Prediction of High Rate GPS Satellite Orbit Using Artificial Neural Networks

Precise real-time GPS orbit at a high rate is required for a number of applications, including real-time Precise Point Positioning (PPP), long range RTK and weather forecasts. To support these applications, the International GNSS Service (IGS) has developed a precise orbital service. At present, users may take advantage of the predicted part of the IGS ultra-rapid orbit for real-time and near real-time applications. Unfortunately, however the data rate of such precise orbits is usually limited to 15 minutes. In addition, the precision of the predicted part of the IGS ultrarapid orbit is limited to about 10 cm. for the 24-hour predicted part, which may not be sufficient for the above applications, This research proposes algorithms for interpolation and prediction methods that are intended to reduce the effect of such limitations. This research examines the performance of four interpolation methods for IGS precise GPS orbits, nameley Lagrange, Newton Divided Difference, Bernese Polynomial, Cubic Spline and Trigonometric Interpolation. In addition, a comparison between this research and earlier studies were conducted. A new approach that utilizes the residuals between the broadcast and precise ephemeris to generate a high-density precise ephemeris is also introduced in this research. A three-step neural network-based model is then developed in this research to generate a 6-hour predicted orbital arc. First, an initial predicted orbit is generated by extrapolating a concentrated group of previous precise ephemeris for 5 days. GPS observations for 35 globally distributed tracking stations, corresponding to the 24-hour period preceding the predicted part, are then utilized within the Bernese software to further enhance the predicted orbit. FInally, the predicted orbit is refined by implementing a modular - three-layer feed-forward back-propagation neural network. A comparison is made between our predicted orbit and the IGS ultra-rapid orbit to verify the efficiency of the newly developed neural network-based model. It is shown that the newly developed neural network-based model improved the orbit prediction by 47%, 22% and 37% for three randomly selected satellites from Blocks IIA, IIR and IIR-M respectively.

Prediction of High Rate GPS Satellite Orbit Using Artificial Neural Networks

Precise real-time GPS orbit at a high rate is required for a number of applications, including real-time Precise Point Positioning (PPP), long range RTK and weather forecasts. To support these applications, the International GNSS Service (IGS) has developed a precise orbital service. At present, users may take advantage of the predicted part of the IGS ultra-rapid orbit for real-time and near real-time applications. Unfortunately, however the data rate of such precise orbits is usually limited to 15 minutes. In addition, the precision of the predicted part of the IGS ultrarapid orbit is limited to about 10 cm. for the 24-hour predicted part, which may not be sufficient for the above applications, This research proposes algorithms for interpolation and prediction methods that are intended to reduce the effect of such limitations. This research examines the performance of four interpolation methods for IGS precise GPS orbits, nameley Lagrange, Newton Divided Difference, Bernese Polynomial, Cubic Spline and Trigonometric Interpolation. In addition, a comparison between this research and earlier studies were conducted. A new approach that utilizes the residuals between the broadcast and precise ephemeris to generate a high-density precise ephemeris is also introduced in this research. A three-step neural network-based model is then developed in this research to generate a 6-hour predicted orbital arc. First, an initial predicted orbit is generated by extrapolating a concentrated group of previous precise ephemeris for 5 days. GPS observations for 35 globally distributed tracking stations, corresponding to the 24-hour period preceding the predicted part, are then utilized within the Bernese software to further enhance the predicted orbit. FInally, the predicted orbit is refined by implementing a modular - three-layer feed-forward back-propagation neural network. A comparison is made between our predicted orbit and the IGS ultra-rapid orbit to verify the efficiency of the newly developed neural network-based model. It is shown that the newly developed neural network-based model improved the orbit prediction by 47%, 22% and 37% for three randomly selected satellites from Blocks IIA, IIR and IIR-M respectively.

New frequency-dependent trigonometric interpolation functions for the dynamic finite element analysis of thin rectangular plates

The Dynamic Finite Element (DFE) formulation is a superconvergent, semianalytical method used to perform vibration analysis of structural components during the early stages of design. It was presented as an alternative to analytical and numerical methods that exhibit various drawbacks, which limit their applicability during the preliminary design stages. The DFE method, originally developed by the second author, has been exploited heavily to study the modal behaviour of beams in the past. Results from these studies have shown that the DFE method is capable of arriving at highly accurate results with a coarse mesh, thus, making it an ideal choice for preliminary stage modal analysis and design of structural components. However, the DFE method has not yet been extended to study the vibration behaviour of plates. Thus, the aim of this study is to develop a set of frequency-dependent, trigonometric shape functions for a 4-noded, 4-DOF per node element as a basis for developing a DFE method for thin rectangular plates. To this end, the authors exploit a distinct quasi-exact solution to the plate governing equation and this solution is then used to derive the new, trigonometric basis and shape functions, based on which the DFE method would be developed.

New frequency-dependent trigonometric interpolation functions for the dynamic finite element analysis of thin rectangular plates

The Dynamic Finite Element (DFE) formulation is a superconvergent, semianalytical method used to perform vibration analysis of structural components during the early stages of design. It was presented as an alternative to analytical and numerical methods that exhibit various drawbacks, which limit their applicability during the preliminary design stages. The DFE method, originally developed by the second author, has been exploited heavily to study the modal behaviour of beams in the past. Results from these studies have shown that the DFE method is capable of arriving at highly accurate results with a coarse mesh, thus, making it an ideal choice for preliminary stage modal analysis and design of structural components. However, the DFE method has not yet been extended to study the vibration behaviour of plates. Thus, the aim of this study is to develop a set of frequency-dependent, trigonometric shape functions for a 4-noded, 4-DOF per node element as a basis for developing a DFE method for thin rectangular plates. To this end, the authors exploit a distinct quasi-exact solution to the plate governing equation and this solution is then used to derive the new, trigonometric basis and shape functions, based on which the DFE method would be developed.

Mimicking relative continuum measurements by electrode data in two-dimensional electrical impedance tomography

This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode model. The upper bounds for the corresponding approximation errors explicitly depend on the number (and size) of the employed electrodes as well as on the regularity of the continuum current that is mimicked. In particular, if the input current and the object boundary are infinitely smooth, the discrepancy associated with the point electrode model converges to zero faster than any negative power of the number of electrodes. The results are first proven for the unit disk via trigonometric interpolation and quadrature rules, and they are subsequently extended to more general domains with the help of conformal mappings.

Calculation of Light Distribution of a Conventionally Point Light Source in an Arbitrarily Oriented Coordinate System

The article reviews calculation of total light distribution of several light sources (LS), which are differently oriented in space with their locations conventionally 1 being the same. It is proposed that luminous intensity curves (photometric body) of LSs are described in IESNA format (or in the format of tables, which is basically the same). Two methods of solving the problem are proposed. The first one is related to preliminary trigonometric interpolation of luminous intensity curves for each LS performed by means of discrete Fourier transformation (DFT). The second one is based on piecewise-linear interpolation of this curves using Delaunay triangulation. Both methods may be implemented by means of popular mathematic software (such as Wolfram Mathematica or Octave) and their applicability is confirmed experimentally.