Bringing GPS into harsh environments for fully automated deformation monitoring

Engineering projects that require deformation monitoring frequently utilize geodetic sensors to measure displacements of target points located in the deformation zone. In situations where control stations and targets are separated by a kilometer or more, GPS can offer higher precision position updates at more frequent intervals than can normally be achieved using total station technology. For large-scale deformation projects requiring the highest precision, it is therefore advisable to use a combination of the two sensors. In response to the need for high precision, continuous GPS position updates in harsh deformation monitoring environments, a software has been developed that employs triple-differenced carrier-phase measurements in a delayed-state Kalman filter. Two data sets were analyzed to test the capabilities of the software. In the first test, a GPS antenna was displaced using a translation stage to mimic slow deformation. In the second test, data collected at a large open pit mine were processed. It was shown that the delayed-state Kalman filter developed could detect millimeter-level displacements of a GPS antenna. The actual precision attained depends upon the amount of process noise infused at each epoch to accommodate the antenna displacements. Higher process noise values result in quicker detection times, but at the same time increase the noise in the solutions. A slow, 25 mm displacement was detected within 30 min of the full displacement with sigma values in E, N and U of ±10 mm or better. The same displacement could also be detected in less than 5 h with sigma values in E, N and U of ±5 mm or better. The software works best for detecting long period deformations (e.g., 20 mm per day or less) for which sigma values of 1–2 mm are attained in all three solution components. It was also shown that the triple-differenced carrier-phase observation can be used to significantly reduce the effects of residual tropospheric delay that would normally plague double-differenced observations in harsh GPS environments.

Geodetic intersection on the ellipsoid

Through each of two known points on the ellipsoid a geodesic is passing in a known azimuth. We solve the problem of intersection of the two geodesics. The solution for the latitude is obtained as a closed formula for the sphere plus a small correction, of the order of the eccentricity of the ellipsoid, which is determined by numerical integration. The solution is iterative. Once the latitude is obtained, the longitude is determined without iteration.     

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.