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Subject: Re: accuracy of automatic celestial navigation
From: Herbert Prinz (hprinz@XXX.XXX)
Date: Sun Dec 08 2002 - 01:34:20 EST
Glenn Geers wrote:
> The algorithms take the motion of the vessel into account and can provide very
> high (30m) accuracy.
Well, the algorithms can do much better. In his article "The Motion of the
Observer in Celestial Navigation", published in "The Navigator's Newsletter" of
the Foundation for the Promotion of the Art of Navigation, Issue 51, Spring 1996,
George H. Kaplan compares several algorithms which account for the motion of the
observer. Two are rigorous, one is an approximative method. Clearly, the two
rigorous methods yield identical results of absolute accuracy. The approximative
method yields a result that is typically within 0.05 arcminutes of the rigorous
solution, degenerating with increasing length of track of the observer between
individual observations. The two rigorous methods remain correct regardless of the
observation span. To avoid any potential misunderstanding, Kaplan concludes the
analysis with the explicit warning: "In any event, the degree of equivalence among
these procedures indicates only mathematical precision and should not be mistaken
for navigational accuracy."
Therefore, the question that George Huxtable raised in a post of Dec 6,
> If that claim related simply to the accuracy of the calculations, then it
> would be easy to accept. It's rather harder to understand if it relates to
> the overall precision of the complete system, which would correspond to
> measuring star altitudes, with respect to the vertical, to 0.5 to 1 second
> of arc.
must be answered affirmatively. The envisaged accuracy of 1" is indeed that of the
entire navigation system and not just that of the algorithm. Since the algorithm
is strict, the 1" error is entirely observational.
This is also confirmed by a statement of G. H. Kaplan in a letter to the
Navigation Foundation in 1996, saying "[...] we decided to anticipate the
possibility that at some time in the future automated shipboard star trackers
might provide the basic observational data. Since these devices are capable of
arcsecond-level measurement precision, our software was designed with one
arcsecond (30 meter) or better precision as a specification".
The system specification of 1" precision was obviously not classified information
in 1996. Whether it has been met or not (or even exceeded) may be classified
information; I don't know. Where the accuracy of the star tracker is concerned,
Kaplan speaks of a fact, not of a specification.
Herbert Prinz
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