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With the impact of the Global Navigation Satellite System (GNSS), dual-GNSS constellations are playing an increasingly significant role in positioning, navigation and timing (PNT) applications. Aiming at improving from the existing method, i.e., linearization, of solving the single-point positioning problem under a dual-GNSS, this paper develops a closed-form method for solving PNT problems in the case of six satellites. This method reduces the positioning problem to a simple mathematical problem of finding solutions to a quadratic equation, thereby needing only one receiver clock bias (RCB) as variable. By solving the RCB, the positioning information in three dimensions is obtained by utilizing a linear equation. Compared with the existing method, the closed-form method requires no initial position or iterations. This method thus provides a direct solution to single-point positioning. Further, how to check the uniqueness and the validity of the solutions is also derived. Experimental results verify the validity, applicability and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: The Crustal Movement Observation Network of China (CMONOC) is one of the major scientific infrastructures, mainly using Global Positioning System (GPS) measurements, to monitor crustal deformation in the Chinese mainland. In this paper, decade-long coordinate time series of 26 continuous GPS sites of CMONOC are analyzed for their noise content using maximum likelihood estimation (MLE). We study the noise properties of continuous GPS time series of CMONOC for the unfiltered, filtered solutions and also the common mode signals in terms of power law plus white noise model. In the spatial filtering, we remove for every time series a common mode error that was estimated from a modified stacking of position residuals from other sites within ∼1000km of the selected site. We find that the common mode signal in our network has a combination of spatially correlated flicker noise and a common white noise with large spatial extent. We demonstrate that for the unfiltered solutions of CMONOC continuous GPS sites the main colored noise is a flicker process, with a mean spectral index of ∼1. For the filtered solutions, the main colored noise is a general power law process, indicating that a major number of the filtered regional solutions have a combination of noise sources or local effects. The velocity uncertainties from CMONOC continuous GPS coordinate time series may be underestimated by factors of 8–16 if a pure white noise model is assumed. In addition, using a white plus flicker noise model, the median values of velocity errors for the unfiltered solutions are 0.16 (north), 0.17 (east) and 0.58 (vertical)mm/yr, and the median values for the filtered solutions are 0.09 (north), 0.10 (east) and 0.40 (vertical)mm/yr. [Copyright &y& Elsevier]

Abstract: This paper presents an analysis of the Total Electron Content (TEC) derived from the International GNSS Service receiver (formerly IGS) at Malindi (2.9°S,40.1°E), Kenya for the periods 2004–2006 during the declining phase of solar cycle 23. The diurnal, monthly and seasonal variations of the TEC are compared with TEC from the latest International Reference Ionosphere model (IRI-2007). The GPS–TEC exhibits features such as an equatorial noon time dip, semi-annual variations, Equatorial Ionization Anomaly and day-to-day variability. The lowest GPS–TEC values are observed near the June solstice and September equinox whereas largest values are observed near the March equinox and December solstice. The mean GPS–TEC values show a minimum at 03:00 UT and a peak value at about 10:00 UT. These results are compared with the TEC derived from IRI-2007 using the NeQuick option for the topside electron density (IRI–TEC). Seasonal mean hourly averages show that IRI-2007 model TEC values are too high for all the seasons. The high prediction primarily occur during daytime hours till around midnight hours local time for all the seasons, with the highest percentage deviation in TEC of more 90% seen in September equinox and lowest percentage deviation in TEC of less than 20% seen in March equinox. Unlike the GPS–TEC, the IRI–TEC does not respond to geomagnetic storms and does overestimate TEC during the recovery phase of the storm. While the modeled and observed data do correlate so well, we note that IRI-2007 model is strongly overestimating the equatorial ion fountain effect during the descending phase of solar cycle, and this could be the reason for the very high TEC estimations. [Copyright &y& Elsevier]

Abstract: Diurnal, seasonal and latitudinal variations of Vertical Total Electron Content (VTEC) over the equatorial region of the African continent and a comparison with IRI-2007 derived TEC (IRI-TEC), using all three options (namely; NeQuick, IRI01-corr and IRI-2001), are presented in this paper. The variability and comparison are presented for 2009, a year of low solar activity, using data from thirteen Global Positioning System (GPS) receivers. VTEC values were grouped into four seasons namely March Equinox (February, March, April), June Solstice (May, June, July), September Equinox (August, September, October), and December Solstice (November, December, January). VTEC generally increases from 06h00 LT and reaches its maximum value at approximately 15h00–17h00 LT during all seasons and at all locations. The NeQuick and IRI01-corr options of the IRI model predict reasonably well the observed diurnal and seasonal variation patterns of VTEC values. However, the IRI-2001 option gave a relatively poor prediction when compared with the other options. The post-midnight and post-sunset deviations between modeled and observed VTEC could arise because NmF2 or the shape of the electron density profile, or both, are not well predicted by the model; hence some improvements are still required in order to obtain improved predictions of TEC over the equatorial region of the Africa sector. [Copyright &y& Elsevier]

Abstract: Since the United States government discontinued Selective Availability (SA) on 1 May 2000, ionospheric effects have been responsible for the largest errors in GPS systems. The standard Differential GPS (DGPS) method is incapable of completely eliminating the ionospheric error. This paper describes a new approach to determine the differential ionospheric error between geographically distributed receiver stations. The ray paths of GPS signals were simulated using a modified Jones 3D ray tracing programme that includes the effect of the geomagnetic field. A Nelder–Mead optimisation algorithm was embedded in the program to precisely determine the satellite-to-station path. A realistic ionospheric model is essential for accurate ray tracing results and for estimates of differential error that are accurate on sub-centimetre scales. Here, the ionospheric model used in the ray tracing programme was developed by fitting realistic ionosphere profiles with a number of exponential functions. Results were compared to the theoretical approach. Results show that the differential delay is about 1–5cm at low elevation angles for a short baseline of 10km, as reported in other literature. This delay is often neglected in DGPS application. The differential delay also shows a pattern similar to that predicted by the Klobuchar model. The method proposed here can be used to improve future GPS applications. [ABSTRACT FROM AUTHOR]

Abstract: Different algorithms have been proposed for the modeling of the ionosphere. The most frequently used method is based on the spherical harmonic functions achieving successful results for global modeling but not for the local and regional applications due to the bounded spherical harmonic representation. Irregular data distribution and data gaps cause also difficulties in the global modeling of the ionosphere. In this paper we propose an efficient algorithm with Multivariate Adaptive Regression Splines (MARS) to represent a new non-parametric approach for regional spatio-temporal mapping of the ionospheric electron density using ground-based GPS observations. MARS can handle very large data sets of observations and is an adaptive and flexible method, which can be applied to both linear and non-linear problems. The basis functions are directly obtained from the observations and have space partitioning property resulting in an adaptive model. This property helps to avoid numerical problems and computational inefficiency caused by the number of coefficients, which has to be increased to detect the local variations of the ionosphere. Since the fitting procedure is additive it does not require gridding and is able to process large amounts of data with large gaps. Additionally the model complexity can be controlled by the user via limiting the maximal number of coefficients and the order of products of the basis functions. In this study the MARS algorithm is applied to real data sets over Europe for regional ionosphere modeling. The results are compared with the results of Bernese GPS Software over the same region. [Copyright &y& Elsevier]

Abstract: The dispersive nature of the ionosphere makes it possible to measure its total electron content (TEC). Thus Global Positioning System, which uses dual-frequency radio signals, is an ideal system to measure TEC. When data from an ionosonde situated in polar region was observed, the height of an approximated thin shell of electrons (shell height) used in GPS studies was seen not to be fixed but rather changing with time. Here we introduce a new method in which we included the varying shell heights derived from the ionosonde to map the slant total electron content from GPS to obtain a more precise vertical total electron content of the ionosphere contrary to some previous methods which used fixed shell heights. In this paper we also compared the ionosonde derived TEC with the GPS derived vertical TEC (vTEC) values. These GPS vTEC values were obtained from GPS slant TEC (sTEC) measurements using both fixed shell height and varying shell heights (from ionosonde measurements). For the polar regions, the varying shell height approach produced better results than the fixed shell height and compared to exponential function, Chapman function seems to be a better function to model the topside ionosphere. [Copyright &y& Elsevier]