Recursive algorithm for fast GNSS orbit fitting

Gaussian elimination is an efficient and numerically stable algorithm for estimating parameters and their precision. However, before estimating the parameters, it is often prudent to perform statistical tests to achieve the best fitting model. We use Gaussian elimination to select the best fitting model among candidate models. A succinct relationship between the weighted sum of squared residuals and the previous one is revealed by a volume formula. For quick parameter estimation and determination of weighted sum of squared residuals, a recursive elimination algorithm is proposed in the context of Gaussian elimination. In order to improve the model selection efficiency, the parameter estimation and the determination of the weighted sum of squared residuals are carried out in parallel using the proposed recursive elimination algorithm in which the improvement at each recursive stage is judged by the Bayesian information criterion. Ultimately, the computational complexity and numerical stability of the recursive elimination proposed are briefly discussed, and a GNSS orbit interpolation example is used to verify the results. It shows that the proposed recursive elimination algorithm inherits the numerical stability of the Gaussian elimination, and this algorithm can be used to examine the gain from the newly introduced parameter, dynamically assess the fitting model, and fix the optimal model efficiently. The optimal fitting model with the lowest information is very close to the real situation verified by checkpoints.     

A new method for specular and diffuse pseudorange multipath error extraction using wavelet analysis

Multipath remains one of the major challenges in Global Navigation Satellite System (GNSS) positioning because it is considered the dominant source of ranging errors, which can be classified into specular and diffuse types. We present a new method using wavelets to extract the pseudorange multipath in the time domain and breaking it down into the two components. The main idea is an analysis-reconstruction approach based on application of both continuous wavelet transform (CWT) and discrete wavelet transform (DWT). The proposed procedure involves the use of L1 code-minus-carrier (CMC) observable where higher-frequency terms are isolated as residuals. CMC residuals are analyzed by applying the CWT, and we propose the scalogram as a technique for discerning time–frequency variations of the multipath signal. Unlike Fourier transform, the potential of the CWT scalogram for examining the non-stationary and multifrequency nature of the multipath is confirmed as it simultaneously allows fine detection and time localization of the most representative frequencies of the signal. This interpretation of the CWT scalogram is relevant when choosing the levels of reconstruction with DWT, allowing accurate time domain extraction of both the specular and diffuse multipath. The performance and robustness of the method and its boundary applicability are assessed. The experiment was carried out using a receiver of Campania GNSS Network. The results are given in which specular multipath error is achieved using DWT level 7 approximation component and diffuse multipath error is achieved using DWT level 6 denoised detail component.     

Impact of different sampling rates on precise point positioning performance using online processing service

In this study, the effect of different sampling rates (i.e. observation recording interval) on the Precise Point Positioning (PPP) solutions in terms of accurac...     

Surface gravitational field and topography changes induced by the Earth’s fluid core motions

Using a Love number formalism, the elastic deformations of the mantle and the mass redistribution gravitational potential within the Earth induced by the fluid pressure acting at the core–mantle boundary (CMB) are computed. This pressure field changes at a decadal time scale and may be estimated from observations of the surface magnetic field and its secular variation. First, using a spherical harmonic expansion, the poloidal and toroidal part of the fluid velocity field at the CMB for the last 40 years is computed, under the hypothesis of tangential geostrophy. Then the associated geostrophic pressure, whose order of magnitude is about 1000 Pa, is computed. The surface topography induced by this pressure field is computed using Love numbers, and is a few millimetres. The mass redistribution gravitational potential induced by these deformations and, in particular, the zonal components of the related surface gravitational potential perturbation (J₂, J₃ and J₄ coefficients), are calculated. Overall perturbations for the J₂ coefficient of about 10^–10, for J₃ of about 10^–11 and for J₄ are found of about 0.3×10^–11. Finally, these theoretical results are compared with recent observations of the decadal variation of J₂ from satellite laser ranging. Results concerning J₂ can be described as follows: first, they are one order of magnitude too small to explain the observed decadal variation of J₂ and, second, they show a significant linear trend over the last 40 years, whose rate of decrease amounts to 7% of the observed value.     

Computerised development control and approval system for City Hall of Kuala Lumpur

This paper will discuss the computerised development control and approval system being developed for the Planning and Development Control Department, City Hall of Kuala Lumpur, with stress on the GIS architecture developed within the system. The prospects and challenges towards implementation of the system are also discussed.     

SDINS/GPS in-flight alignment using GPS carrier phase rate

The alignments of the strapdown inertial navigation system (SDINS) utilizing GPS carrier phase rate measurements is introduced. In this paper, a measurement model of GPS carrier phase rate under two antenna configurations is derived in order to be used for the SDINS alignment process. For in-flight alignment, the performance of the proposed SDINS/GPS integration method is analyzed using the covariance analysis and the overall performance is briefly confirmed by the navigation result of a van test. Furthermore, we find that during in-flight alignment the proposed SDINS/GPS integrated system using GPS carrier phase rate measurements can be implemented in real time because the integer ambiguity problem resulting from carrier phase measurements is avoided.     

An analysis of carrier phase differential kinematic GPS positioning using DynaPos

A series of activities have been carried out at the University of New Brunswick in an effort to evaluate advances in long-range marine kinematic differential positioning. These activities involved processing and analysis of GPS carrier phase kinematic data sets. Some of the data was collected by UNB and some was provided by The XYZs of GPS Inc. Data were collected using Trimble 5700 and Ashtech Z-12 receivers. The data sets were processed using the software DynaPos provided by the The XYZs of GPS Inc. The best results obtained in our analysis indicate an agreement of 5 cm RMS for the horizontal component and 12 cm RMS for the vertical component between two ionospheric-delay free solutions, in baselines varying from 40 to 100 km.     

On the reliability of the VCV Matrix: A case study based on GAMIT and Bernese GPS Software

Commonly, the variance-covariance (VCV) matrix derived from GPS processing software underestimates the magnitude of the error, mainly due to the fact that physical correlations are normally neglected. The GAMIT and Bernese software packages serve the scientific community as important tools for GPS measurement processing and analyzing, especially in precise applications. Therefore, the reliability of the VCV matrices derived by the GAMIT and Bernese packages is of great importance. Formal accuracies derived from both software need to be scaled by applying a scaling factor (SF) that multiplies the software-derived formal errors. However, to the best of our knowledge, no standard approach approved by the GPS community exists. In this report, an analysis is carried out in order to test the reliability and the validity of the VCV matrices in both software, and to provide SFs needed to calculate the realistic accuracies reflecting the actual error levels. The method applied in this study allows deriving SFs for formal accuracies obtained from GAMIT and Bernese. The results attained from the time series of eight days for eight baselines (lengths of 20–415 km) indicate that the overall SF for GAMIT is more than 10 times smaller than for Bernese (1.9 and 23.0, respectively). Although no distance-dependent SF was detected in either case, the session-duration dependence was detected for the Bernese software, while no clear session-duration dependence was observed for the GAMIT. Furthermore, no receiver/antenna dependence could be deduced from the results of this analysis.     

The ellipsoidal corrections to the topographic geoid effects

The topographic effects by Stokes formula are typically considered for a spherical approximation of sea level. For more precise determination of the geoid, sea level is better approximated by an ellipsoid, which justifies the consideration of the ellipsoidal corrections of topographic effects for improved geoid solutions. The aim of this study is to estimate the ellipsoidal effects of the combined topographic correction (direct plus indirect topographic effects) and the downward continuation effect. It is concluded that the ellipsoidal correction to the combined topographic effect on the geoid height is far less than 1 mm. On the contrary, the ellipsoidal correction to the effect of downward continuation of gravity anomaly to sea level may be significant at the 1-cm level in mountainous regions. Nevertheless, if Stokes formula is modified and the integration of gravity anomalies is limited to a cap of a few degrees radius around the computation point, nor this effect is likely to be significant.AcknowledgementsThe author is grateful for constructive remarks by J Ågren and the three reviewers.     

Position and velocity reliability testing in degraded GPS signal environments

Reliability testing, namely receiver autonomous integrity monitoring (RAIM), consists of statistical testing of least-squares residuals of observations, e.g., on an epoch-by-epoch basis aiming towards reliable navigation fault detection and exclusion (FDE). In this paper, classic RAIM and FDE methods are extended with testing of range-rate residuals to find inconsistent velocity solutions in order to contribute to the reliability of the system with special focus on degraded signal environments. Reliability enhancement efforts discussed include a Backward-FDE scheme based on statistical outlier detection and an iteratively reweighted robust estimation technique, a modified Danish method. In addition, measurement weighting assigned to code and Doppler observations is assessed in the paper in order to allow fitting a priori variance models to the estimation processes. The schemes discussed are also suitable in terms of computational convenience for a combined GPS/Galileo system. The objective of this paper is to assess position and velocity reliability testing and enhancement in urban and indoor conditions and to analyze the navigation accuracy conditions with high sensitivity GPS (HSGPS) tests. The results show the necessity of weighted estimation and FDE for reliability enhancement in degraded signal-environment navigation.