Abstract
In the movie Magic Town, Jimmy Stewart plays a public opinion consultant who’s obsessed with finding a cheap, fast way to report how the American public feels about current events, issues, marketable products, election candidates (is that redundant?), etc. Not satisfied with traditional polling methods that canvass large numbers of people scattered across the United States, Stewart instead searches for a small town whose population is a perfect cross-section of the country.
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Notes
- 1.
H. Black, A Passive System for Determining the Attitude of a Satellite, AIAA Journal 2(7), pp. 1350–1351, 1964.
- 2.
Wahba, G., A least-squares estimate of satellite attitude, SIAM Rev. 7(3), 409 (1965).
- 3.
Documented by J. Keat, Analysis of Least-Squares Attitude Determination Routine, DOAOP, Computer Sciences Corporation Technical Memorandum CSC/TM-77/6034, Feb. 1977; see also F. Markley and J. Crassidis, Fundamentals of Spacecraft Attitude Determination and Control, Sect. 5.3.1, 2014.
- 4.
- 5.
The constraint is applied using “the method of Lagrange multipliers,” developed by the French mathematician Joseph Louis Lagrange (1736–1813). Good descriptions of the method are available in many text books. You will likely encounter reference to the method again during the course of your professional career. Tie it in your mind to the notion of minimizing or maximizing a function subject to some constraint. As a simpler example, consider finding the highest point in the Rocky Mountains subject to the constraint that you stay on a particular cross country highway.
- 6.
Lefferts, E.J., Markley, F.L., and Shuster, M.D., Kalman filtering for spacecraft attitude estimation, Journal of Guidance and Control Dynamics, 5(5), 417–429 (1982).
- 7.
ibid.
- 8.
R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, March 1960, pp 35–46; or see also A. Gelb et al., Applied Optimal Estimation, MIT Press, 1974.
- 9.
G. Wilson, “If You Survive: From Normandy to the Battle of the Bulge to the End of World War II, One American Officer’s Riveting True Story”, Paperback Edition: Ballantine Books, June 1997.
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Hallock, H.L., Welter, G., Simpson, D.G., Rouff, C. (2017). Onboard Attitude Determination. In: ACS Without an Attitude. NASA Monographs in Systems and Software Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-7325-0_7
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