NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: That darned old cocked hat
From: Geoffrey Kolbe
Date: 2010 Dec 10, 20:25 +0000
Peter Fogg replied:
Well Peter, there is no direct way of measuring azimuth using a sextant, so the slope may be in error because of an error in longitude. Consider the case of observing bodies high in the sky from equatorial latitudes. For bodies towards the North or South, the slope will vary with time (and so longitude) quite quickly. In such circumstances, one might even determine the error in longitude by the difference in slopes between the calculated slope from the estimated position, and the least squares fit to the data.
Given that:
1) In these special circumstances the least squares fit is obviously going to be the best fit.
2) The fact that if the estimated position is not the actual position, it follows that the calculate slope from the estimated position cannot be the "best" fit.
It would seem that in general it is better to use a least squares fit rather the calculated slope from the estimated position. Is that logical?
Geoffrey.
From: Geoffrey Kolbe
Date: 2010 Dec 10, 20:25 +0000
Geoffrey Kolbe wrote:
- The calculated slope is for your estimated position. Suppose you are not at, or anywhere close to the estimated position - the calculated slope will not be what it should be for your actual position. Is that not correct Peter?
Peter Fogg replied:
The calculated slope is derived from the latitude of observation and azimuth of the body being observed. So if you assume you are at one latitude but are instead a very long way away then I guess that your calculated slope, in that case, could be incorrect. Is that helpful, Geoffrey?
Well Peter, there is no direct way of measuring azimuth using a sextant, so the slope may be in error because of an error in longitude. Consider the case of observing bodies high in the sky from equatorial latitudes. For bodies towards the North or South, the slope will vary with time (and so longitude) quite quickly. In such circumstances, one might even determine the error in longitude by the difference in slopes between the calculated slope from the estimated position, and the least squares fit to the data.
Given that:
1) In these special circumstances the least squares fit is obviously going to be the best fit.
2) The fact that if the estimated position is not the actual position, it follows that the calculate slope from the estimated position cannot be the "best" fit.
It would seem that in general it is better to use a least squares fit rather the calculated slope from the estimated position. Is that logical?
Geoffrey.
