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Vector Solution for the Intersection of Two Circles of Equal Altitude

Published online by Cambridge University Press:  25 March 2008

Andrés Ruiz González
Andrés Ruiz González*
Affiliation:
(Navigational Algorithms. San Sebastián.)
*
(Email: [email protected])
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Abstract

A direct method for obtaining the two possible positions derived from two sights using vector analysis instead of spherical trigonometry is presented. The geometry of the circle of equal altitude and of the two body fixes is analyzed, and the vector equation for simultaneous sights is constructed. The running fix problem is also treated.

Keywords

Circle of Equal AltitudeCelestial NavigationSight ReductionVector Analysis
Type
Research Article
Information
The Journal of Navigation , Volume 61 , Issue 2 , April 2008 , pp. 355 - 365
Copyright
Copyright © The Royal Institute of Navigation 2008

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References

REFERENCES

1. Bowditch, Nathaniel, (1995). The American Practical Navigator. Pub. N°9, DMA.Google Scholar
2. Admiralty Manual of Navigation, Volume 1, BR 45 (1), General, Coastal Navigation and Pilotage. (1987–2006), TSO London. ISBN: 978-0-11-772880-6Google Scholar
3. Admiralty Manual of Navigation, Volume2, BR 45 (2), AstroNavigation. (2004) TSO London. ISBN: 1-870077-65-2Google Scholar
4. Watkins, R. and Janiczek, . (1978–79) P. M., Sight Reduction with Matrices, NAVIGATION, Journal of The Institute of Navigation, Vol. 25, No. 4, 447–48.Google Scholar
5. Severance, W. Robert. (1989). Overdetermined celestial fix by iteration. IoN Vol. 36, No. 4.Google Scholar
6. Metcalf, T. R. (1991). Advancing Celestial Circles of Position, NAVIGATION, Vol. 38, No. 3, 285–288.Google Scholar
7. Kaplan, G. H. (1996). The Motion of the Observer in Celestial Navigation, Navigator's Newsletter, Issue 51, 10–14.Google Scholar
8. Navigational Algorithms - Vectorial equation of the circle of equal altitude. (2006). Andrés Ruiz González, http://www.geocities.com/andresruizgonzalezGoogle Scholar
9. Max, Kurtz. (1991) Handbook of Applied Mathematics for Engineers and Scientist. McGraw-Hill. ISBN 07-035685-8Google Scholar
10. Gery, W. Stanley. (1997). The Direct Fix Of Latitude And Longitude From Two Observed Altitudes. NAVIGATION Vol. 44, No. 1.Google Scholar
11. Van Allen, A. James. (1981). An Analytical Solution Of The Two Star Sight Problem Of Celestial Navigation. NAVIGATION Vol. 28, No. 1.Google Scholar
12. Torben, Kjer. (1981). Unambiguous two body fix methods derived from crystallographic principles. NAVIGATION Vol. 28, No. 1.Google Scholar
13. Kotlaric, S. (1981). K-12 Method By Calculator: A Single Program For All Celestial Fixes, Directly Or By Position Lines NAVIGATION Vol. 28, No. 1, 1981Google Scholar
14. Bennett, G. G. (1979). General Conventions And Solutions-Their Use In Celestial Navigation. NAVIGATION Vol. 26, No. 4.Google Scholar
15. Daub, C. T. (1979). A Completely Programmable Method Of Celestial Navigation. NAVIGATION Vol. 26, No. 1,Google Scholar
16. Ogilvie, R. E. (1977) A New Method Of Celestial Navigation. NAVIGATION Vol. 24, No. 1Google Scholar
17. A'Hearn, M. F., and Rossano, G. S.. (1977) Two Body Fixes By Calculator. NAVIGATION Vol. 24, No. 1Google Scholar
18. Flynn, R. W.. (1972). Computer Sight Reduction Based On Intersection Of Equal Altitude Circles. NAVIGATION Vol. 19, No. 1Google Scholar
19. Kotlaric, Stjepo. (1971). New Short Method Tables (K11) For Direct Finding Of A Two Star Fix Without Use Of Altitude Difference Method. NAVIGATION Vol. 18, No. 4Google Scholar
20. Earle, Michael, A. (2000). A Vector Solution for Navigation on a Great Ellipse. Journal of Navigation, 53, 473–481.Google Scholar
21. Chih-Li, Chen, Tien-Pen, Hsu and Jiang-Ren, Chang. (2004). A Novel Approach to Great Circle Sailings: The Great Circle Equation. Journal of Navigation, 57, 311–320.Google Scholar
22. Earle, Michael, A. (2005). Vector Solutions for Great Circle Navigation. Journal of Navigation, 58, 451–457.CrossRefGoogle Scholar
23. Wei-Kuo, Tseng and Hsuan-Shih, Lee. (2007). The Vector Function for Distance Travelled in Great Circle Navigation. Journal of Navigation, 60, 158–164.Google Scholar
24. Wight, C. (1976). Direct Methods Of Latitude And Longitude Determination By Mini-Computer. NAVIGATION Vol. 23, No. 2Google Scholar
25. Fox, C. (1975) Finding Latitude And Longitude By Calculators. NAVIGATION Vol. 22, No. 4Google Scholar
26. Dozier Charles, T. (1949). A Simultaneous Two-Star Fix. NAVIGATION Vol. 2, No. 4, 1949Google Scholar
27. Little, Joseph, W. (1967). An Engineering Approach To The Mathematics Of Celestial Navigation. NAVIGATION Vol. 14, No. 3Google Scholar