Volume 9, Issue 2

In order to achieve high-accuracy positioning, either Real-Time Kinematic (RTK) or Precise Point Positioning (PPP) techniques can be used. While RTK normally delivers higher accuracy with shorter convergence times, PPP has been an attractive technology for maritime applications, as it delivers uniform positioning performance without the direct need of a nearby reference station. Traditional PPP has been based on ambiguity-­float solutions using GPS and Glonass constellations. However, the addition of new satellite systems, such as Galileo and BeiDou, and the possibility of fixing integer carrier-phase ambiguities (PPP-AR) allow to increase PPP accuracy. In this article, a performance assessment has been done between RTK, PPP and PPP-AR, using GNSS data collected from two antennas installed on a ferry navigating in Oslo (Norway). RTK solutions have been generated using short, medium and long baselines (up to 290 km). For the generation of PPP-AR solutions, Uncalibrated Hardware Delays (UHDs) for GPS, Galileo and BeiDou have been estimated using reference stations in Oslo and Onsala. The performance of RTK and multi-­constellation PPP and PPP-AR are presented.

The Open Source GNSS Reference Server (OSGRS) exploits the GNSS Reference Interface Protocol (GRIP) to provide assistance data to GPS receivers. Assistance can be in terms of signal acquisition and in the processing of the measurement data. The data transfer protocol is based on Extensible Mark-up Language (XML) schema. The first version of the OSGRS required a direct hardware connection to a GPS device to acquire the data necessary to generate the appropriate assistance. Scenarios of interest for the OSGRS users are weak signal strength indoors, obstructed outdoors or heavy multipath environments. This paper describes an improved version of OSGRS that provides alternative assistance support from a number of Global Navigation Satellite Systems (GNSS). The underlying protocol to transfer GNSS assistance data from global casters is the Networked Transport of RTCM (Radio Technical Commission for Maritime Services) over Internet Protocol (NTRIP), and/or the RINEX (Receiver Independent Exchange) format. This expands the assistance and support model of the OSGRS to globally available GNSS data servers connected via internet casters. A variety of formats and versions of RINEX and RTCM streams become available, which strengthens the assistance provisioning capability of the OSGRS platform. The prime motivation for this work was to enhance the system architecture of the OSGRS to take advantage of globally available GNSS data sources. Open source software architectures and assistance models provide acquisition and data processing assistance for GNSS receivers operating in weak signal environments. This paper describes test scenarios to benchmark the OSGRSv2 performance against other Assisted-GNSS solutions. Benchmarking devices include the SPOT satellite messenger, MS-Based & MS-Assisted GNSS, HSGNSS (SiRFstar-III) and Wireless Sensor Networks Assisted-GNSS. Benchmarked parameters include the number of tracked satellites, the Time to Fix First (TTFF), navigation availability and accuracy. Three different configurations of Multi-GNSS assistance servers were used, namely Cloud-Client-Server, the Demilitarized Zone (DMZ) Client-Server and PC-Client-Server; with respect to the connectivity location of client and server. The impact on the performance based on server and/or client initiation, hardware capability, network latency, processing delay and computation times with their storage, scalability, processing and load sharing capabilities, were analysed. The performance of the OSGRS is compared against commercial GNSS, Assisted-GNSS and WSN-enabled GNSS devices. The OSGRS system demonstrated lower TTFF and higher availability.

This article introduces a new model for precise point positioning (PPP), which combines dual-frequency GPS and Galileo observations. Our model is based on the between-satellite single-difference (BSSD) linear combination, which cancels out some receiver-related biases, including receiver clock error and non-zero initial phase bias of the receiver’s oscillator. Two different scenarios are considered when forming BSSD linear combinations. In the first scenario, either a GPS or a Galileo satellite is selected as a reference for both GPS and Galileo observables. The second scenario, on the other hand, selects two reference satellites: a GPS reference satellite for the GPS observables and a Galileo satellite for the Galileo observables. Natural Resources Canada’s GPSPace PPP software is modified to enable a combined GPS/Galileo PPP solution and to handle the newly introduced biases. A total of 12 data sets representing two-day GPS/Galileo measurements at six IGS stations are processed to verify the developed PPP model. Precise satellite orbit and clock products from the IGS-MGEX network are used to correct both of the GPS and Galileo measurements. It is shown that using one reference satellite to form the BSSD linear combinations improves the precision of the estimated parameters by about 25 % compared with the GPS-only PPP solution. When two reference satellites are used, however, the precision of the estimated parameters improves by about 50 % compared with the GPS-only PPP solution. Additionally, the solution convergence time is reduced to 10 min for both BSSD scenarios, which represents about 50 % improvement in comparison with the GPS-only PPP solution.

Geoid determinations by the Remove-Compute-­Restore (R-C-R) technique involves the application of Stokes’ integral on reduced gravity anomalies. Numerical Stokes’ integration produces an error depending on the choice of the integration radius, grid resolution and Stokes’ kernel function. In this work, we aim to evaluate the accuracy of Stokes’ integral through a study on synthetic gravitational signals derived from EGM2008 on three different landscape areas with respect to the size of the integration domain and the resolution of the anomaly grid. The influence of the integration radius was studied earlier by several authors. Using real data, they found that the choice of relatively small radii (less than 1°) enables to reach an optimal accuracy. We observe a general behaviour coherent with these earlier studies. On the other hand, we notice that increasing the integration radius up to 2° or 2.5° might bring significantly better results. We note that, unlike the smallest radius corresponding to a local minimum of the error curve, the optimal radius in the range 0° to 6° depends on the terrain characteristics. We also find that the high frequencies, from degree 600, improve continuously with the integration radius in both semi-­mountainous and mountain areas. Finally, we note that the relative error of the computed geoid heights depends weakly on the anomaly spherical harmonic degree in the range from degree 200 to 2000. It remains greater than 10 % for any integration radii up to 6°. This result tends to prove that a one centimetre accuracy cannot be reached in semi-mountainous and mountainous regions with the unmodified Stokes’ kernel.

The identification of outliers in measurement data is hindered if they are present in leverage points as well as in rest of the data. A promising method for their identification is the Monte Carlo estimation (MCE), which is subject of the present investigation. In MCE the data are searched for data subsamples without leverage outliers and with few (or no) non-leverage outliers by a random generation of subsamples. The required number of subsamples by which several of such subsamples are generated with a given probability is derived. Each generated subsample is rated based on the residuals resulting from an adjustment. By means of a simulation it is shown that a least squares adjustment is suitable. For the rating of the subsamples, the sum of squared residuals is used as a measure of the fit. It is argued that this (unweighted) sum is also appropriate if data have unequal weights. An investigation of the robustness of a final Bayes estimation with the result of the Monte Carlo search as prior information reveals its inappropriateness. Furthermore, the case of an unknown variance factor is considered. A simulation for different scale estimators for the variance factor shows their impracticalness. A new resistant scale estimator is introduced which is based on a generalisation of the median absolut deviation. Taking into account the results of the investigations, a new procedure for MCE considering a scale estimation is proposed. Finally, this method is tested by simulation. MCE turns out to be more reliable in the identification of outliers than a conventional resistant estimation method.