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.     

Integrated Navigation System and Experiment of a Low-Cost and Low-Accuracy SINS/GPS

When SINS (strap-down inertial navigation system) is combined with GPS, the observability of the course angle is weak. Although the course angle error is improved to some extent through Kalman filtering, the course angle still assumes a divergent trend. This trend is aggravated further when using low-cost and low-accuracy SINS. In order to restrain this trend, a method that uses AHRS to substitute for SINS course angle information is put forward aimed at the hardware component characteristic of the low-cost and low-accuracy SINS including AHRS (attitude and heading reference system) and IMU (inertial measurement unit). Real static and dynamic experiments show that the method can restrain the divergent trend of the navigation system angle effectively, and the positioning accuracy is high.     

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.     

Road Surface Modeling and Representation from Point Cloud Based on Fuzzy Clustering

A scheme for an automatic road surface modeling from a noisy point cloud is presented. The normal vectors of the point cloud are estimated by distance-weighted fitting of local plane. Then, an automati...     

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%.     

Application of Refactoring and Design Pattern in Land Information System Development

The unceasing change problem of land information systems can be resolved through the refactoring and design pattern. To promote the implementation of design pattern and refactoring methods in developin...     

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.