Felipe G. Nievinski

Forward modeling of GPS multipath for near-surface reflectometry and positioning applications

Multipath is detrimental for both GPS positioning and timing applications. However, the benefits of GPS multipath for reflectometry have become increasingly clear for soil moisture, snow depth, and vegetation growth monitoring. Most multipath forward models focus on the code modulation, adopting arbitrary values for the reflection power, phase, and delay, or they calculate the reflection delay based on a given geometry and keep reflection power empirically defined. Here, a fully polarimetric forward model is presented, accounting for right- and left-handed circularly polarized components of the GPS broadcast signal and of the antenna and surface responses as well. Starting from the fundamental direct and reflected voltages, we have defined the interferometric and error voltages, which are of more interest in reflectometry and positioning applications. We examined the effect of varying coherence on signal-to-noise ratio, carrier phase, and code pseudorange observables. The main features of the forward model are subsequently illustrated as they relate to the broadcast signal, reflector height, random surface roughness, surface material, antenna pattern, and antenna orientation. We demonstrated how the antenna orientation—upright, tipped, or upside-down—involves a number of trade-offs regarding the neglect of the antenna gain pattern, the minimization of CDMA self-interference, and the maximization of the number of satellites visible. The forward model was also used to understand the multipath signature in GPS positioning applications. For example, we have shown how geodetic GPS antennas offer little impediment for the intake of near-grazing reflections off natural surfaces, in contrast to off metal, because of the lack of diversity with respect to the direct signal—small interferometric delay and Doppler, same sense of polarization, and similar direction of arrival.

The Accidental Tide Gauge: A GPS Reflection Case Study From Kachemak Bay, Alaska

For the last decade, it has been known that reflected GPS signals observed with specialized instruments could be used to measure sea level. In this letter, data from an existing geodetic-quality GPS site near Kachemak Bay, Alaska, are analyzed for a one-year time period. Daily sea-level variations are more than 7 m. Tidal coefficients have been estimated and compared with coefficients estimated from records from a traditional tide gauge at Seldovia Harbor, ~ 30 km away. The GPS and Seldovia estimates of M2 and S2 coefficients agree to better than 2%; much of this residual can be attributed to true differences in the tide over 30 km as it propagates up Kachemak Bay. For daily mean sea levels the agreement is 2.3 cm. Because a standard geodetic GPS receiver/antenna is used, this GPS instrument can measure long-term sea-level changes in a stable terrestrial reference frame.

Inverse Modeling of GPS Multipath for Snow Depth Estimation—Part I: Formulation and Simulations

Snowpacks provide reservoirs of freshwater. The amount stored and how fast it is released by melting are vital information for both scientists and water supply managers. GPS multipath reflectometry (GPS-MR) is a new technique that can be used to measure snow depth. Signal-to-noise ratio data collected by GPS instruments exhibit peaks and troughs as coherent direct and reflected signals go in and out of phase. These interference fringes are used to retrieve the unknown land surface characteristics. In this two-part contribution, a forward/inverse approach is offered for GPS-MR of snow depth. Part I starts with the physically based forward model utilized to simulate the coupling of the surface and antenna responses. A statistically rigorous inverse model is presented and employed to retrieve parameter corrections responsible for observation residuals. The unknown snow characteristics are parameterized, the observation/parameter sensitivity is illustrated, the inversion performance is assessed in terms of its precision and its accuracy, and the dependence of model results on the satellite direction is quantified. The latter serves to indicate the sensing footprint of the reflection.

An open source GPS multipath simulator in Matlab/Octave

Abstract Multipath is detrimental for both GPS positioning and timing applications. However, the benefits of GPS multipath for reflectometry have become increasingly clear for monitoring soil moisture, snow depth, and vegetation growth. In positioning applications, a simulator can support multipath mitigation efforts in terms of, e.g., site selection, antenna design, receiver performance assessment, and in relating different observations to a common parameterization. For reflectometry, in order to convert observed multipath parameters into useable environmental products, it is important to be able to explicitly link the GPS observables to known characteristics of the GPS receiver/antenna and the reflecting environment. Existing GPS multipath software simulators are generally not readily available for the general scientific community to use and/or modify. Here, a simulator has been implemented in Matlab/Octave and is made available as open source code. It can produce signal-to-noise ratio, carrier phase, and code pseudorange observables, based on L1 and L2 carrier frequencies and C/A, P(Y), and L2C modulations. It couples different surface and antenna types with due consideration for polarization and coherence. In addition to offering predefined material types (water, concrete, soil, etc.), it allows certain dimensional properties to be varied, such as soil moisture and snow density.

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.

Inverse Modeling of GPS Multipath for Snow Depth Estimation—Part II: Application and Validation

GPS multipath reflectometry (GPS-MR) is a technique that uses geodetic quality GPS receivers to estimate snow depth. The accuracy and precision of GPS-MR retrievals are evaluated at three different sites: grasslands, alpine, and forested. The assessment yields a correlation of 0.98 and an rms error of 6-8 cm for observed snow depths of up to 2.5 m. GPS-MR underestimates in situ snow depth by 10%-15% at these three sites, although the validation methods do not measure the same footprint as GPS-MR.

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.

First results from an airborne GPS radio occultation system for atmospheric profiling

Global Positioning System (GPS) radio occultation (RO) from low Earth-orbiting satellites has increased the quantity of high-vertical resolution atmospheric profiles, especially over oceans, and has significantly improved global weather forecasting. A new system, the Global Navigation Satellite Systems Instrument System for Multistatic and Occultation Sensing (GISMOS), has been developed for RO sounding from aircraft. GISMOS also provides high-vertical resolution profiles that are insensitive to clouds and precipitation, and in addition, provides greater control on the sampling location, useful for targeted regional studies. The feasibility of the system is demonstrated with a flight carried out during development of an Atlantic tropical storm. The data have been evaluated through a comparison with dropsonde data. The new airborne RO system will effectively increase by more than 50% the number of profiles available for studying the evolution of tropical storms during this campaign and could potentially be deployed on commercial aircraft in the future.

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.

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