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.     

Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition

We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm for space-geodetic applications: firstly, we investigate how convergence can be accelerated by means of both subspace and block-diagonal preconditioning. The efficiency of the latter dominates if the design matrix exhibits block-dominant structure. Secondly, we address Tikhonov-Phillips regularization in general. Thirdly, we demonstrate an effective implementation of the algorithm in a high-performance computing environment. In this context, an important issue is to avoid the twofold computation of the design matrix in each iteration. The computational platform is a 64-processor shared-memory supercomputer. The runtime results prove the successful parallelization of the LSQR solver. The numerical examples are chosen in view of the forthcoming satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer). The closed-loop scenario covers 1 month of simulated data with 5 s sampling. We focus exclusively on the analysis of radial components of satellite accelerations and gravity gradients. Our extensions to the basic algorithm enable the method to be competitive with well-established inversion strategies in satellite geodesy, such as conjugate gradient methods or the brute-force approach. In its current development stage, the LSQR method appears ready to deal with real-data applications.     

The ionospheric eclipse factor method (IEFM) and its application to determining the ionospheric delay for GPS

A new method for modeling the ionospheric delay using global positioning system (GPS) data is proposed, called the ionospheric eclipse factor method (IEFM). It is based on establishing a concept referred to as the ionospheric eclipse factor (IEF) λ of the ionospheric pierce point (IPP) and the IEF’s influence factor (IFF) . The IEF can be used to make a relatively precise distinction between ionospheric daytime and nighttime, whereas the IFF is advantageous for describing the IEF’s variations with day, month, season and year, associated with seasonal variations of total electron content (TEC) of the ionosphere. By combining λ and with the local time t of IPP, the IEFM has the ability to precisely distinguish between ionospheric daytime and nighttime, as well as efficiently combine them during different seasons or months over a year at the IPP. The IEFM-based ionospheric delay estimates are validated by combining an absolute positioning mode with several ionospheric delay correction models or algorithms, using GPS data at an international Global Navigation Satellite System (GNSS) service (IGS) station (WTZR). Our results indicate that the IEFM may further improve ionospheric delay modeling using GPS data.     

Prediction of UT1–UTC,LOD and AAM χ<Subscript>3</Subscript> by combination of least-squares and multivariate stochastic methods

This article presents the application of a multivariate prediction technique for predicting universal time (UT1–UTC), length of day (LOD) and the axial component of atmospheric angular momentum (AAM χ ₃). The multivariate predictions of LOD and UT1–UTC are generated by means of the combination of (1) least-squares (LS) extrapolation of models for annual, semiannual, 18.6-year, 9.3-year oscillations and for the linear trend, and (2) multivariate autoregressive (MAR) stochastic prediction of LS residuals (LS + MAR). The MAR technique enables the use of the AAM χ ₃ time-series as the explanatory variable for the computation of LOD or UT1–UTC predictions. In order to evaluate the performance of this approach, two other prediction schemes are also applied: (1) LS extrapolation, (2) combination of LS extrapolation and univariate autoregressive (AR) prediction of LS residuals (LS + AR). The multivariate predictions of AAM χ ₃ data, however, are computed as a combination of the extrapolation of the LS model for annual and semiannual oscillations and the LS + MAR. The AAM χ ₃ predictions are also compared with LS extrapolation and LS + AR prediction. It is shown that the predictions of LOD and UT1–UTC based on LS + MAR taking into account the axial component of AAM are more accurate than the predictions of LOD and UT1–UTC based on LS extrapolation or on LS + AR. In particular, the UT1–UTC predictions based on LS + MAR during El Niño/La Niña events exhibit considerably smaller prediction errors than those calculated by means of LS or LS + AR. The AAM χ ₃ time-series is predicted using LS + MAR with higher accuracy than applying LS extrapolation itself in the case of medium-term predictions (up to 100 days in the future). However, the predictions of AAM χ ₃ reveal the best accuracy for LS + AR.     

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.

Using GPS multipath to measure soil moisture fluctuations: initial results

Measurements of soil moisture are important for studies of climate and weather forecasting, flood prediction, and aquifer recharge studies. Although soil moisture measurement networks exist, most are sparsely distributed and lack standardized instrumentation. Measurements of soil moisture from satellites have extremely large spatial footprints (40–60 km). A methodology is described here that uses existing networks of continuously-operating GPS receivers to measure soil moisture fluctuations. In this technique, incoming signals are reflected off and attenuated by the ground before reception by the GPS receiver. These multipath reflections directly affect signal-to-noise ratio (SNR) data routinely collected by GPS receivers, creating amplitude variations that are a function of ground reflectivity and therefore soil moisture content. After describing this technique, multipath reflection amplitudes at a GPS site in Tashkent, Uzbekistan are compared to estimates of soil moisture from the Noah land surface model. Although the GPS multipath amplitudes and the land surface model are uncalibrated, over the 70-day period studied, they both rise sharply following each rainfall event and slowly decrease over a period of ∼10 days.     

Low multipath antennas for GNSS-based attitude determination systems applied to high-altitude platforms

High-altitude platforms (HAPs) are a flexible and attractive technology for providing innovative wireless services. These aerial platforms can be successfully employed for mobile or broadband communications and for disaster monitoring or response. However, one of the open issues is whether HAP stations can provide reliable services without temporal outages owing to stratospheric winds that can cause positional and attitude instabilities thus affecting the communication system operation. To counteract this issue, one possible solution is to use reconfigurable antennas whose pointing direction can be adjusted depending on the platform spatial orientation. However, this would require real-time three-axial attitude data. As a possible solution, this paper will review the potential of GNSS-based attitude determination systems with reference to HAP stations. In particular, it will be shown how the use of a particular class of low multipath and lightweight antennas can provide a high degree of accuracy without altering the avionic ballast.     

An approach to aid INS using time-differenced GPS carrier phase (TDCP) measurements

This paper presents a simple and effective approach that incorporates single-frequency, L1 time-differenced GPS carrier phase (TDCP) measurements without the need of ambiguity resolution techniques and the complexity to accommodate the delayed-state terms. Static trial results are included to illustrate the stochastic characteristics and effectiveness of the TDCP measurements in controlling position error growth. The formulation of the TDCP observation model is also described in a 17-state tightly-coupled GPS/INS iterative, extended Kalman filter (IEKF) approach. Preliminary land vehicle trial results are also presented to illustrate the effectiveness of the TDCP which provides sub-meter positional accuracies when operating for more than 10 min.     

GPS signal acquisition using the repeatability of successive code phase measurements

This paper introduces a new method for GPS signal acquisition, which is based on the repeatability of successive code phase measurements and the M-of-N search algorithm. The performance of the proposed method in terms of probability of signal detection is similar to that of traditional methods, except that the calculation of the probability of detection does not rely on the noise distribution or the Carrier-to-Noise ratio (C/N₀). The code phase repeatability-based method is presented along with equations for probability of detection and probability of false detection. If the distribution of the noise is known, it also provides an estimate of the C/N₀. The proposed method is illustrated for coherent and non-coherent acquisition and C/N₀ estimation.