[NavList 1437] Re: Navigator's Newsletter, and other forums.
From: jrvz---net
Date: 17 Oct 2006 22:45

…

(It does require inverting 3x3 matrices, so it's not well suited to

hand calculation.)

If someone remembers seeing something like this, I would appreciate a

reference.  Otherwise I'll write it up in more detail.

---------------------------------------------------------

Now I am writing some articles to be published on my web page under the name Navigational Algorithms.

The draft of one about circles of position is:

Input data: 3 observations

Fix: BF LF

M3 = x1*y2*z3+y1*z2*x3+z1*x2*y3-(z1*y2*x3+x1*z2*y3+y1*x2*z3)

Mx = y2*z3+y1*z2+y3*z1-(y2*z1+y1*z3+y3*z2)

My = z2*x3+z1*x2+z3*x1-(z2*x1+z1*x3+z3*x2)

Mz = x2*y3+x1*y2+x3*y1-(x2*y1+x1*y3+x3*y2)

Example by hand

| -2.432  0.569  0.876 | | 0.006|   | 1 |

| -0.354  0.750  0.666 | | 0.731| = | 1 |

| -0.924 -0.990  2.537 | | 0.682|   | 1 |

B [0-90][+N/-S]

L [0-360][+ W->E]

Fix(42.982085093299339, 89.566484629127913)

This method work only for one point of intersection. Otherwise a least squares method must be used to find the most probable celestial position.  

Help:

I am looking for some information about sight reduction with matrices, I have find two articles:

Dewit, C., “Some Remarks on Sight Reduction with Matrices,” Navigation: J. Inst. Naviga., Vol. 26, No. 3, pp. 252-253 (1979).

Watkins. R. and Janiczek. P. M., Sight Reduction with Matrices, NAVIGATION, Journal of The Institute of Navigation, Vol. 25, No. 4, Winter 1978-79, pp. 447-48.

if someone could send me some copies or additional information by e-mail, I,ll be very thankful.

Andrés

http://www.geocities.com/andresruizgonzalez