3.6
A strategy for accelerating the first convergence
As discussed in Section 3.4, re-convergences can be significantly accelerated by applying iono- spheric delays precisely predicted by users themselves. We can imagine that the convergences, including the first one, can be significantly accelerated if these ionospheric delays are provided for users by a service provider with a precise ionosphere model. Note that this model should generate ionospheric delays at an accuracy of less than a few centimeters, i.e. ≤0.3 TECU for the L1 frequency. This section thus first introduces the advancement of current real-time ionosphere products, and then addresses a strategy for rapid convergences based on interpolated ionospheric delays from a dense network of reference stations.
3.6.1
Real-time ionosphere products
Precise ionosphere imaging in real time is a challenging issue in the Earth ionosphere community (Bust and Mitchell 2008). The ionosphere is characterized by a significant number of ionized neutral atoms, hence leading to a mixture of free electrons and ions. The ionization level is governed by solar extreme ultraviolet radiation and particle precipitation. Moreover, the ionosphere is embedded within the Earth’s magnetic field and hence is constrained by the inter- actions of the ionized particles with the magnetic field. Consequently, ionosphere scintillations, large-scale TEC gradients and irregularities frequently occur, especially in low-latitude regions and during ionosphere storms (Skone 2000). Despite the complexity of the ionosphere physics, the most important quantity among all physical parameters is the electron density (Bust and Mitchell 2008). Ionosphere imaging of the electron density provides snapshots of the global ionosphere structure and its temporal evolution. Ionosphere imaging relates to using integrated measurements of electron density, known as TEC measurements, in order to generate 2-, 3- or 4-dimensional maps of electron density. Such imaging is extremely important because the electron density governs all effects on radio signals. Hence, in the following, current methods for real-time ionosphere imaging and their respective accuracy are briefly introduced.
A Klobuchar model
A straightforward method for the real-time mitigation of ionospheric delays is the Klobuchar model (Klobuchar 1986) which has been included in the GPS broadcast navigation message. The coefficients of this model are daily updated. However, only 50% of TEC can be eliminated by this model, which is far from sufficient for assisting wide-lane or narrow-lane ambiguity resolution.
B Ionosphere grid
An ionosphere grid is a thin shell at a specific height of 350–450 km above the Earth’s surface. This shell is sampled on a regularly spaced grid along latitude and longitude. Vertical TEC at the grid points are estimated using GPS measurements from a network of reference stations. Users then interpolate their required slant TEC based on this grid model with a mapping function (El- Arini et al. 1995). However, an ionosphere grid has two defects (Liu 2003): On the one hand, a specific height for the ionosphere grid is presumed, which is only an approximation of the reality and is not physically true; on the other hand, a grid model is 2-dimensional and hence it cannot depict the vertical profile of the ionosphere structure. The global ionosphere maps by the IGS are grid-based, and currently the accuracy for the rapid products is between 2 and 9 TECU with
a latency of below 24 hours (see http://igscb.jpl.nasa.gov/components/prods.html). WAAS and EGNOS employ regional grids to quantify ionospheric delays, but the real-time accuracy can be up to 55 cm (∼3 TECU) (e.g. Jensen et al. 2007). Due to these poor accuracies, some authors are still trying to improve the ionosphere grid model (e.g. Yuan et al. 2008).
C Ionosphere tomography
An ionosphere tomography outperforms an ionosphere grid by its imaging of the ionosphere’s vertical profile. Hence, an ionosphere tomography is a 3-dimensional model. It is constructed by a set of spherical harmonic functions and empirical orthogonal functions. The spherical harmonic functions describe the horizontal ionospheric characteristics whereas the empirical orthogonal functions depict the vertical ionosphere properties (Liu 2003; Bust and Mitchell 2008). Hern´andez-Pajares et al. (1999) reported that real-time tomography can provide an accuracy of better than 1 TECU for double-difference slant TEC based on a sparse network of up to 1300-kilometer inter-station distances under an active ionosphere condition. However, this conclusion has not been confirmed with extensive tests. Moreover, Liu and Gao (2004) assessed 5-minute TEC predictions over a regional reference network and achieved an accuracy of about 2.8 TECU in the vertical direction.
3.6.2
Accelerating convergences with a dense network
Considering the accuracy level of current real-time ionosphere products, unfortunately, it is still quite difficult to interpolate sufficiently precise ionospheric delays based on a quite sparse reference network at scales of many hundred kilometers. Nonetheless, if a dense network of reference stations at scales of several tens of kilometers is available, ionospheric delays can be estimated at the reference stations and then interpolated for single users to assist rapid convergences. In this case, the first ambiguity-fixed solutions can also be rapidly achieved.
Interpolated ionospheric delays are more reliable than those estimated and predicted by users themselves. As discussed in Section 3.4, the prerequisite for a rapid re-convergence is that the previous solution is correctly ambiguity-fixed. An incorrect ambiguity-fixed solution will fail the subsequent rapid re-convergences. Due to the precisely known positions and the good observation environments at reference stations, the generation of ionospheric delays becomes relatively easier and more reliable than that by users themselves. Normally, this generation is continuous and is independent of the users. Hence, users do not have to worry too much about the quality of interpolated ionospheric delays.
However, the deficiency of interpolated ionospheric delays is also obvious, i.e. a dense network of reference stations have to be used. This augmentation will significantly devalue the most attractive advantage of PPP, i.e. no need of any nearby reference stations. Moreover, even if such dense networks are available, the foremost question is then whether this augmented PPP can outperform the NRTK which has been well established in many areas.
Therefore, accelerating the first convergence to the ambiguity-fixed solution based on a dense network is feasible in theory, but its value in practice should be carefully assessed.
3.7 Summary 51
3.7
Summary
This chapter reviews the up-to-date attempts to achieve rapid convergences in real-time PPP. It is shown that these attempts are not sufficiently effective in speeding up convergences. On the other hand, in order to rapidly re-converge to ambiguity-fixed solutions, this thesis originally develops a novel method in which ionospheric delays estimated at previous ambiguity-fixed epochs are precisely predicted to the succeeding epochs in order to significantly accelerate ambiguity resolution in case of a re-convergence. Finally, a strategy for achieving the first ambiguity-fixed solution is suggested in which a dense network of reference stations is required. Chapter 6 will present empirical results to assess these methods for the rapid convergences to ambiguity-fixed solutions.
Chapter 4
PANDA Software
4.1
Introduction
PANDA (Positioning And Navigation Data Analyst) software was originally developed at Wuhan University in China (Liu and Ge 2003). It is a versatile tool for the scientific analysis of GPS positioning and navigation data, and currently serves as a fundamental platform for scientific studies in China. The University of Nottingham signed an agreement with Wuhan University for a free version of the Unix-based PANDA software package in 2007. This software package is capable of simultaneously processing various types of measurements from GNSS, SLR, KBR (K- Band Ranging) (Kang et al. 2003), star trackers and accelerometers in order to estimate ground station coordinates, ZTDs, ERPs (Earth Rotation Parameters) and orbits for GNSS satellites, LEOs and GEOs (Geosynchronous Earth Orbiters) (Geng et al. 2006; Li et al. 2008; Shi et al. 2006, 2008b).
Since 2003, PANDA software has been contributing to the Chinese GNSS research and applications. For example, it was extensively used in two key National High-Tech Research and Development Programs of China, i.e. Real-Time National PPP Service for Decimeter Positioning Accuracy (Geng et al. 2007b) and Near Real-Time Precise Orbit Determination of LEOs (Geng et al. 2007a). On the Wenchuan earthquake in 2008, the PANDA software generated one of the most excellent 1-Hz position time series with near-field GPS measurements (Shi et al. 2010).
The PANDA software is also used by a number of international renowned research institutes, such as DEOS (Delft–Institute of Earth-Oriented Space Research), NCTU (National Chiao Tung University) and IESSG (Insitute of Engineering Surveying and Space Geodesy). DEOS used PANDA software to determine precise orbits of CHAMP (CHAllenging Minisatellite Payload) and GRACE (GRAvity Climate Experiment) satellites in order to recover the time-varying Earth gravity (Liu et al. 2010). NCTU used PANDA software to determine the precise orbits of COSMIC (Constellation Observing System for Meteorology Ionosphere and Climate) satellites in order to validate their own results which were based on Bernese GPS software 5.0 (Dach et al. 2007; Hwang et al. 2009). IESSG used PANDA software for the research of rapid integer ambiguity resolution at a single receiver, and this thesis is mainly supported by this software (Geng et al. 2009).
This chapter first briefly exhibits the overall structure of PANDA software, and then details my adaptation and development of PANDA software. Note that the algorithm design and program development are also important contributions of this thesis. Finally, two software
Figure 4.1: Brief structure of the PANDA software. The solid arrows denote processing sequences and the dashed arrows denote input/output. The squares represent the data processing modules while others represent the data and results (adapted based on Shi et al. (2008b))
suites, i.e. post-processing PPP and real-time PPP, are schematically introduced.