A non-singular horizontal position representation

Author
Gade, Kenneth
Date Issued
2010-07-03
Keywords
Navigasjon
Posisjonsbestemmelse
Koordinatsystemer
Interpolasjon
Avstandsmåling
Permalink
http://hdl.handle.net/123456789/96310
http://hdl.handle.net/20.500.12242/2614
DOI
10.1017/S0373463309990415
Collection
Articles
Description
Gade, Kenneth. A non-singular horizontal position representation. Journal of navigation 2010 ;Volum 63.(3) s. 395-417 FFI
338735.pdf
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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 degrees. 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.
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