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Dear Gary,

If doing Marcq St. Hilaire sight reduction, instead of advance each LoP from 
the same DR, EP, AP or initial point, advance your observation DR position by 
course an distance to the time of fix and use this (B, L) in the equation for 
altitude Hc = asin( sin B sin DEC + cos B cos Dec cos LHA )
This is the fundament of the algorithm.

Thanks for your praise, ;-)

Andr�s Ruiz
Navigational Algorithms
https://sites.google.com/site/navigationalalgorithms/


-----Mensaje original-----
De: navlist-bounce@fer3.com [mailto:navlist-bounce@fer3.com] En nombre de Gary LaPook
Enviado el: viernes, 19 de febrero de 2010 8:38
Para: NavList@fer3.com
Asunto: [NavList] Re: Advancing LOPs for precision fixes

Andres' site is really impressive and it is well worth looking at.

It has been at least 40 years since I tried doing matrix math so his 
explanation left me in the dust. But, in looking at his formulas and 
those in the N.A. I think, conceptually, that the first two formulas 
provide for adjusting the A.P. (of E.P.) for the movement of the vessel 
so I guess that this is what allows for a moving fix but, I must admit, 
I don't understand why it works.

His methodology for determining a fix by least squares makes sense and 
reminds me of how attacked this problem in the past. In the late '70's I 
programed my TI 52 calculator to come up with an approximation of a fix 
from three LOPs. Lacking Andres' math skills and working with a lesser 
level of accuracy commensurate with flight navigation, I programmed the 
calculator to determine the intersection of the first two LOPs.Then it 
used this position as the AP for computation of the third LOP. Then, to 
approximate the center of the triangle of position, my program took the 
bisector of the first two azimuths and then moved the fix 2/3rds of the 
distance of the third intercept along that bisector from the 
intersection of the first two LOPs and took this as the position of the 
fix. Not elegant, not perfect,  but close enough for flight navigation..

gl

   

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