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The Federal Aviation Administration's wide-area augmentation system (WAAS) for GPS positioning requires near real-time calibration of ionospheric vertical delays at a set of Earth-fixed grid points.
The conical-domain model is a computational model, now undergoing development, for estimating ionospheric delays of Global Positioning System (GPS) signals. Relative to the standard ionospheric delay model described below, the conical-domain model offers improved accuracy. In the absence of selective availability, the ionosphere is the largest source of error for single-frequency users of GPS. Because ionospheric signal delays contribute to errors in GPS position and time measurements, satellite-based augmentation systems (SBASs) have been designed to estimate these delays and broadcast corrections. Several national and international SBASs are currently in various stages of development to enhance the integrity and accuracy of GPS measurements for airline navigation. In the Wide Area Augmentation System (WAAS) of the United States, slant ionospheric delay errors and confidence bounds are derived from estimates of vertical ionospheric delay modeled on a grid at regularly spaced intervals of latitude and longitude. The estimate of vertical delay at each ionospheric grid point (IGP) is calculated from a planar fit of neighboring slant delay measurements, projected to vertical using a standard, thin-shell model of the ionosphere. Interpolation on the WAAS grid enables estimation of the vertical delay at the ionospheric pierce point (IPP) corresponding to any arbitrary measurement of a user. (The IPP of a given user s measurement is the point where the GPS signal ray path intersects a reference ionospheric height.) The product of the interpolated value and the user s thin-shell obliquity factor provides an estimate of the user s ionospheric slant delay. Two types of error that restrict the accuracy of the thin-shell model are absent in the conical domain model: (1) error due to the implicit assumption that the electron density is independent of the azimuthal angle at the IPP and (2) error arising from the slant-to-vertical conversion. At low latitudes or at mid-latitudes under disturbed conditions, the accuracy of SBAS systems based upon the thin-shell model suffers due to the presence of complex ionospheric structure, high delay values, and large electron density gradients. Interpolation on the vertical delay grid serves as an additional source of delay error. The conical-domain model permits direct computation of the user s slant delay estimate without the intervening use of a vertical delay grid. The key is to restrict each fit of GPS measurements to a spatial domain encompassing signals from only one satellite. The conical domain model is so named because each fit involves a group of GPS receivers that all receive signals from the same GPS satellite (see figure); the receiver and satellite positions define a cone, the satellite position being the vertex. A user within a given cone evaluates the delay to the satellite directly, using (1) the IPP coordinates of the line of sight to the satellite and (2) broadcast fit parameters associated with the cone. The conical-domain model partly resembles the thin-shell model in that both models reduce an inherently four-dimensional problem to two dimensions. However, unlike the thin-shell model, the conical domain model does not involve any potentially erroneous simplifying assumptions about the structure of the ionosphere. In the conical domain model, the initially four-dimensional problem becomes truly two-dimensional in the sense that once a satellite location has been specified, any signal path emanating from a satellite can be identified by only two coordinates; for example, the IPP coordinates. As a consequence, a user s slant-delay estimate converges to the correct value in the limit that the receivers converge to the user s location (or, equivalently, in the limit that the measurement IPPs converge to the user s IPP).
In one embodiment, a method for ionospheric delay compensation is provided. The method includes determining an ionospheric delay based on a signal having propagated from the navigation satellite to a location below the ionosphere. A scale factor can be applied to the ionospheric delay, wherein the scale factor corresponds to a ratio of an ionospheric delay in the vertical direction based on an altitude of the satellite navigation system receiver. Compensation can be applied based on the ionospheric delay.
The multi-cone model is a computational model for estimating ionospheric delays of Global Positioning System (GPS) signals. It is a direct descendant of the conical-domain model. A primary motivation for the development of this model is the need to find alternatives for modeling slant delays at low latitudes, where ionospheric behavior poses an acute challenge for GPS signal-delay estimates based upon the thin-shell model of the ionosphere.
Current satellite-based augmentation systems estimate ionospheric delay using algorithms that assume the electron density of the ionosphere is non-negligible only in a thin shell located near the peak of the actual profile. In its initial operating capability, for example, the Wide Area Augmentation System incorporated the thin shell model into an estimation algorithm that calculates vertical delay using a planar fit. Under disturbed conditions or at low latitude where ionospheric structure is complex, however, the thin shell approximation can serve as a significant source of estimation error. A recent upgrade of the system replaced the planar fit algorithm with an algorithm based upon kriging. The upgrade owes its success, in part, to the ability of kriging to mitigate the error due to this approximation. Previously, alternative delay estimation algorithms have been proposed that eliminate the need for invoking the thin shell model altogether. Prior analyses have compared the accuracy achieved by these methods to the accuracy achieved by the planar fit algorithm. This paper extends these analyses to include a comparison with the accuracy achieved by kriging. It concludes by examining how a satellite-based augmentation system might be implemented without recourse to the thin shell approximation.
In the absence of selective availability, the ionosphere represents the largest source of positioning error for single-frequency users of the GPS. In differential GPS systems such as the Wide Angle Augmentation System, vertical ionospheric delays are modeled at regularly-spaced intervals in latitude and longitude. The broadcast bound on the error at each of these points is designated the grid ionospheric vertical erorr (GIVE). A critical integrity requirement of WAAS is that the broadcast GIVE bounds residual error with a very high degree of confidence.
Several spaceborne altimeters have been built and flown, and others are being developed to provide measurements of ocean and ice sheet topography. Until the launch of TOPEX, altimeters were single frequency systems incapable of removing the effects of ionospheric delay on the radar pulse. With the current state of the art in satellite altimetry, the ionosphere causes the largest single error when using single frequency altimeters. Ionospheric models provide the only recourse short of adding a second frequency to the altimeter. Unfortunately, measurements of the ionosphere are lacking over the oceans or ice sheets where they are most needed. A possible solution to the lack of data density may result from an expanded use of the Global Positioning System (GPS). This paper discusses how the reflection of the GPS signal from the ocean can be used to extend ionospheric measurements by simply adding a GPS receiver and downward-pointing antenna to satellites carrying single frequency altimeters. This paper presents results of a study assessing the feasibility and effectiveness of adding a GPS receiver and downward-pointing antenna to satellites carrying single frequency altimeters.
This study is a preliminary analysis of the accuracy of various ionosphere models to correct single frequency altimeter height measurements for Ionospheric path delay. In particular, research focused on adjusting empirical and parameterized ionosphere models in the parameterized real-time ionospheric specification model (PRISM) 1.2 using total electron content (TEC) data from the global positioning system (GPS). The types of GPS data used to adjust PRISM included GPS line-of-sight (LOS) TEC data mapped to the vertical, and a grid of GPS derived TEC data in a sun-fixed longitude frame. The adjusted PRISM TEC values, as well as predictions by IRI-90, a climatotogical model, were compared to TOPEX/Poseidon (T/P) TEC measurements from the dual-frequency altimeter for a number of T/P tracks. When adjusted with GPS LOS data, the PRISM empirical model predicted TEC over 24 1 h data sets for a given local time to with in a global error of 8.60 TECU rms during a midnight centered ionosphere and 9.74 TECU rms during a noon centered ionosphere. Using GPS derived sun-fixed TEC data, the PRISM parameterized model predicted TEC within an error of 8.47 TECU rms centered at midnight and 12.83 TECU rms centered at noon. From these best results, it is clear that the proposed requirement of 3-4 TECU global rms for TOPEX/Poseidon Follow-On will be very difficult to meet, even with a substantial increase in the number of GPS ground stations, with any realizable combination of the aforementioned models or data assimilation schemes.
When both S-band and X-band data are recorded for a signal which has passed through the ionosphere, it is possible to calculate the ionospheric contribution to signal delay. In Very Long Baseline Interferometry (VLBI) this method is used to calibrate the ionosphere. In the absence of dual frequency data, the ionospheric content measured by Faraday rotation, using a signal from a geostationary satellite, is mapped to the VLBI observing direction. The purpose here is to compare the ionospheric delay obtained by these two methods. The principal conclusions are: (1) the correlation between delays obtained by these two methods is weak; (2) in mapping Faraday rotation measurements to the VLBI observing direction, a simple mapping algorithm which accounts only for changes in hour angle and elevation angle is better than a more elaborate algorithm which includes solar and geomagnetic effects; (3) fluctuations in the difference in total electron content as seen by two antennas defining a baseline limit the application of Faraday rotation data to VLBI.
This paper presents an alternative model of slant delay measurements that allows direct computation of the user's slant delay estimate without the intervening use of a vertical delay grid.
We report a methodology for assessing the impact on WAAS posed by a sudden increase in the level of ionospheric disturbance. The methodology is based upon the forming an estimate of the probability P(D) that a WAAS user will confront a sudden increase in the level of ionospheric disturbance following a period of relative calm. By restricting the tabulation of fit residuals to only those fits where the spatial coverage of the fit points is sufficiently good, we have determined a limiting upper bound of P(D) to be 2x10(sup -6).
The Federal Aviation Administration (FAA) is implementing a satellite-based navigation system for aircraft using the Global Positioning System (GPS). Positioning accuracy of a few meters will be achieved by broadcasting corrections to the direct GPS signal. These corrections are derived using the wide-area augmentation system (WAAS), which includes a ground network of at least 24 GPS receivers across the Continental US (CONUS). WAAS will provide real-time total electron content (TEC) measurements that can be mapped to fixed grid points using a real-time mapping algorithm. These TECs will be converted into vertical delay corrections for the GPS L1 frequency and broadcast to users every five minutes via geosynchronous satellite. Users will convert these delays to slant calibrations along their own lines-of-sight (LOS) to GPS satellites. Uncertainties in the delay calibrations will also be broadcast, allowing users to estimate the uncertainty of their position. To maintain user safety without reverting to excessive safety margins an empirical model of user calibration errors has been developed. WAAS performance depends on factors that include geographic location (errors increase near WAAS borders), and ionospheric conditions, such as the enhanced spatial electron density gradients found during ionospheric storms.
The Federal Aviation Administration (FAA) is implementing a satellite-based navigation system for aircraft using the Global Positioning System (GPS).
Time domain measurements, taken between the NAVSTAR 6 Spacecraft Vehicle (SV) and the Vandenberg Global Positioning System (GPS) Monitor Site, by a pseudo random noise receiver, were collected over an extended period of time and analyzed to estimate the long term frequency stability of the NAVSTAR 6 onboard frequency standard, referenced to the Vandenberg MS frequency standard. The technique employed separates the clock offset from the composite signal by first applying corrections for equipment delays, ionospheric delay, tropospheric delay, Earth rotation and the relativistic effect. The data are edited and smoothed using the predicted SV ephemeris to calculate the geometric delay. Then all available passes from each of the four GPS monitor stations, are collected at 1-week intervals and used to calculate the NAVSTAR orbital elements. The procedure is then completed by subtracting the corrections and the geometric delay, using the final orbital elements, from the composite signal, thus leaving the clock offset and random error.
A consider error covariance analysis was performed in order to investigate the orbit-determination performance attainable using two-way (coherent) 8.4-GHz (X-band) Doppler data for two segments of the planned Mars Observer trajectory. The analysis includes the effects of the current level of calibration errors in tropospheric delay, ionospheric delay, and station locations, with particular emphasis placed on assessing the performance of several candidate elevation-dependent data-weighting functions. One weighting function was found that yields good performance for a variety of tracking geometries. This weighting function is simple and robust; it reduces the danger of error that might exist if an analyst had to select one of several different weighting functions that are highly sensitive to the exact choice of parameters and to the tracking geometry. Orbit-determination accuracy improvements that may be obtained through the use of calibration data derived from Global Positioning System (GPS) satellites also were investigated, and can be as much as a factor of three in some components of the spacecraft state vector. Assuming that both station-location errors and troposphere calibration errors are reduced simultaneously, the recommended data-weighting function need not be changed when GPS calibrations are incorporated in the orbit-determination process.
Technique determines ionospheric phase delay on real-time universally applicable basis in terms of electrons per meter squared by coherently modulating two L-band carrier frequencies received from two Global Positioning System satelites. Two pseudorandom number sequences cross-correlated to derive delay time.
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