The method of least squares used to invert an orbit problem

American Journal of Physics

Volumn 71, Issue 12, 2003, Pages 1268-1275

  Bannister, Ross ^a  

^a UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345581691     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1613270     Document Type: Article

References (23)

1. Mary L. Boas. Mathematical Methods in the Physical Sciences (Wiley, New York, 1966), Chap. 13.
2. Albert Tarantola, Inverse Problem Theory (Elsevier, Amsterdam, 1994), 2nd ed., pp. XIII-XV.
3. Cornelius Lanczos, Applied Analysis (Dover, New York, 1988), Chap. II.
4. Thomas W. Schlatter, "Variational assimilation of meteorological observations in the lower atmosphere: a tutorial on how it works," J. Atmos. Sol.-Terr. Phys. 62, 1057-1070 (2000).
5. Douglas O. Gough, J. W. Leibacher, and P. H. Schemer, "Perspectives in helioseismology," Science 272, 1281-1283 (1996).
6. D. W. Oldenburg, "An introduction to linear inverse theory," IEEE Trans. Geosci. Remote Sens. GE-22 (6), 665-674 (1984).
7. Roger R. Bate, Donald D. Mueller, and Jerry E. White, Fundamentals of Astrodynamics (Dover, New York, 1971), Sec. 2.1.
8. Ref. 2, Sec. 4.1.
9. L. G. Taff, Celestial Mechanics: A Computational Guide for the Practitioner (Wiley, New York, 1985).
10. Ref. 7, Sec. 2.12.
11. A. Armitage, Edmond Halley (Nelson, London, 1966).
12. E. T. Bell, The Prince of Mathematicians in The World of Mathematics (Simon and Schuster, New York, 1956), Vol. 1.
13. Parameters for the planets and other bodies are provided by NASA at 〈http:/ /ssd.jpl.nasa.gov/〉.
14. If the observations are not independent, then the correlations are represented by additional off-diagonal elements in R. Off-diagonal elements are called covariances and are a generalization of the standard deviation. See, for example, Roger J. Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences (Wiley, Chichester, 1989), Sec. 2.6.3.
15. Yoshikazu Sasaki, "Some basic formalisms in numerical variational analysis," Mon. Weather Rev. 98, 875-883 (1970).
16. Clive D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, Singapore, 2000), Vol. 2, Sec. 2.3.2.
17. William H. Press, Saul A. Teukolsky, William T. Vettering, and Brian P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge U. P., Cambridge, 1986), Sec. 10.7.
18. Ref. 14, Sec. 6.4.
19. Ref. 2. Sec. 4.3.
20. T. E. Sterne, An Introduction to Celestial Mechanics (Interscience, New York, 1960), Chaps. 1 and 3.
21. Ref. 20, Sec. 1.5.
22. Ref. 20, Sec. 3.2.
23. Our code (in Fortran 77) and user documentation is available at 〈http:/ /darc.nerc.ac.uk/models〉.