scholarly journals A Numeric-Symbolic Solution of GNSS Phase Ambiguity

2020 ◽  
Author(s):  
Béla Paláncz ◽  
Lajos Völgyesi
Keyword(s):  
Global Navigation Satellite Systems ◽  
Mixed Integer ◽  
Phase Ambiguity ◽  
Satellite Systems ◽  
Weighting Matrix ◽  
The Third ◽  
Integer Problem ◽  
Geometric Dilution Of Precision ◽  
Global Navigation Satellite ◽  
Quadratic Mixed Integer Programming

Solution of the Global Navigation Satellite Systems (GNSS) phase ambiguity is considered as a global quadratic mixed integer programming task, which can be transformed into a pure integer problem with a given digit of accuracy. In this paper, three alter-native algorithms are suggested. Two of them are based on local and global linearization via McCormic Envelopes, respectively. These algorithms can be effective in case of simple configuration and relatively modest number of satellites. The third method is a locally nonlinear, iterative algorithm handling the problem as {-1, 0, 1} programming and also lets compute the next best integer solution easily. However, it should keep in mind that the algorithm is a heuristic one, which does not guarantee to find the global integer optimum always exactly. The procedure is very powerful utilizing the ability of the numeric-symbolic abilities of a computer algebraic system, like Wolfram Mathematica and it is properly fast for minimum 4 satellites with normal configuration, which means the Geometric Dilution of Precision (GDOP) should be between 1 and 8. Wolfram Alpha and Wolfram Clouds Apps give possibility to run the suggested code even via cell phones. All of these algorithms are illustrated with numerical examples. The result of the third one was successfully compared with the LAMBDA method, in case of ten satellites sending signals on two carrier frequencies (L1 and L2) with weighting matrix used to weight the GNSS observation and computed as the inverse of the corresponding covariance matrix.

GNSS Guidance for All Phases of Flight: Practical Results

2001 ◽  
Vol 54 (1) ◽  
pp. 1-13
Author(s):  
S. J. Leighton ◽  
A. E. McGregor ◽  
D. Lowe ◽  
A. Wolfe ◽  
A. A. Macaulay
Keyword(s):  
Service Providers ◽  
Low Cost ◽  
Air Traffic ◽  
Global Navigation Satellite Systems ◽  
European Symposium ◽  
Navigation Satellite ◽  
Satellite Systems ◽  
The Third ◽  
Potential Benefits ◽  
Global Navigation Satellite

This, and the following three papers, were first presented at GNSS 2000, the Third European Symposium on Global Navigation Satellite Systems held in Edinburgh, Scotland from 1st to 4th May 2000.GNSS, or more specifically, Satellite Based Augmentation System (SBAS), guidance provides the prospect of a low-cost means for aircraft to become equipped to fly area navigation (RNAV) operations. The implementation of such RNAV operations within UK airspace offers potential benefits to both the airline operators and the Air Traffic Service Providers (ATSPs).

scholarly journals Statistical models to provide meaningful information to GNSS users in the presence of ionospheric scintillation

GPS Solutions ◽  
2021 ◽  
Vol 25 (2) ◽  
Author(s):  
S. Vadakke Veettil ◽  
M. Aquino
Keyword(s):  
Statistical Models ◽  
Mean Squared Error ◽  
Global Navigation Satellite Systems ◽  
Ionospheric Scintillation ◽  
Phase Measurements ◽  
Satellite Systems ◽  
Positioning Errors ◽  
3D Positioning ◽  
Geometric Dilution Of Precision ◽  
Global Navigation Satellite

AbstractIonospheric scintillation is one of the most challenging problems in Global Navigation Satellite Systems (GNSS) positioning and navigation. Scintillation occurrence can not only lead to an increase in the probability of losing the GNSS signal lock but also reduce the precision of the pseudorange and carrier phase measurements, thus leading to positioning accuracy degradation. Statistical models developed to estimate the probability of loss of lock and Geometric Dilution of Precision normalized 3D positioning errors as a function of scintillation levels are presented. The models were developed following the statistical approach of nonlinear regression on data recorded by Ionospheric Scintillation Monitoring Receivers operational at high and low latitudes. The validation of the probability of loss of lock models indicated average correlation coefficient values above 0.7 and average Root Mean Squared Error (RMSE) values below 0.35. The validation of the positioning error models indicated average RMSE values below 10 cm. The good performance of the developed models indicates that these can provide GNSS users with information on the satellite loss of lock probability and the error in the 3D position under scintillation.

Estimability in Rank-Defect Mixed-Integer Models: Theory and Applications

2020 ◽  
Author(s):  
Peter Teunissen
Keyword(s):  
Network Models ◽  
Global Navigation Satellite Systems ◽  
Mixed Integer ◽  
Research Centre ◽  
Navigation Satellite ◽  
Satellite Systems ◽  
Estimable Functions ◽  
Rank Defect ◽  
Global Navigation ◽  
Global Navigation Satellite

<p><strong>G1.1 Session: Recent Developments in Geodetic Theory</strong></p><p><strong> </strong></p><p><strong>Estimability in Rank-Defect Mixed-Integer Models: Theory and Applications</strong></p><p><strong> </strong></p><p>PJG Teunissen<sup>1,2</sup></p><p><sup>1</sup>GNSS Research Centre, Curtin University, Perth, Australia</p><p><sup>2</sup>Geoscience and Remote Sensing, Delft University of Technology, The Netherlands</p><p>Email: [email protected]; [email protected]</p><p><strong> </strong></p><p>Although estimability is one of the foundational concepts of todays’ estimation theory, we show that the current concept of estimability is not adequately equipped to cover the estimation requirements of mixed-integer models, for instance like those of interferometric models, cellular base transceiver network models or the carrier-phase based models of Global Navigation Satellite Systems (GNSSs). We therefore need to generalize the estimability concept to that of integer-estimability. Next to being integer and estimable in the classical sense, functions of integer parameters then also need to guarantee that their integerness corresponds with integer values of the parameters the function is taken of. This is particularly crucial in the context of integer ambiguity resolution. Would this condition not be met, then the integer fixing of integer functions that are not integer-estimable implies that one can fix the undifferenced integer ambiguities to non-integer values and thus force the model to inconsistent and wrong constraints.</p><p>In this paper we present a generalized concept of estimability and one that now also is applicable to mixed-integer models. We thereby provide the operationally verifiable necessary and sufficient conditions that a function of integer parameters needs to satisfy in order to be integer-estimable. As one of the conditions we have that estimable functions become integer-estimable if they can be unimodulair transformed to canonical form. Next to the conditions, we also show how to create integer-estimable functions and how a given design matrix can be expressed in them. We then show how these results are to be applied to interferometric models, cellular base transceiver network models and FDMA GNSS models.</p><p> </p><p><strong>Keywords: </strong>Estimability, S-system theory, Mixed-integer Models, Integer-Estimability, Admissible Ambiguity Transformation, Interferometry, Global Navigation Satellite Systems (GNSSs)</p><p> </p>

Hydrogeophysical Survey of Groundwater Development at Okada Community Ovia North – East L.G.A. Edo State

2018 ◽  
Vol 2 (1) ◽  
pp. 39-45
Author(s):  
M. O. Ehigiator
Keyword(s):  
Global Navigation Satellite Systems ◽  
Geophysical Investigation ◽  
Satellite Systems ◽  
North East ◽  
Long Time ◽  
Electrical Sounding ◽  
Edo State ◽  
Global Navigation Satellite ◽  
Water Problems ◽  
Aquifer Unit

Geophysical investigation was conducted at Okada community in ovia North Local Govertment area of Edo state to determine the prospect of aquifer zone. The Petrozenith PZ-02 Terrameter, one of the Electrical Resistivity Equipment was used to conduct a Vertical Electrical Sounding (VES) in the study area. The Garmin Etrex 10 Global Navigation satellite systems (GNSS) was used to acquire Geodetic coordinates of point where VES observations were made. This research was carried out as a pre-drilling Hydro-geophysical survey conducted for the purpose of surveying and studying the proposed water borehole site at Okada Community that has suffered acute water problems for a very long time. There have been series of boreholes drilled in the studied area but all are dry wells. This survey was conducted to investigate the subsurface complexity of the sites in respect of lithology and to recommend the total drill depth based on the prospective aquifer unit so identified. Result of interpretation suggests that the area is underlain with substantive aquiferous formation but at a depth not exceeding 121.60 m (398.95 ft), which is the lower aquifer unit. The value of elevation at point of observation referenced to mean sea level is 94 m.

scholarly journals Forty-three years of absolute gravity observations of the Fennoscandian postglacial rebound in Finland

2021 ◽  
Vol 95 (2) ◽  
Author(s):  
Mirjam Bilker-Koivula ◽  
Jaakko Mäkinen ◽  
Hannu Ruotsalainen ◽  
Jyri Näränen ◽  
Timo Saari
Keyword(s):  
Gravity Data ◽  
Gravity Change ◽  
Global Navigation Satellite Systems ◽  
Absolute Gravity ◽  
Data Sets ◽  
Postglacial Rebound ◽  
Land Uplift ◽  
Satellite Systems ◽  
Gravity Measurements ◽  
Global Navigation Satellite

AbstractPostglacial rebound in Fennoscandia causes striking trends in gravity measurements of the area. We present time series of absolute gravity data collected between 1976 and 2019 on 12 stations in Finland with different types of instruments. First, we determine the trends at each station and analyse the effect of the instrument types. We estimate, for example, an offset of 6.8 μgal for the JILAg-5 instrument with respect to the FG5-type instruments. Applying the offsets in the trend analysis strengthens the trends being in good agreement with the NKG2016LU_gdot model of gravity change. Trends of seven stations were found robust and were used to analyse the stabilization of the trends in time and to determine the relationship between gravity change rates and land uplift rates as measured with global navigation satellite systems (GNSS) as well as from the NKG2016LU_abs land uplift model. Trends calculated from combined and offset-corrected measurements of JILAg-5- and FG5-type instruments stabilized in 15 to 20 years and at some stations even faster. The trends of FG5-type instrument data alone stabilized generally within 10 years. The ratio between gravity change rates and vertical rates from different data sets yields values between − 0.206 ± 0.017 and − 0.227 ± 0.024 µGal/mm and axis intercept values between 0.248 ± 0.089 and 0.335 ± 0.136 µGal/yr. These values are larger than previous estimates for Fennoscandia.

scholarly journals Injury prevention in Super-G alpine ski racing through course design

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matthias Gilgien ◽  
Philip Crivelli ◽  
Josef Kröll ◽  
Live S. Luteberget ◽  
Erich Müller ◽  
...  
Keyword(s):  
Ground Reaction Force ◽  
Course Design ◽  
Reaction Force ◽  
Global Navigation Satellite Systems ◽  
World Cup ◽  
Satellite Systems ◽  
Turn Radius ◽  
Energy Dissipated ◽  
Global Navigation Satellite ◽  
High Level

AbstractIn Super-G alpine ski racing mean speed is nearly as high as in Downhill. Hence, the energy dissipated in typical impact accidents is similar. However, unlike Downhill, on Super-G courses no training runs are performed. Accordingly, speed control through course design is a challenging but important task to ensure safety in Super-G. In four male World Cup alpine Super-G races, terrain shape, course setting and the mechanics of a high-level athlete skiing the course were measured with differential global navigation satellite systems (dGNSS). The effects of course setting on skier mechanics were analysed using a linear mixed effects model. To reduce speed by 0.5 m/s throughout a turn, the gate offset needs to be increased by + 51%. This change simultaneously leads to a decrease in minimal turn radius (− 19%), an increase in impulse (+ 27%) and an increase in maximal ground reaction force (+ 6%). In contrast, the same reduction in speed can also be achieved by a − 13% change in vertical gate distance, which also leads to a small reduction in minimal turn radius (− 4%) impulse (− 2%), and no change in maximal ground reaction force; i.e. fewer adverse side effects in terms of safety. It appears that shortening the vertical gate distance is a better and safer way to reduce speed in Super-G than increasing the gate offset.

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