Comparison of 4D tomographic mapping versus thin-shell approximation for ionospheric delay corrections for single-frequency GPS receivers over North America

The majority of navigation satellite receivers operate on a single frequency. They compensate for the ionospheric delay using either an ionospheric model which typically only corrects for 50% of the delay or a thin-shell map of the ionosphere. A 4D tomographic imaging technique is used to map the free electron density over the full-height of the ionosphere above North America during autumn 2003. The navigation solutions computed using correction based upon the thin-shell and the full-height maps are compared in this paper. The maps are used to calculate the excess propagation delay on the L1 frequency experienced by GPS receivers at selected locations across North America. The excess delay is applied to correct the single-frequency pseudorange observations at each location, and the improvements to the resulting positioning are calculated. It is shown that the thin-shell and full-height maps perform almost as well as a dual-frequency carrier-smoothed benchmark and for most receivers better than the unfiltered dual-frequency benchmark. The full-height corrections perform well and are considerably better than thin-shell corrections under extreme storm conditions.     

Approximating covariance matrices estimated in multivariate models by estimated auto- and cross-covariances

Quantities like tropospheric zenith delays or station coordinates are repeatedly measured at permanent VLBI or GPS stations so that time series for the quantities at each station are obtained. The covariances of these quantities can be estimated in a multivariate linear model. The covariances are needed for computing uncertainties of results derived from these quantities. The covariance matrix for many permanent stations becomes large, the need for simplifying it may therefore arise under the condition that the uncertainties of derived results still agree. This is accomplished by assuming that the different time series of a quantity like the station height for each permanent station can be combined to obtain one time series. The covariance matrix then follows from the estimates of the auto- and cross-covariance functions of the combined time series. A further approximation is found, if compactly supported covariance functions are fitted to an estimated autocovariance function in order to obtain a covariance matrix which is representative of different kinds of measurements. The simplification of a covariance matrix estimated in a multivariate model is investigated here for the coordinates of points of a grid measured repeatedly by a laserscanner. The approximations are checked by determining the uncertainty of the sum of distances to the points of the grid. To obtain a realistic value for this uncertainty, the covariances of the measured coordinates have to be considered. Three different setups of measurements are analyzed and a covariance matrix is found which is representative for all three setups. Covariance matrices for the measurements of laserscanners can therefore be determined in advance without estimating them for each application.     

Safety factor nomograms for homogeneous earth dams less than ten meters high

Homogeneous earth dams that are waterproofed with geomembranes are a suitable option for storing water and other sorts of liquids, like leachates from landfills. Such dams do not require complicated engineering technical calculations, their cost is usually low and they are not difficult to construct. To ensure the geotechnical safety of the dam, the slopes of the embankment must be correctly designed and constructed. This paper provides a set of nomograms which allow the user to get the safety factor of the slopes immediately. In some cases, it is only necessary to know previously the material classification according to the Unified Soil Classifications System. From this information it can be determined whether the material is appropriate or not. If the material classification is not available, geotechnical data of the material used in the construction of the embankment are needed. Examples of the application of nomograms are presented. Secondly, the paper includes a set of equations to calculate quickly the safety factor of a slope of earth upper than 7.5 m height.     

External atmospheric corrections in geodetic very-long-baseline interferometry

Three methods to correct for the atmospheric propagation delay in very-long-baseline interferometry (VLBI) measurements were investigated. In the analysis, the NASA R&D experiments from January 1993 to June 1995 were used. The methods were compared in correcting for the excess propagation delay due to water vapour, the “wet” delay, at one of the sites, the Onsala Space Observatory on the west coast of Sweden. The three methods were: (1) estimating the wet delay using the VLBI data themselves; (2) inferring the wet delay from water vapour radiometer (WVR) data, and (3) using independent estimates based on data from the global positioning system (GPS). Optimum elevation cutoff angles were 22^∘ and 26^∘ when using WVR and GPS data, respectively. The results were found to be similar in terms of reproducibility of the estimated baseline lengths. The shortest baselines tend to benefit from external measurements, whereas the lack of improvement in the longer baselines may be partly due to the large amount of data thrown away when removing observations at low elevation angles. Over a 2 week period of intensive measurements, the two methods using external data showed an overall improvement, for all baseline lengths, compared to the first method. This indicates that there are long-term systematic errors in the wet delay data estimated using WVR and GPS data. Received: 27 October 1998 / Accepted: 20 May 1999     

A new approach to GPS ambiguity decorrelation

Ambiguity decorrelation is a useful technique for rapid integer ambiguity fixing. It plays an important role in the least-squares ambiguity decorrelation adjustment (Lambda) method. An approach to multi-dimension ambiguity decorrelation is proposed by the introduction of a new concept: united ambiguity decorrelation. It is found that united ambiguity decorrelation can provide a rapid and effective route to ambiguity decorrelation. An approach to united ambiguity decorrelation, the HL process, is described in detail. The HL process performs very well in high-dimension ambiguity decorrelation tests. Received: 9 March 1998 / Accepted: 1 June 1999     

Tectonic evolution of early precambrian south indian shield (rocks) using remotely sensed data

The interpretation of satellite imagery of part of South India falling South of 15 degree North latitude shows that the regional anticlines, synclines, domes and basins of the Precambrian group of metamorphites are aligned in three major hill ranges/domains such as Chitra-durga domain in the north, the Mangalore-Ootacamund-Bangalore domain in the centre and the Cochin-Cape Comorin-Madurai-Chittoor domain in the south. These hills are crescent shaped with their axes of elongation oriented in NNW-SSE direction. The lineaments with ENE-WSW, NE-SW/WNW-ESE and NNW-SSE azimuthal frequencies respectively exhibit extensional, shear and release geometries. Such deformational fabric shows that the tectonic evolution of South India was controlled by two major compressive forces, the first one aligned in N-S direction and the second in ENE-WSW direction.     

The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation

The GPS double difference carrier phase measurements are ambiguous by an unknown integer number of cycles. High precision relative GPS positioning based on short observational timespan data, is possible, when reliable estimates of the integer double difference ambiguities can be determined in an efficient manner. In this contribution a new method is introduced that enables very fast integer least-squares estimation of the ambiguities. The method makes use of an ambiguity transformation that allows one to reformulate the original ambiguity estimation problem as a new problem that is much easier to solve. The transformation aims at decorrelating the least-squares ambiguities and is based on an integer approximation of the conditional least-squares transformation. This least-squares ambiguity decorrelation approach, flattens the typical discontinuity in the GPS-spectrum of ambiguity conditional variances and returns new ambiguities that show a dramatic improvement in correlation and precision. As a result, the search for the transformed integer least-squares ambiguities can be performed in a highly efficient manner.