the wavelength which is much smaller than the baseband signal resolu- tion (i.e., for a legacy Global Positioning System (GPS) L1 C/A signal, the wavelength is approximately 19 cm while the baseband signal resolu- tion is 300 m). Unfortunately, exploiting this phase information implies solving a much more complicated problem, mainly because the carrier phase measurement is ambiguous (i.e., unknown number of cycles inside the baseband signal resolution), then being such ambiguity resolution the bottleneck [2, Chap 21, 23]. To this end two different schemes can be advocated. The first approach to resolve phase ambiguities is to turn to the class of so-called differential techniques, where the relative position to a geo-referenced GNSS station is obtained. Real-Time Kinematics (RTK) [2, Chap 26] is an example of such a technique. Nevertheless, this kind of solution requires the use of a reference station with a communication link between the two receivers, and is only valid for short ranges from the base-station to ensure that the two receivers observe the same propagation errors. Another approach is the family of Precise Point Positioning (PPP) techniques [2, Chap 25], which allow to get rid of the reference station but to reach decimetric precision in turn need i) precise carrier phase mea- surements, which is not the case in harsh propagation conditions, ii) high accuracy satellite orbits, clock and propagation (ionospheric and tropo- spheric) error corrections, and/or iii) multi-frequency/multi-system archi- tectures to compensate the ionospheric effects. These kind of techniques received much attention in the literature (see  and references therein) and are still under research to reach the maturity needed for their broad real-time applicability. The price to be paid is the need to access a net- work broadcasting real-time precise corrections (i.e., International GNSS Service (IGS) products), and a long convergence time of tens of minutes. As stated in , these drawbacks limit the use of PPP for many practical real-time applications.
For RTK positioning, the new CRB and the proposed analysis provided even more interesting results. In fact, it was shown that the SNR threshold region is driven by the time-delay precision and not the phase one. Using fast codes, we may have up to 10 dB of gain in the threshold, which in turn implies the validity of such RTK solutions in a wider range of applications. Also, notice that this threshold can be used to determine for which operation regions it is worth to exploit phase measurements, because above the threshold the RTK fixed solution rapidly converges to the float (i.e. real) one. These results hold whatever the signal carrier frequency. To summarise, if a new GNSS signal was to be designed for precise positioning, the recommendation would be to use a carrier frequency as high as possible and a signal modulation with the largest signal bandwidth, the former driving the asymptotic RTK performance, and the latter the threshold region.
The European Space Agency (ESA) PolarGap airborne gravimetry campaign was carried out from December 7, 2015 to January 19, 2016 to cover the gravity gap over central Antarctica. A Twin- Otter aircraft was used with three antennas named AIR2, 0158 and SPAN installed on the aircraft to collect the GNSS data. Here, we choose the data collected on day 19 December 2015 for analysis, which covers about 10.5 h from 10:30 to 21:00 (UTC). Most of the flight tracks were done from the South Pole along the meridian to the edge of the region and then back. A dedicated reference station SP2X was installed at the South Pole, i.e., in the middle of the region. Such a track pattern is beneficial for traditional relative kinematic positioning. However, the observation data of SP2X on day December 19 is not available, and we use the data from another reference station called FD83 which was installed in a tented field camp (Figure 7). As the observed satellites on these kinematic receivers are at low elevation angles (less than 60°), a cut-off angle of 7° is applied to fully use all satellites. Since AIR2 observes GR data, 0158 and SPAN observe GPS data, only GPS data is processed for the three antennas in DD, PPP and POP mode for validation. For DD processing only one reference
Robust statistics provides an alternative framework for the definition of navigation methods resilient against multiple erroneous observations. Originally suggested for general data analysis in the early 1970s [ 11 – 13 ], robust estimators have experienced substantial research growth and their use has extended to manifold fields: signal processing [ 14 – 16 ], biomedical [ 17 , 18 ], power systems [ 19 ], etc. Within the scope of GNSS, robust methods have been successfully applied to enhance receivers with anti-jamming capabilities based on the so-called Robust Interference Mitigation [ 20 – 26 ]. The application of robust estimators to compute position, velocity, and time (PVT) solutions in satellite-based navigation has also appealed numerous authors, both for memory-less SPP [ 27 – 30 ] and for recursive estimation [ 31 – 33 ]. In that PVT context, the performance of robust techniques has been demonstrated on both simulated and real data, and this paper attempts to characterize those estimators in terms of quantities relevant to the robust statistics literature. This paper focuses on the SPP problem, thus purposely does not consider precise point positioning (PPP) or real-time kinematic (RTK) approaches, which typically involve more complex estimates and the application of different methodologies [ 34 – 36 ] to the ones investigated here.
As the position is determined by a simple projection in a 3D space, the linearity of the process preserves the nature of the distribution. The position is also impacted with a 3D white Gaussian effect due to the selective availability. The dispersion of the points along the 3 axis coupled with a rela- tively low number of samples gives these fluctuations of the probability density functions. One should use more sam- ples in order to smooth this effect. Nevertheless, it is still possible to explore these results. Obviously, as in the previ- ous subsection, both curves of probability density functions are superimposed see Fig. 18 to Fig. 20. The x axis of these graphics doesn’t permit to distinguish a shift (too big scale) but by looking at Tab. 12 there is a not negligible difference between biases along each axis.
In this work we establish a systematic approach to design optimum chip pulse shapes for DS-CDMA systems which are absolutely band-limited, whose energy is mainly concentrated in one chip duration, and that minimize the Cramer-Rao lower bound for the time-delay. The proposed methodology makes it possible to formulate the problem of designing optimum chip pulse shapes in terms of achieving a trade-off between synchronization accuracy and acquisition and tracking robustness as an optimization problem. Additionally, spectral separation to non-interoperable signals in the same band is considered. This methodology is based on the prolate spheroidal wave functions (PSWF), which enable to transform the primal variational problem into the dual, tractable parametric optimization problem. This work shows the interesting capabilities of the presented signal design approach for DS-CDMA systems. This methodology is further developed according to the needs of Galileo-2 signal design.
Figure 5 shows the average convergence time of b1, b2 and b3 single-frequency PPP with different schemes on all days over all the test stations. Table 5 summarizes the RMS errors of the single-frequency PPP in multi-constellation combinations, which is calculated from the convergence epoch to the end epoch of a day. The GLONASS-only and Beidou-only solutions clearly perform worse than other solutions, which is caused by the strong correlation between IFBs and slant ionospheric delays in GLONASS and the current distribution and orbit determination accuracy of the Beidou constellation . The results also indicate that the integration of the multi-GNSS can improve the single-frequency PPP performance in terms of convergence time and positioning accuracy. As it is shown in Figure 5 and Table 5, the GRAPHIC and UC approaches have much the same performance for the equivalence of two solutions. By introducing external ionosphere information, the average convergence time of PPP solutions is reduced. For instance, the improvement in convergence time of BIM-, NTCM- and GIM-constrained quad-constellation b2 single-frequency PPP is 15.2%, 24.8% and 28.6%, respectively, compared with the UC solution. The positioning accuracy of the quad-constellation single-frequency PPP can reach 1-3 cm horizontally and 8–9 cm vertically. The improvement in the positioning accuracy of the ionosphere-constrained PPP, for giving higher weighting after convergence, was not significant. The positioning accuracy of the GIM-constrained PPP solutions is the best and NTCM-constrained PPP solutions perform better than the BIM- constrained solutions in the E and U components.
1. In applying a K\SRWKHWLFRGHGXFWLYHVWUDWHJ\the mere fact of a co-occurrence is itself regarded as evidence or counter-evidence for a certain hypothesis. If the researcher pro- ceeds in this way the techniques for searching for co-occurring codes provided by Aquad, NUD • IST or HyperResearch have a similar function to hypothesis testing in statistical analysis. The primary purpose is not to provide the researcher with text seg- ments but to use the information about the co-occurrence of codes in a given document as a basis for decision making. As in statistical significance testing, the decision making process is strictly rule governed and hence algorithmic. So it parallels very much the kind of hypothesis testing which is regularly applied in quantitative content analysis. How- ever, there are certain methodological requirements and limitations to the use of such a hypothesis tester for qualitative hypothesis examination, which are usually taken into account by content analysts. These requirements relate mainly to the nature of codes employed, since the codes must represent Boolean facts if an automatic hypothesis tester is to produce meaningful results. Furthermore, the reliability of the codes used is of utmost importance. But these requirements diametrically oppose the analysis strategy usually applied in qualitative research. In an interpretive analysis strategy codes tend to represent general topics of interest and not precisely defined Boolean facts. Furthermore, hypotheses are not logically stated propositions about the presence, absence or relation- ship of certain facts, but sometimes vague ideas about the relations between two or more concepts. A hypothetico-deductive strategy where the mere fact of the co-occurrence of certain codes in a given text passage is regarded as evidence or counterevidence can thus rarely be regarded as an adequate strategy of hypothesis examination in interpretive research. There are further reasons why the application of
target the presence of single faults . More recently, the Advanced RAIM is based on solution separation test statistics in order to be able to detect the presence of multiple faults or hypothesis . These algorithms are accompanied of overbounded pseudorange error models, where the different error components are upper bounded in order to protect the worst-case signal in space error. In the literature, we can find several attempts to adapt the methodology from (A)RAIM to different land-based applications [3, 4]. The first problem of implementing ARAIM algorithms for urban navigation is that it is still a challenge in practice to find realistic bounds for the effect of the local threats. Another problem with the use of solution separation fault detector is that a position solution must be computed for each possible hypothesis. Whereas in aviation due to the low risk of having a satellite fault, the number of hypothesis are normally considered only for 1 or 2 simultaneous satellite faults, in urban scenarios any measurement could be in principle corrupted simultaneously. This means that a very large number of hypotheses would be required to be tested with the associated computer requirement in order to guarantee a real-time operation.
The average ambiguity float and fixed single-epoch posi- tioning precision for the east, north, and up component is given in Table 2 for different systems. The ambiguity-fixed precision values are derived from the conditional coordi- nate covariance matrices and do not reflect whether it is possible to reliably resolve the ambiguities. For the GLO- NASS only cases, only epochs with six or more visible satel- lites are included. As mentioned above, the F least precise LAMBDA-transformed ambiguities are removed for GLO- NASS. The single-system GLONASS results are worse com- pared to single-system GPS, which can be attributed to fewer visible satellites. However, sub-centimeter-level horizontal positioning results should also be possible already with sin- gle-frequency GLONASS data. The gain of combined sys- tem GPS + Galileo and GPS + GLONASS compared to GPS only is on a similar level, in particular when considering the lower number of GLONASS satellites. Even for the already very strong four-system GPS + Galileo + BeiDou-2 + QZSS case, adding GLONASS data still improves the precision.
The ability to derive closed-form solution for the Doppler frequencies depends mainly on the adequate selection of an appropriate coordinate system. In the case of V2V communication, the prolate spheroidal coordinate system (PSCS) represents a suitable coordinate system for two center problems as shown in . The PSCS is a three-dimensional, curvilinear, orthogonal coordinate system as shown in Fig. 1. The origin of the coordinate system is by definition always in the middle between Tx an Rx and co-moves with the movement of both. The relationship between Cartesian and prolate spheroidal coordinates is given by 
In the literature, relay-assisted systems with NC can be divided into two categories: the physical layer network coding (PNC) – and the bit-level network coding (BNC) , . Generally, PNC needs two phases for each trans- mission cycle, and the time and phase synchronization are precisely required. Additionally, transmit power also needs to be well controlled. Otherwise PNC performance will be dramatically degraded. In the study of PNC, Zhang et al.  proved that with poor time and phase synchronization, power penalty of PNC is 1.57dB and 3.4dB, respectively. The instantaneous channel state information (CSI) is also needed in PNC, which consumes considerable signaling over- head. These disadvantages restrict the employment of PNC. Compared to PNC, BNC is a simple and efficient method. It was initially proposed in the butterfly network, and the main purpose is on data compression. Prior work found that BNC can efficiently reduce the transmission time and enhance the system throughput performance . In the study of , , BNC was applied to exploit the broadcast nature of the wireless channel and reduce the energy consumption. By following a similar analytical procedure, we focus on the EE performance of BNC protocol in this paper.
ANASTASIA (Airborne New and Advanced Satellite techniques and Technologies in A System Integrated Approach) was an integrated project funded by the European Community’s Sixth Framework Programme (DG research); see www.anastasia-fp6.org. The core of ANASTASIA research was to provide on-board Communication, Navigation and Surveillance (CNS) solutions to cope with the expected increase in air traffic by 2020. A receiver mock-up has been designed under the Thales expertise for three Galileo bands (L1, E5a, E5b), which is compliant to the MOPS current standards . A DME measurement campaign was carried out and the receiver was tested up to its limits regarding interferences, multi-paths and low level signals.
Fig. 1 represents the conceptual design of the testbed. A computer generates in phase and quadrature (IQ) waveform data and forwards them to a Software Defined Radio (SDR) device where the simulated signal is frequency modulated to AIS Class-A, Class-B or both channels in parallel. A signal attenuator is used to match testing signal power needs and to avoid saturation of the AIS receiver under test. The output of the receiver is then connected to the same computer to perform real-time comparison and data evaluation. During a run of the testbed the binary data used to generate waveforms is written to file. The output of the receiver is packet-wise encapsulated AIVDM messages. A message-by-message comparison be- tween the input bytes of the waveform generator and the output data of the receiver provides the test result data set for the per- formance evaluation. As the smallest AIS packet is 256 bits long, it is also the packet size for test runs used. The received data stream is in real-time compared with the generated data and the results are plotted as graphs while the test is running.
Within global navigation satellite systems (GNSS), such as the Global Positioning System (GPS) or the future Eu- ropean satellite navigation system Galileo, the user position is determined based upon the code division multiplex access (CDMA) navigation signals received from different satellites using the time-of-arrival (TOA) method . A major error source for positioning comes from multipath, the reception of additional signal replica due to reﬂections caused by the receiver environment. The reception of multipath introduces a bias into the time delay estimate of the delay lock loop (DLL) of a conventional navigation receiver, which ﬁnally leads to a bias in the receiver’s position estimate.
The reference coordinates for the processed datasets are the IGS SINEX positions. The processing is performed in un-combined mode, meaning that linear combinations of measurements are not formed and that the raw measurements on each frequency are processed. Additional corrections such as the Earth rotation, phase windup, relativistic effects, solid earth tides, etc. are performed following the IERS conventions [ 34 ]. The IGS14 ANTEX corrections are used to correct for satellite antenna errors for GPS, Galileo, and BeiDou on all the used frequencies. However, since GPS L5 antenna corrections are not available in the IGS ANTEX file, the L2 corrections are applied for the L5 signals. Similarly, ANTEX corrections are not available for the BeiDou-3 B1 and B2a signals. B1-2 and B2b corrections are applied in that case. Due to the existence of Inter-System Biases (ISB), one receiver clock parameter is used for each constellation. All receiver clocks are estimated as white noise and are independent of one another. As discussed in Section 3.2 , BeiDou-2 and BeiDou-3 have been processed as if they were different constellations at the user-side. This distinction means that each BeiDou generation has a different receiver clock. Therefore, in total, four receiver clocks are estimated: GPS, Galileo, BeiDou-2, and BeiDou-3. Although Galileo satellites E14 and E18 are on eccentric orbits, they were deemed functional and included in the processing.
Abstract: Benefits from the modernized US Global Positioning System (GPS), the revitalized Russian GLObal NAvigation Satellite System (GLONASS), and the newly-developed Chinese BeiDou Navigation Satellite System (BDS) and European Galileo, multi-constellation Global Navigation Satellite System (GNSS) has emerged as a powerful tool not only in positioning, navigation, and timing (PNT), but also in remote sensing of the atmosphere and ionosphere. Both precise positioning and the derivation of atmospheric parameters can benefit from multi-GNSS observations. In this contribution, extensive evaluations are conducted with multi-GNSS datasets collected from 134 globally-distributed ground stations of the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) network in July 2016. The datasets are processed in six different constellation combinations, i.e., GPS-, GLONASS-, BDS-only, GPS + GLONASS, GPS + BDS, and GPS + GLONASS + BDS + Galileo precise point positioning (PPP). Tropospheric gradients are estimated with eight different temporal resolutions, from 1 h to 24 h, to investigate the impact of estimating high-resolution gradients on position estimates. The standard deviation (STD) is used as an indicator of positioning repeatability. The results show that estimating tropospheric gradients with high temporal resolution can achieve better positioningperformance than the traditional strategy in which tropospheric gradients are estimated on a daily basis. Moreover, the impact of estimating tropospheric gradients with different temporal resolutions at various elevation cutoff angles (from 3 ◦ to 20 ◦ ) is investigated. It can be observed that with increasing elevation cutoff angles, the improvement in positioning repeatability is decreased.
The aim of this research is to support the design a system that generates integrity signals suitable for GNSS application. The conceptual design and key mathematical models were recently developed by the Italian Air Force Experimental Flight Test Centre (CSV-RSV) [1, 2]. Such a system, would be able to provide steering information to the pilot, allowing for real-time and continuous integrity monitoring, avoidance of safety/mission-critical flight conditions and fast recovery of the required navigation performance in case of GNSS data losses.
Ein anderes Kriterium zur Einteilung der Atmosphäre ist für GNSS-Anwendungen von ebenso großer Bedeutung und bezieht sich auf den Grad der Ionisierung. Die Begriffe Ionisierung oder Ionisation beschreiben das Aufspalten von Molekülen in Ionen und freie Elektronen. Die Gasmoleküle der Erdatmosphäre werden durch das Eintreffen von kosmischer Strahlung ionisiert. In den Atmosphärenbereichen oberhalb der Ozonschicht ist die Ionisation dauerhafter als unterhalb der Ozonschicht, da diese die kosmische Strahlung absorbiert. So entstehen eine stark ionisierte Schicht oberhalb der Ozonschicht, die Ionosphäre, und eine elektrisch neutrale Schicht unterhalb der Ozonschicht, die Neutrosphäre. Die Neutrosphäre beinhaltet Tropo- und Stratosphäre sowie Teile der Mesosphäre. Dabei ist die Troposphäre bezüglich GNSS-Auswertungen der entscheidende Bestandteil der Neutrosphäre. Daher werden die Begriffe Tropo- und Neutrosphäre in der GNSS- Literatur oft synonym verwendet. Häufig wird der Begriff troposphärische Laufzeitverzögerung gebraucht, obwohl eigentlich die Laufzeitverzögerung im gesamten elektrisch neutralen Bereich der Atmosphäre gemeint ist. Um dieses Problem zu umgehen, führt [Seeber, 2003, S. 48] als weiteres Kriterium zur Unterteilung der Atmosphäre die Signalausbreitung (Propagation) ein und bezeichnet den gesamten unterhalb der Ozonschicht liegenden Bereich als Troposphäre und alles darüber liegende als Ionosphäre. In dieser Arbeit wird im Bezug auf Laufzeitverzögerungen im elektrisch neutralen Bereich der Atmosphäre der korrekte Begriff Neutrosphäre verwendet. Weil Iono- und Neutrosphäre GNSS-Signale in unterschiedlicher Art und Weise beeinflussen, werden sie in den nächsten Abschnitten auch im Hinblick auf die Handhabung in einer GNSS-Auswertung näher betrachtet.