Zenith Path Delay Research Articles

Calibration of atmospheric effects on SAR interferograms by GPS and local atmosphere models: first results

A comparison between the zenith path delay (ZPD), obtained from GPS measurements, and the expected delay, derived from models used to compensate tropospheric effects on SAR interferograms, is made. The results of the two methods are comparable, though the available data set is not large enough for a complete statistical validation of the methods. The results of this preliminary study suggest a possible integration of GPS-based ZPD data with cheap and standard meteorological data, since the estimated atmospheric component proved to be similar. Furthermore, the impact on volcanology of the effects measured by GPS, and in particular on the determination of the depth of the volcanic sources, is discussed.

Atmospheric modeling in GPS data analysis for high accuracy positioning

In this paper we review the atmospheric modeling methods used in GPS data analysis. Due to the strong spatial inhomogeneity and temporal variability of atmospheric constituents, especially water vapor, accurate modeling of path delay in GPS signals is necessary for high-accuracy positioning (e.g., tectonics and sea-level change) and meteorological applications (climatology and weather forecasting). State-of-the-art path delay modeling consists primarily in parameter estimation. In this strategy, zenith path delays are estimated during the GPS data reduction. External correction is another common strategy, in which the wet path delay is measured by a remote sensing instrument (usually a microwave radiometer). However, the latter is not as generalized, and is rather used for specific field campaigns or local long term observations. Both strategies have led to quite similar coordinate accuracies (using daily GPS observations), at the level of 1–2 mm in the horizontal component and 5–10 mm in the vertical component. The external correction strategy is capable of achieving even higher accuracy under specific conditions. Recent models, including gradients in the parameter estimation strategy have only led to marginal improvement. A major limitation of both strategies seems to be the use of mapping functions for the hydrostatic path delay correction. With the parameter estimation strategy, this limitation applies also to wet path delay correction. The use of numerical weather prediction and analysis models, and/or spaceborne sounding instruments, is suggested for replacing mapping functions and possibly for performing directly the hydrostatic correction. New instruments, such as Raman lidars, might also be used for a more accurate external wet path delay correction in the presence of strong atmospheric inhomogeneity. Further work is still needed for achieving measurements of absolute water vapor distribution in the atmosphere for this purpose.

IGS ultra rapid products for (near-) real-time applications

Since GPS week 1052, 5 March 2000, the IGS is producing a new combined orbit called the IGS Ultra rapid product, IGU. The combined IGS Ultra rapid products are being made available twice every day, at 3:00 and 15:00 UTC, with a delay of 3 hours after the end of the included data interval, and are based on solutions from up to seven different IGS Analysis Centers. The main reason for the generation of the Ultra rapid products are the requirements, in both timeliness and accuracy, for near-real-time atmospheric monitoring, e.g., weather predictions. Each ultra rapid orbit file covers 48 hours. The first 24 hours of the orbit are based on actual GPS observations (real orbit), the second 24 hours are extrapolated (predicted orbit). Like the IGS Predicted (IGP) orbits, the Ultra rapid orbits are available for real-time usage. However, the quality of the Ultra rapid orbits should be significantly better because the average age of the predictions is reduced from 36 hours (IGP) to 9 hours (IGU). At the 2000 IGS Analysis Center workshop, held at the USNO in Washington, D.C., it was decided that the IGU products were of sufficient quality to replace the IGP products. This change took effect on November 5 with the start of GPS week 1087.We will demonstrate that the accuracy of the IGS Ultra rapid orbits is at the 30 cm level, in a weighted RMS sense, which is significantly better than the 70 cm accuracy of the IGS Predicted orbits. We will also demonstrate that with this orbit quality it is possible to derive tropospheric zenith path delay estimates with a precision of 7 mm, which corresponds to approximately 1 mm precipitable water vapor. This level of precision is only achieved when “bad” satellite predictions are (automatically) detected and handled.

GPS precise point positioning using IGS orbit products

The International GPS Service (IGS) has provided GPS orbit products to the scientific community with increased precision and timeliness. Many users interested in geodetic positioning have adopted the IGS precise orbits to achieve cm-level accuracy and ensure long-term reference frame stability. Currently, a differential positioning approach that requires the combination of observations from a minimum of two GPS receivers, with at least one occupying a station with known coordinates is commonly used. The user position can then be estimated relative to one or multiple reference stations using carrier phase observations and a baseline or network estimation approach. Double-differencing observations is a popular way to cancel out common GPS satellite and receiver clock errors. Baseline or network processing is effective in connecting the user position to the coordinates of the reference stations while the precise orbit virtually eliminates the errors introduced by the GPS space segment. This mode of processing has proven to be very effective and has received widespread acceptance. One drawback is that it requires that simultaneous observations be made at reference stations, with the practical constraint that involves. The following details a post-processing approach that uses un-differenced dual-frequency pseudorange and carrier phase observations along with IGS precise orbit products, for stand-alone precise geodetic point positioning (static or kinematic) with cm precision. This is possible if one takes advantage of the satellite clock estimates that are available with the satellite coordinates in the IGS precise orbit products and models systematic effects that cause cm-variations in the satellite to user range. This paper will describe the approach, summarize the adjustment procedure and specify the earth and space based models that must be implemented to achieve cm-level positioning in static mode. Furthermore, station tropospheric zenith path delays with cm-precision and GPS receiver clock estimates precise to 100 picoseconds are also obtained using this approach.

Influence of the ocean loading effect on GPS derived precipitable water vapor

For meteorology the precipitable water vapor becomes a more and more important product in the data analysis of the Global Positioning System (GPS). It is derived from the wet part of the tropospheric refraction obtained as zenith path delay in the data analysis. However, the estimates of the zenith path delay and of the station height are strongly correlated. The ocean loading effect has a periodic influence on station heights with major frequencies in the diurnal and semidiurnal band and with amplitudes up to several centimeters. If one ignores this effect it affects the estimates of the zenith path delay and thus the precipitable water vapor. This will be demonstrated by some examples.

Structure analysis of path delay variations in the neutralatmosphere

Abstract An analysis of the temporal zenith path delay variations in the Earth's neutral atmosphere is presented for three sites with different climates. Using the radiosonde data the temporal structure functions for total path delay and separately for its hydrostatic and the wet components are calculated. The relation and the cross-correlation between the hydrostatic and the wet components are presented. An estimation of spatial structure function at the saturation level is given.

Comparison of Kalman filter estimates of zenith atmospheric path delays using the Global Positioning System and very long baseline interferometry

Kalman filter estimates of zenith nondispersive atmospheric path delays at Westford, Massachusetts, Fort Davis, Texas, and Mojave, California, were obtained from independent analyses of data collected during January and February 1988 using the Global Positioning System (GPS) and very long baseline interferometry (VLBI). The apparent accuracy of the path delays is inferred by examining the estimates and covariances from both sets of data. The ability of the geodetic data to resolve zenith path delay fluctuations is determined by comparing further the GPS Kalman filter estimates with corresponding wet path delays derived from water vapor radiometric (WVR) data available at Mojave over two 8‐hour data spans within the comparison period. GPS and VLBI zenith path delay estimates agree well within one standard deviation formal uncertainties (from 10–20 mm for GPS and 3–15 mm for VLBI) in four out of the five possible comparisons, with maximum differences of 5 and 21 mm over 8‐ to 12‐hour data spans. For one comparison, the maximum difference between GPS and VLBI is 50 ± 20 mm and clearly shows an unexplained systematic difference which is probably related to poor elevation angle coverage in the VLBI data at the time, GPS fiducial network sensitivity, and poor azimuthal coverage. The root‐mean‐square differences between GPS estimates of the total path delays and WVR measurements added to the hydrostatic delay component determined from surface barometric pressure data are between 9 and 15 mm, however, with biases of 10–15 mm.

Stochastic estimation of tropospheric path delays in global positioning system geodetic measurements

Water vapor radiometric (WVR) and surface meteorological (SM) measurements taken during three Global Positioning System (GPS) geodetic experiments are used to calculate process noise levels for random walk and first-order Gauss-Markov temporal models of tropospheric path delays. Entire wet and combined wet and dry zenith delays at each network site then are estimated simultaneously with the geodetic parameters without prior calibration. The path delays and corresponding baseline estimates are compared to those obtained with calibrated data and stochastic residual delays. In this manner, the marginal utility of a priori tropospheric calibration is assessed given the ability to estimate the path delays directly using only theGPS data. Estimation of total zenith path delays with appropriate random walk or Gauss-Markov models yields baseline repeatabilities of a few parts in 108. This level of geodetic precision, and accuracy as suggested by analyses on collocated baselines estimated independently by very long baseline interferometry, is comparable to or better than that obtained after path delay calibration usingWVR and/orSM measurements. Results suggest thatGPS data alone have sufficient strength to resolve centimeter-level zenith path delay fluctuations over periods of a few minutes.