Marcelo C. Santos

Comparison of Ray-Tracing Packages for Troposphere Delays

A comparison campaign to evaluate and compare troposphere delays from different ray-tracing software was carried out under the umbrella of the International Association of Geodesy Working Group 4.3.3 in the first half of 2010 with five institutions participating: the GFZ German Research Centre for Geosciences (GFZ), the Groupe de Recherche de Geodesie Spatiale, the National Institute of Information and Communications Technology (NICT), the University of New Brunswick, and the Institute of Geodesy and Geophysics of the Vienna University of Technology. High-resolution data from the operational analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) for stations Tsukuba (Japan) and Wettzell (Germany) were provided to the participants of the comparison campaign. The data consisted of geopotential differences with respect to mean sea level, temperature, and specific humidity, all at isobaric levels. Additionally, information about the geoid undulations was provided, and the participants computed the ray-traced total delays for 5° elevation angle and every degree in azimuth. In general, we find good agreement between the ray-traced slant factors from the different solutions at 5° elevation if determined from the same pressure level data of the ECMWF. Standard deviations and biases are at the 1-cm level (or significantly better for some combinations). Some of these discrepancies are due to differences in the algorithms and the interpolation approaches. If compared with slant factors determined from ECMWF native model level data, the biases can be significantly larger.

Assessment of troposphere mapping functions using three-dimensional ray-tracing

The troposphere delay is an important source of error for precise GNSS positioning due to its high correlation with the station height parameter. It has been demonstrated that errors in mapping functions can cause sub-annual biases as well as affect the repeatability of GNSS solutions, which is a particular concern for geophysical studies. Three-dimensional ray-tracing through numerical weather models (NWM) is an excellent approach for capturing the directional and daily variation of the tropospheric delay. Due to computational complexity, its use for positioning purposes is limited, but it is an excellent tool for evaluating current state-of-the-art mapping functions used for geodetic positioning. Many mapping functions have been recommended in the past such as the Niell Mapping Function (NMF), Vienna Mapping Function 1 (VMF1), and the Global Mapping Function (GMF), which have been adopted by most IGS analysis centers. A new Global Pressure Temperature model (GPT2) has also been developed, which has been shown to improve upon the original atmospheric model used for the GMF. Although the mapping functions mentioned above use the same functional formulation, they vary in terms of their atmospheric source and calibration approach. A homogeneous data set of three-dimensional ray-traced delays is used to evaluate all components of the mapping functions, including their underlying functional formulation, calibration, and compression method. Additionally, an alternative representation of the VMF1 is generated using the same atmospheric source as the truth data set to evaluate the differences in ray-tracing methods and their effect on the end mapping function. The results of this investigation continue to support the use of the VMF1 as the mapping function of choice when geodetic parameters are of interest. Further support for the GPT2 and GMF as reliable back-ups when the VMF1 is not available was found due to their high consistency with the NWM-derived mapping function. Additionally, a small latitude-dependent bias in station height was found in the current mapping functions. This bias was identified to be due to the assumption of a constant radius of the earth and was largest at the poles and at the equator. Finally, an alternative version of the VMF1 is introduced, namely the UNB-VMF1 which provides users with an independent NWM-derived mapping function to support geodetic positioning.

Initial results from a long baseline, kinematic, differential GPS carrier phase experiment in a marine environment

The University of Southern Mississippi (USM) and the University of New Brunswick (UNB) have collaborated to devise and carry out a long-term experiment in precise GPS positioning over long distances in a marine environment. A pair of GPS reference stations have been deployed on either side of the Bay of Fundy in Canada, at the terminals of an approximately 75 km ferry route. A geodetic receiver has been installed on the ferry. Surface meteorological equipment has also been collocated with the three receivers. The primary goal of the study, over the course of one year of data collection from the daily ferry runs, realizing that the differential troposphere is a major limiting factor in marine positioning, is to attempt to advance positioning results by means of improved differential tropospheric modeling. The results presented in the paper include a full description of the experiment, and descriptions of the GPS and meteorological data collected, as well as the software used in the processing. Initial PPK data processing results are presented illustrating positioning accuracy versus baseline length. And results from tests using various tropospheric delay values are presented.

Generation and Assessment of VMF1-Type Grids Using North-American Numerical Weather Models

Numerical weather models (NWM) have become an important source of atmospheric data for modeling error sources in geodetic positioning. One example of this is the development of the Vienna Mapping Functions (VMF1) and ray-traced zenith delays which are derived from the European Centre for Medium-range Weather Forecasts (ECMWF) datasets. These products are provided on an operational basis through the GGOS Atmosphere project. In general, relatively little consideration has been given to the choice of NWM on the derived mapping functions and zenith delay products. In this investigation we compare the gridded-VMF1 mapping functions and ray-traced zenith delays derived from the ECMWF to equivalent products derived by ray-tracing through the National Center for Environmental Prediction (NCEP) Reanalysis model. We have chosen to compare the gridded version of these products as they are available for any location on Earth, rather than only specific stations and have been shown to be essentially equivalent in terms of accuracy. This paper also includes a discussion about a systematic production of gridded-VMF1 and ray-traced zenith delays derived from the NCEP datasets (and from the Canadian Meteorological Center GEM model) on an operational basis. The benefits of the service would include: (1) a backup in the event of the ECMWF VMF1 or zenith delays being unavailable; (2) greater compatibility with other NWM derived corrections, such as atmospheric pressure loading and; (3) the availability of tropospheric delay products derived from an independent source and ray-tracing algorithms should provide more robustness for combination products which use these models.

Testing Stokes-Helmert geoid model computation on a synthetic gravity field: experiences and shortcomings

We report on testing the UNB (University of New Brunswick) software suite for accurate regional geoid model determination by use of Stokes-Helmert’s method against an Australian Synthetic Field (ASF) as “ground truth”. This testing has taken several years and has led to discoveries of several significant errors (larger than 5mm in the resulting geoid models) both in the UNB software as well as the ASF. It was our hope that, after correcting the errors in UNB software, we would be able to come up with some definite numbers as far as the achievable accuracy for a geoid model computed by the UNB software. Unfortunately, it turned out that the ASF contained errors, some of as yet unknown origin, that will have to be removed before that ultimate goal can be reached. Regardless, the testing has taught us some valuable lessons, which we describe in this paper. As matters stand now, it seems that given errorless gravity data on 1′ by 1′ grid, a digital elevation model of a reasonable accuracy and no topographical density variations, the Stokes-Helmert approach as realised in the UNB software suite is capable of delivering an accuracy of the geoid model of no constant bias, standard deviation of about 25 mm and a maximum range of about 200 mm. We note that the UNB software suite does not use any corrective measures, such as biases and tilts or surface fitting, so the resulting errors reflect only the errors in modelling the geoid.

Searching for the Optimal Relationships Between SIRGAS2000, South American Datum of 1969 and Córrego Alegre in Brazil

Brazil has moved towards the adoption of a geocentric system, SIRGAS2000. With the adoption of this system, starting in 2005, a great demand has been created towards transforming the current data sets from the South American Datum of 1969 (SAD69), in its two distinct realizations, and the Corrego Alegre frames into SIRGAS2000. The fact that these four frames will co-exist until 2014 creates positive and negative situations. Due to the distortion between those frames, the relationships among them cannot be well established with Helmert transformation parameters alone. To solve this problem, five Study Groups were created to look for the optimal relationships for coordinate transformation between those frames. The approaches being investigated to augment the parameter transformation are based on: Collocation, Delaunay, Regular grids (NTv2 and Sheppard method) and Neural Networks. The research is currently going on. This paper describes the current efforts towards defining the optimal relationships among these four frames, from the mathematical point-of-view. The work described in the paper has been carried out under the scope of the National Geospatial Framework Project (www.pign.org), sponsored by the Canadian International Development Agency. Leonardo C. Oliveria Secao de Ensino de Engenharia Cartografica, Instituto Militar de Engenharia, Praca General Tiburcio, 80-6◦ andar, Rio de Janeiro, RJ, 22290-270 Brazil Marcelo C. Santos Department of Geodesy and Geomatics Engineering, University of New Brunswick, P.O.Box 4400, Fredericton NB., Canada E3B 5A3

First Steps Using Two GPS Satellites for Monitoring the Dynamic Behavior of a Small Concrete Highway Bridge

AbstractThis work presents the results of global positioning system (GPS) data processing using the phase residuals method (PRM)—L1 carrier phase from two satellites—to monitor the dynamic behavior of a small concrete bridge. The bridge tested, the Jaguari Bridge, is a small, curvd, reinforced concrete bridge. The bridge over the Jaguari River is a reinforced concrete bridge built in 1999, located on Fernao Dias Highway (BR 381), positioned at Kilometer 946, Minas Gerais, Brazil. The small concrete bridge was chosen for this study because its construction type is found in great numbers throughout Brazil. In parallel, there was a significant increase of pathologies in these structures as a result of lack of maintenance procedures. The detection of small vibrations of spans, for example, which is a good indicator of the health of a structure, can be monitored by GPS. The challenge in this case is trying to detect with GPS the dynamic displacement that has an amplitude close to 5 mm. Application of the PRM o...

Experimental assessment of a PPP-based P2-C2 bias estimation

The inception of C2 brought with it new issues to be considered, such as the merger of C2-capable and legacy receivers and the processing of data collected by a C2-capable receiver with satellite clock values generated using a legacy receiver network. Since receiver and satellite hardware delays for C2 measurements may not be necessarily the same of those for P2, a bias between P2 and C2 code measurements should be considered. We refer to this as the P2-C2 bias using the same standard nomenclature used for P1-C1 biases. The knowledge of this bias allows the use of C2 as an observable for positioning, applying satellite clock values computed using P2 as the observable on L2, as in the case of IGS clock products. This paper presents two estimation strategies for obtaining P2-C2 bias. The first strategy takes the mean of the difference between time series of P2 and C2 observations. This strategy relies on receivers tracking simultaneously P2 and C2. The second strategy takes advantage of the residuals of PPP estimation. This PPP-based approach for P2-C2 bias estimation was developed at the University of New Brunswick and has been realized in GAPS, the GPS Analysis and Positioning Software. The P2-C2 values are estimated from a network of C2-capable receivers (a sub-set of the IGS L2C Test Network), and used in the point positioning of a C2-capable receiver, a Trimble R7 receiver, located on the roof of a TU Delft building. The PPP position of the R7 receiver is computed without applying P2-C2 bias, and applying the P2-C2 biases computed from the two approaches. Results show an improvement in the 3D position and their spread of 19% and 3% (1-sigma), respectively, if using the mean P2-C2 values, and of 16% and 8% (1-sigma), respectively, if using the PPP-based P2-C2 bias values.

The use of smooth piecewise algebraic approximation in the determination of vertical crustal movements in Eastern Canada

The objective of this study is to compile a physically meaningful map of vertical crustal movements (VCM) for Eastern Canada. Average vertical velocities over the past century are determined by repeated precise levelling and monthly mean sea level observations from 17 tide gauges. The spatial vertical velocities may be mathematically expressed in any number of ways.

Accessing the New SIRGAS2000 Reference Frame through a Modernized Brazilian Active Control Network

Since the beginning of its establishment, in December of 1996, the Brazilian Network for Continuous Monitoring of GPS - RBMC has been playing the role as the fundamental geodetic frame in the country, providing users with a direct connection to the Brazilian Geodetic System - SGB. This role has become more relevant with the adoption of the new geodetic system, SIRGAS2000, as of February 25, 2005. In this paper, the current RBMC status is presented, as well as the expansion and modernization plans for its structure, functionality and services to be provided to users. RBMC currently works in post-mission mode, where users are able to freely download from the Internet data collected by each of its 19 stations 24 hours after the observations are collected. The modernization plans specify, in a first step, the network expansion with six additional stations in the Amazon region, including the reactivation of Manaus station, and the connection of all stations to the Internet, to support real time transfer of 1 Hz data to the control center, in Rio de Janeiro. When available at the control center, the data will support WADGPS (Wide Area Differential GPS) corrections to be transmitted, in real time, to users in Brazil and surrounding areas. This new service is under development based on a cooperation signed at the end of 2004 with the University of New Brunswick, supported by the Canadian International Development Agency and the Brazilian Cooperation Agency. It is estimated that users will be able to achieve a horizontal accuracy around 0.5 m (1-σ) in static and kinematic positioning. The expected accuracy for dual frequency receiver users is even better. The availability of the WADGPS service — at no cost -will allow users to tie to the new SIRGAS2000 system in a more rapid and transparent way in positioning and navigation applications. It should be emphasized that support to post-mission static positioning will continue to be provided to users interested in higher accuracy levels.