower altitude over the experiment area. With regard to the noise of the observables, there are no significant differences between all Galileo satellites. Furthermore, the study confirmed that the precision of Galileo data is higher than that of GPS, especially in the case of code measurements. Next analysis considered selected domains of precise instantaneous medium-range positioning: ambiguity resolution and coordinate accuracy as well as observable residuals. On the basis of test solutions, with and without E14 & E18 data, we found that these satellites did not noticeably influence the ambiguity resolution process. The discrepancy in ambiguity success rate between test solutions did not exceed 2%. The differences between standard deviations of the fixed coordinates did not exceed 1 mm for horizontal components. The standard deviation of the L1/E1 phase residuals, corresponding to regular GPS and Galileo, and E14 & E18 satellite signals, was at a comparable level, in the range of 6.5–8.7 mm. The study revealed that the Galileo satellites with incorrect orbits were fully usable in most geodetic, surveying and many other post-processed applications and may be beneficial especially for positioning during obstructed visibility of satellites. This claim holds true when providing precise ephemeris of satellites.