NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Peter Hakel
Date: 2009 Nov 4, 09:21 -0800
The Van Allen's method works fine for me even in this singular case, see the attached screenshot of the lops.xls spreadsheet.
At the core of this method is a solution of a quadratic equation whose discriminant D, as always, defines three cases:
D>0, two distinct solutions (LOPs intersect, the usual CelNav case)
D=0, one solution (LOPs touch, like in this artificial test case)
D<0, no solution
I was concerned about round-off errors for the D=0 case when I was writing that spreadsheet. If D comes out ever so slightly negative instead of zero, then SQRT(D) has a problem. So far, however, Excel numerics has passed all such tests OK, including this one.
Peter Hakel
From: Andres Ruiz <aruiz@orona.es>
To: navlist@fer3.com
Sent: Wed, November 4, 2009 2:12:28 AM
Subject: [NavList 10426] Re: Two-body fix caveat
Solving this singular case with Van Allen’s method: no solution. Vector Solution works fine.
An analytical solution of the two star sight problem of celestial navigation
James A. Van Allen. NAVIGATION Vol. 28, No. 1, 1981
iter Err Be Le B1 L1 B2 L2 GHA1f dec1f GHA2f dec2f
0 NaN NaN NaN NaN NaN NaN NaN 10.000000 0.000010 0.000000 -0.000010
I1: NaN NaN
I2: NaN NaN
Vector Solution for the Intersection of two Circles of Equal Altitude
THE JOURNAL OF NAVIGATION (2008), 61, 355-365. The Royal Institute of Navigation
Andrés Ruiz González - Navigational Algorithms - http://sites.google.com/site/navigationalalgorithms/
iter Err Be Le B1 L1 B2 L2 GHA1f dec1f GHA2f dec2f
0 134.146176409012696 0.000058 -20.000000 0.000058 -20.000000 0.000001 -20.000000 10.000000 0.000010 0.000000 -0.000010
I1: 0.00000 -20.000000
I2: 0.00000 -20.000000
Andrés Ruiz
Navigational Algorithms
http://sites.google.com/site/navigationalalgorithms/
--~--~---------~--~----~------------~-------~--~----~
NavList message boards: www.fer3.com/arc
Or post by email to: NavList@fer3.com
To , email NavList+@fer3.com
-~----------~----~----~----~------~----~------~--~---
