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A Non-singular Horizontal Position Representation

Published online by Cambridge University Press:  28 May 2010

Kenneth Gade*
Affiliation:
(Norwegian Defence Research Establishment (FFI))

Abstract

Position calculations, e.g. adding, subtracting, interpolating, and averaging positions, depend on the representation used, both with respect to simplicity of the written code and accuracy of the result. The latitude/longitude representation is widely used, but near the pole singularities, this representation has several complex properties, such as error in latitude leading to error in longitude. Longitude also has a discontinuity at ±180°. These properties may lead to large errors in many standard algorithms. Using an ellipsoidal Earth model also makes latitude/longitude calculations complex or approximate. Other common representations of horizontal position include UTM and local Cartesian ‘flat Earth’ approximations, but these usually only give approximate answers, and are complex to use over larger distances. The normal vector to the Earth ellipsoid (called n-vector) is a non-singular position representation that turns out to be very convenient for practical position calculations. This paper presents this representation, and compares it with other alternatives, showing that n-vector is simpler to use and gives exact answers for all global positions, and all distances, for both ellipsoidal and spherical Earth models. In addition, two functions based on n-vector are presented, that further simplify most practical position calculations, while ensuring full accuracy.

Type
Research Article
Copyright
Copyright © The Royal Institute of Navigation 2010

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References

Aeronautical Systems Div Wright-Patterson AFB OH (1986). Specification for USAF Standard Form, Fit and Function Medium Accuracy Inertial Navigation Unit (SNU-84.1).Google Scholar
Britting, K.R. (1971). Inertial Navigation Systems Analysis. Wiley Interscience.Google Scholar
Craig, J.J. (1989). Introduction to Robotics. Addison-Wesley Publishing Company, Boston, 2nd edn.Google Scholar
Fortescue, P.W., Stark, J. and Swinerd, G. (2003). Spacecraft Systems Engineering. John Wiley and Sons, 3rd edn.Google Scholar
Gade, B.H., and Gade, K. (2007). n-vector – formulas with derivations. FFI/RAPPORT 2007/00633, Norwegian Defence Research Establishment (FFI).Google Scholar
Gade, K. (2004). NavLab, a Generic Simulation and Post-processing Tool for Navigation. European Journal of Navigation, 2, 5159.Google Scholar
Hagen, P.E., Storkersen, N., and Vestgard, K. (2003). The HUGIN AUVs – multi-role capability for challenging underwater survey operations. EEZ International.Google Scholar
Hager, J.W., Behensky, J.F., and Drew, B.W. (1989). The Universal Grids: Universal Transverse Mercator (UTM) and Universal Polar Stereographic (UPS). DMA Technical Manual 8358.2, Defence Mapping Agency.Google Scholar
Hofmann-Wellenhof, B., Wieser, M., and Lega, K. (2003). Navigation: Principles of Positioning and Guidance. Springer.CrossRefGoogle Scholar
Jalving, B., Gade, K., Hagen, O.K., and Vestgard, K. (2004). A Toolbox of Aiding Techniques for the HUGIN AUV Integrated Inertial Navigation System. Modeling, Identification and Control, 25, 173190.CrossRefGoogle Scholar
Levine, W.S. (2000). Control System Applications. CRC Press.Google Scholar
Longley, P.A., Goodchild, M.F., Maguire, D.J. and Rhind, D.W. (2005). Geographic Information Systems and Science. John Wiley and Sons, 2nd edn.Google Scholar
Marthiniussen, R, Faugstadmo, J. E. and Jakobsen, H. P. (2004). HAIN an integrated acoustic positioning and inertial navigation system. Proceedings from MTS/IEEE Oceans 2004, Kobe, Japan.Google Scholar
McGill, D.J., and King, W.W. (1995). Engineering Mechanics. PWS-KENT, Boston, 3rd edn.Google Scholar
Moore, J.R. and Blair., W.D. (2000). Practical Aspects of Multisensor Tracking, in Multitarget-Multisensor Tracking: Applications and Advances, Volume III, Eds: Bar-Shalom, Y. and Blair, W.D., Artech House.Google Scholar
National Imagery and Mapping Agency (2000). Department of Defense World Geodetic System 1984: Its Definition and Relationships With Local Geodetic Systems. NIMA Technical Report TR8350.2, 3rd edn.Google Scholar
Obaidat, M.S. and Papadimitriou, G.I. (2003). Applied System Simulation: Methodologies and Applications. Springer.CrossRefGoogle Scholar
Phillips, W.F. (2004). Mechanics of Flight. John Wiley and Sons.Google Scholar
Savage, P.G. (2000). Strapdown Analytics. Strapdown Associates, Inc., Maple Plain.Google Scholar
Sinnott, R.W. (1984). Virtues of the Haversine. Sky and Telescope, 68, 159.Google Scholar
Snyder, J.P. (1987). Map Projections – A Working Manual. U. S. Geological Survey Professional Paper 1395. U. S. Government Printing Office.Google Scholar
Strang, G., and Borre, K. (1997). Linear Algebra, Geodesy, and GPS. Wellesley-Cambridge Press, Wellesley.Google Scholar
Stuelpnagel, J. (1964). On the Parametrization of the Three-Dimensional Rotation Group, SIAM Review, 6, 422430.Google Scholar
Vermeille, H. (2004). Computing geodetic coordinates from geocentric coordinates. Journal of Geodesy, 78, 9495.CrossRefGoogle Scholar
Weisstein, E.W. (2003). CRC Concise Encyclopedia of Mathematics. CRC Press.Google Scholar
Zipfel, P.H. (2000). Modeling and Simulation of Aerospace Vehicle Dynamics. AIAA Education Series, Reston.Google Scholar
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