Applications of Lodrigues Matrix in 3D Coordinate Transformation

Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: ① the traditional rotation angles θ , φ ,ψ are substituted with a , b, c which are three re-spective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.     

Comparison of Two Fading Filters anc Adaptively Robust Filter

Two kinds of fading filters and their principles are introduced. An adaptive robust filter is given with corresponding principle. The basic abilities of the fading filters and adaptively robust filter in controlling the influences of the kinematic model errors are analyzed. A practical example is given. The results of the fading filter and adaptively robust filter are compared and analyzed.     

Affine distortion of small GPS networks with large height differences

GPS is a promising tool for real-time monitoring of deformations of slopes or large structures. However, remaining systematic effects in GPS phase observations after double differencing and application of a priori models affect the resulting coordinates. They complicate the proper separation of the actual deformations from pseudo-deformations induced by the systematic effects. This paper shows that for small monitoring networks (baseline lengths <5 km) only affine distortions of the network geometry are generated by the remaining distance dependent systematic effects, e.g. unmodelled tropospheric and ionospheric propagation effects, or satellite orbit errors. Hence, a generic correction model is given by a three-dimensional affine transformation involving a maximum of 12 transformation parameters. For the determination of these parameters, four high quality GPS stations are necessary which are not affected by the actual deformations to be monitored. Based on the analysis of network geometries of synthetic GPS networks with large height differences and considering the physics of the GPS observations it is shown, however, that less than 12 parameters are sufficient for the computation of the corrections. The proposed 8 parameter model was applied to the GPS monitoring network of the Gradenbach landslide. For this small network with large height differences, it was shown that the distortions can be reduced by about 75%.     

Modeling errors in upward continuation for INS gravity compensation

Accurate upward continuation of gravity anomalies supports future precision, free-inertial navigation systems, since the latter cannot by themselves sense the gravitational field and thus require appropriate gravity compensation. This compensation is in the form of horizontal gravity components. An analysis of the model errors in upward continuation using derivatives of the standard Pizzetti integral solution (spherical approximation) shows that discretization of the data and truncation of the integral are the major sources of error in the predicted horizontal components of the gravity disturbance. The irregular shape of the data boundary, even the relatively rough topography of a simulated mountainous region, has only secondary effect, except when the data resolution is very high (small discretization error). Other errors due to spherical approximation are even less important. The analysis excluded all measurement errors in the gravity anomaly data in order to quantify just the model errors. Based on a consistent gravity field/topographic surface simulation, upward continuation errors in the derivatives of the Pizzetti integral to mean altitudes of about 3,000 and 1,500 m above the mean surface ranged from less than 1 mGal (standard deviation) to less than 2 mGal (standard deviation), respectively, in the case of 2 arcmin data resolution. Least-squares collocation performs better than this, but may require significantly greater computational resources.     

Small-world characteristics on transportation networks: a perspective from network autocorrelation

Studies on small-world networks have received intensive interdisciplinary attention during the past several years. It is well-known among researchers that a small-world network is often characterized by high connectivity and clustering, but so far there exist few effective approaches to evaluate small-world properties, especially for spatial networks. This paper proposes a method to examine the small-world properties of spatial networks from the perspective of network autocorrelation. Two network autocorrelation statistics, Moran’s I and Getis–Ord’s G, are used to monitor the structural properties of networks in a process of “rewiring” networks from a regular to a random network. We discovered that Moran’s I and Getis–Ord’s G tend to converge and have relatively low values when properties of small-world networks emerge. Three transportation networks at the national, metropolitan, and intra-city levels are analyzed using this approach. It is found that spatial networks at these three scales possess small-world properties when the correlation lag distances reach certain thresholds, implying that the manifestation of small-world phenomena result from the interplay between the network structure and the dynamics taking place on the network.      

Correcting superconducting gravity time-series using rainfall modelling at the Vienna and Membach stations and application to Earth tide analysis

We demonstrate the possibility to improve the signal-to-noise ratio of superconducting gravity time-series by correcting for local hydrological effects. Short-term atmospheric events associated with heavy rain induce step-like gravity signals that deteriorate the frequency spectrum estimates. Based on 4D modeling constrained by high temporal resolution rain gauge data, rainfall admittances for the Vienna and Membach superconducting gravity stations are calculated. This allows routine correction for Newtonian rain water effects, which reduces the standard deviation of residuals after tidal parameter adjustment by 10%. It also improves the correction of steps of instrumental origin when they coincide with step-like water mass signals.     

Hyperspectral Radiometry to Quantify the Grades of Iron Ores of Noamundi and Joda Mines,Eastern India

This paper present the results of a preliminary study to assess the potential of the visible, NIR and SWIR energy of the EMR in differentiating iron ores of different grades in a rapid manner using hyperspectral radiometry. Using different iron ore samples from Noamundi and Joda mines, Jharkhand and Orissa, states of India, certain spectro-radiometric measurements and geochemical analysis were carried out and the results have been presented. It was observed that the primary spectral characteristics of these iron ores lie in the 850 to 900 nm and 650–750 nm regions. The spectral parameters for each curve used for studying the iron ores are: (i) the slopes of the spectral curve in 685–725 nm region; (ii) position of the peak with respect to wavelength in 730–750 nm region and (iii) radius of curvature of the absorption trough in the 850–900 nm region. Comparison of these spectral parameters and the geochemistry of the samples indicates that the position of the peak of the curve in 730–750 nm region shifts towards longer wavelength with increasing iron oxide content, while the slope of the curvature in the 685–725 nm region has a strong negative correlation with the iron oxide content of the samples. Similarly, a strong negative correlation is observed between the radius of curvature of the 850–900 nm absorption trough and the iron oxide content. Such strong correlations indicate that hyperspectral radiometry in the visible and NIR regions can give a better estimate and quantification of the grades of iron ores. This study has demonstrated that generation of empirical models using hyperspectral radiometric techniques is helpful to quantify the grade of iron ores with limited geochemical analysis.     

TAZ-level variation in work trip mode choice between 1990 and 2000 and the presence of rail transit

Rail transit continues to be a popular alternative for cities as a tool for alleviating automobile congestion and for redeveloping areas into transit and pedestrian-friendly environments. Ideally, rail transit will draw trips away from cars, but the quantitative work that tests this notion has often been either case studies of neighborhoods, in which conclusions are tough to generalize, or citywide comparisons where important spatial variation is lost in aggregation. This study seeks to narrow this gap in the research by using multivariate analysis of covariance to isolate the effect of covariates and cities on changes in work trip mode choice at the traffic analysis zone (TAZ) level for nine cities between 1990 and 2000. The results suggest differences by city in the change at the TAZ level of the proportion of people driving alone and taking transit. Increases in transit usage were associated with cities that built rail transit, while increases in automobile commuting and decreases in transit usage were associated with cities that did not.     

Analytical methods for error propagation in planar space–time prisms

The space–time prism demarcates all locations in space–time that a mobile object or person can occupy during an episode of potential or unobserved movement. The prism is central to time geography as a measure of potential mobility and to mobile object databases as a measure of location possibilities given sampling error. This paper develops an analytical approach to assessing error propagation in space–time prisms and prism–prism intersections. We analyze the geometry of the prisms to derive a core set of geometric problems involving the intersection of circles and ellipses. Analytical error propagation techniques such as the Taylor linearization method based on the first-order partial derivatives are not available since explicit functions describing the intersections and their derivatives are unwieldy. However, since we have implicit functions describing prism geometry, we modify this approach using an implicit function theorem that provides the required first-order partials without the explicit expressions. We describe the general method as well as details for the two spatial dimensions case and provide example calculations.