Satellite navigation is critical in signal-degraded environments where signals are corrupted and GNSS systems do not guarantee an accurate and continuous positioning. In particular measurements in urban scenario are strongly affected by gross errors, degrading navigation solution; hence a quality check on the measurements, defined as RAIM, is important. Classical RAIM techniques work properly in case of single outlier but have to be modified to take into account the simultaneous presence of multiple outliers. This work is focused on the implementation of random sample consensus (RANSAC) algorithm, developed for computer vision tasks, in the GNSS context. This method is capable of detecting multiple satellite failures; it calculates position solutions based on subsets of four satellites and compares them with the pseudoranges of all the satellites not contributing to the solution. In this work, a modification to the original RANSAC method is proposed and an analysis of its performance is conducted, processing data collected in a static test. 1. Introduction GNSS (global navigation satellite systems) are worldwide and all weather navigation systems are able to provide three-dimensional position, velocity, and time synchronization to UTC (coordinated universal time) scale. The multiconstellation based on GPS-GLONASS is the standard for most receivers, from survey ones to smartphones, and it is able to ensure the estimation of the user location by using the pseudorange observable in single point, with an accuracy of about 10 meters in good visibility conditions [1]. The main disadvantage of GNSS is the need of having a good satellites visibility; for this reason, the environments characterized by strong signal degradation, such as urban areas, are particularly critical for satellite navigation [2]. In fact, buildings can mask some signals, thereby reducing the satellites availability and causing geometric configuration worsening, up to cases in which it is not possible to calculate the position because of the lack of measurements. Buildings can also reflect signals from in-view satellites, producing the multipath effects, or from non-line-of-sight (NLOS) ones. These two effects are not the same, although they sometimes occur together, but cause gross errors in measurements even though different [3]. With the rise of enhanced GNSS systems over the next decade the number of satellites and therefore of ranging sources available for positioning will significantly increase to more than double the current value. Hence it is no longer possible to assume that the
References
[1]
E. D. Kaplan and J. Hegarty, “Fundamentals of satellite navigation,” in Understanding GPS: Principles and Applications, E. D. Kaplan, Ed., Artech House Mobile Communications Series, 2nd edition, 2006.
[2]
L. Wang, P. D. Groves, and M. K. Ziebart, “Multi-constellation GNSS performance evaluation for urban canyons using large virtual reality city models,” Journal of Navigation, vol. 65, no. 3, pp. 459–476, 2012.
[3]
Z. Jiang and P. D. Groves, “GNSS NLOS and multipath error mitigation using advanced multi-constellation consistency checking with height aiding,” in Proceedings of the 25th International Technical Meeting of The Satellite Division of the Institute of Navigation, pp. 79–88, 2012.
[4]
N. L. Knight, J. Wang, and C. Rizos, “Generalised measures of reliability for multiple outliers,” Journal of Geodesy, vol. 84, no. 10, pp. 625–635, 2010.
[5]
M. A. Sturza, “Navigation system integrity monitoring using redundant measurements,” Navigation, Journal of the Institute of Navigation, vol. 35, no. 4, pp. 483–501, 1988.
[6]
B. W. Parkinson and P. Axelrad, “Autonomous GPS Integrity Monitoring using the Pseudorange Residual,” Navigation, Journal of the Institute of Navigation, vol. 35, no. 2, pp. 255–274, 1988.
[7]
H. Kuusniemi, G. Lachapelle, and J. H. Takala, “Position and velocity reliability testing in degraded GPS signal environments,” GPS Solutions, vol. 8, no. 4, pp. 226–237, 2004.
[8]
S. Hewitson and J. Wang, “GNSS receiver autonomous integrity monitoring (RAIM) performance analysis,” GPS Solutions, vol. 10, no. 3, pp. 155–170, 2006.
[9]
M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Communications of the Association for Computing Machinery, vol. 24, no. 6, pp. 381–395, 1981.
[10]
G. Schroth, A. Ene, J. Blanch, T. Walter, and P. Enge, “Failure detection and exclusion via range consensus,” in Proceedings of the European Navigation Conference, Toulouse, France, 2008.
[11]
G. Schroth, M. Rippl, A. Ene, J. Blanch, T. Walter, and P. Enge, “Enhancements of the range consensus algorithm (RANCO),” in ION GNSS Conference, 2008.
[12]
P. D. Groves and Z. Jiang, “Height aiding, C/N0 weighting and consistency checking for gnss nlos and multipath mitigation in urban areas,” Journal of Navigation, vol. 66, no. 5, pp. 653–669, 2013.
[13]
H. Kuusniemi, User-level reliability and quality monitoring in satellite-based personal navigation [Ph.D. thesis], Tampere University of Technology, Tampere, Finland, 2005, publication 544.
[14]
A. Angrisano, C. Gioia, S. Gaglione, and G. Del Core, “GNSS reliability testing in signal-degraded scenario,” International Journal of Navigation and Observation, vol. 2013, Article ID 870365, 12 pages, 2013.
[15]
M. G. Petovello, M. E. Cannon, and G. Lachapelle, “Benefits of using a tactical-grade IMU for high-accuracy positioning,” Navigation, vol. 51, no. 1, pp. 1–12, 2004.
[16]
O. Mezentsev, Sensor aiding of HSGPS pedestrian navigation [Ph.D. thesis], Department of Geomatics Engineering, University of Calgary, 2005.
[17]
S. Kuang, Geodetic Network Analysis and Optimal Design, AnnArbor Press, Michigan, Mich, USA, 1996.
[18]
R. G. Brown and G. Y. Chin, “GPS RAIM: calculation of threshold and protection radius using chi-square methods—a geometric approach,” in Global Positioning Systems: Inst Navigation, vol. 5, pp. 155–179, 1997.
[19]
M. Zuliani, “RANSAC for Dummies,” 2011.
[20]
J. Wang and P. B. Ober, “On the availability of fault detection and exclusion in GNSS receiver autonomous integrity monitoring,” Journal of Navigation, vol. 62, no. 2, pp. 251–261, 2009.
[21]
G. H. Golub and C. F. van Loan, Matrix Computations, Johns Hopkins University Press, London, UK, 3rd edition, 1996.
[22]
C. Park, I. Kim, G. I. Jee, and J. G. Lee, “Relationships between positioning error measures in global positioning system,” Journal of Guidance, Control, and Dynamics, vol. 20, no. 5, pp. 1045–1047, 1997.
[23]
G. Castaldo, Tecnica RANSAC/RANCO per il posizionamento in ambiente urbano [M.S. thesis], Departement of Science and Technology, Parthenope University of Naples, 2014.
[24]
S. Ackermann, A. Angrisano, S. Del Pizzo, S. Gaglione, C. Gioia, and S. Troisi, “Digital surface models for GNSS mission planning in critical environments,” Journal of Surveying Engineering, vol. 140, no. 2, Article ID 0000119, 2014.
