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I found another book of mine which I haven't read for a long time which
is even better than the other book I mentioned for this topic:

T: An Introduction to The Mathematics and Methods of Astrodynamics
A: Richard H. Battin
D: 1987
P: American Institute of Aeronautics & Astronautics, NY

Lots of math, Kepler's equation, 2 and 3 body dynamics, variation of
parameters and other advanced math occupy the bulk of the book (796
pages in hardback), but the last two chapters are gems:

Chapter 13: The Celestial Position Fix
Error analysis, a method of correcting clock errors by having 4
independent measurements to ascertain a position in 3 dimensions and to
check on time (sounds like a lunar, eh?)

Chapter 14: Space Navigation
Recursive estimation, correlated measurement errors, and other ways of
using statistics to improve position accuracy

The first paragraph of chapter 13 lays out the problem as follows:

   "In many respects the navigation position fix obtained from celestial
observations made aboard a spacecraft is similar to the problem
encountered by the seagoing and airborne navigators.  The fundamental
differences are (1) the spacecraft problem is truly three dimensional
and (2) the forces governing the motion of the spacecraft are far
better known than the motions of the terrestrial seas and air masses.
Therefore, although the first difference noted tends to complicate the
problem, the second makes the task somewhat easier and the resulting
computations and extrapolations capable of greater precision." (Battin
1987: page 623)

Dan

   

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