Reply

Salut,

You can see a nav.c program, it is an matrix approach to resolve the
sight by direct computation.
Algorithms are from Thomas R. METCALF implemented in C language.

     Djamel AIT AMRANE

Andres Ruiz wrote:
> [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:
>
>
>
>
> 3 COPs analytical solution
>
>
>
>
> Input data: 3 observations
>
>
>
> K
>
> Body
>
> Ho
>
> GHA
>
> Dec
>
> 1
>
> Body1
>
> Ho1
>
> GHA1
>
> Dec1
>
> 2
>
> Body2
>
> Ho2
>
> GHA2
>
> Dec2
>
> 3
>
> Body3
>
> Ho3
>
> GHA3
>
> Dec3
>
>
>
>
>
>
>
> Fix: BF LF
>
>
>
>
>
>
>
> Manual Solution
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> 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
>
>
>
>
> K
>
> Body
>
> Ho
>
> GHA
>
> Dec
>
> 1
>
> Arcturus
>
> 22.2
>
> 166.829
>
> 19.335
>
> 2
>
> Vega
>
> 70.15
>
> 115.277
>
> 38.758
>
> 3
>
> Dubhe
>
> 20.35
>
> 226.98
>
> 61.909
>
>
>
>
>
> | -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.
>
>
>
> Andr�s
>
> http://www.geocities.com/andresruizgonzalez
>
>
>
>
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> X-Google-AttachSize: 24915
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> 
>
> 
> 
> 
>
> 
> 
> 
>
> 
>
> 

>
> 

>
> 
 style='font-size:10.0pt;font-family:"Courier New"'>[NavList 1437] Re:
> Navigator's Newsletter, and other forums.

> From: jrvz---net

> Date: 17 Oct 2006 22:45
>
> 
…
 size=2 face="Courier New">(It does 
require inverting 3x3 matrices, so it's not well suited 
to
 size=2 face="Courier New">hand 
calculation.)
 size=2 face="Courier New">If 
someone remembers seeing something like this, I would appreciate 
a
 size=2 face="Courier New">reference.  Otherwise I'll write it up in more 
detail.
>
> 
---------------------------------------------------------
>
> 
 size=2 color=navy face=Arial> 
>
> 
 size=2 color=navy face=Arial> 
>
> 
 size=2 face=Arial>Now
> I am writing some articles to be published on my web page under the name  style='font-weight:bold;font-style:italic'>Navigational Algorithms.
>
> 
 size=2 face=Arial>The
> draft of one about circles of position is:
>
> 
 
>
> 

>
> 
3 COPs
> analytical solution
>
> 
>
> 
 
>
> 
Input data: 3 observations
>
> 
 
>
>   style='border-collapse:collapse'>
>  
>   
>   
>   
>   
>   
>  
>  
>   
>   
>   
>   
>   
>  
>  
>   
>   
>   
>   
>   
>  
>  
>   
>   
>   
>   
>   
>  
> 

>   
   face=Arial>K
>   

>   
   face=Arial>Body
>   

>   
   face=Arial>Ho
>   

>   
   face=Arial>GHA
>   

>   
   face=Arial>Dec
>   

>   
1
>   

>   
   face=Arial>Body1
>   

>   
   face=Arial>Ho1
>   

>   
   face=Arial>GHA1
>   

>   
   face=Arial>Dec1
>   

>   
2
>   

>   
   face=Arial>Body2
>   

>   
   face=Arial>Ho2
>   

>   
   face=Arial>GHA2
>   

>   
   face=Arial>Dec2
>   

>   
3
>   

>   
   face=Arial>Body3
>   

>   
   face=Arial>Ho3
>   

>   
   face=Arial>GHA3
>   

>   
   face=Arial>Dec3
>   
>
> 
 
src="https://NavList.net/feed.aspx?m2=1&cid=img/101449.image001-jpg-01C6F2AA-04F86E70">
>
> 
 
>
> 
 
>
> 
Fix: BF LF
>
> 
 
>
> 

>
> 
 
>
> 
Manual
> Solution
>
> 
>
> 
 
>
>   style='border-collapse:collapse'>
>  
>   
>   
>  
> 

>   
   
src="https://NavList.net/feed.aspx?m2=1&cid=img/101449.image010-gif-01C6F2A9-46607840">
>   

>   
   
src="https://NavList.net/feed.aspx?m2=1&cid=img/101449.image012-gif-01C6F2A9-46607840">
>   
>
> 
 
>
> 
 style='font-size:12.0pt;font-family:"Courier New";color:navy'> 
>
> 
 
>
> 
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)
>
> 
 style='font-size:12.0pt;font-family:"Courier New"'>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)
>
> 
 
>
> 
 clear=all style='page-break-before:always'>
> 
>
> 
 style='font-size:16.0pt'>Example by hand
>
> 
 
>
>   style='border-collapse:collapse'>
>  
>   
>   
>   
>   
>   
>  
>  
>   
>   
>   
>   
>   
>  
>  
>   
>   
>   
>   
>   
>  
>  
>   
>   
>   
>   
>   
>  
> 

>   
   face=Arial>K
>   

>   
   face=Arial>Body
>   

>   
   face=Arial>Ho
>   

>   
   face=Arial>GHA
>   

>   
   face=Arial>Dec
>   

>   
1
>   

>   
Arcturus
>   

>   
   face=Arial>22.2
>   

>   
   face=Arial>166.829
>   

>   
   face=Arial>19.335
>   

>   
2
>   

>   
Vega
>   

>   
   face=Arial>70.15
>   

>   
   face=Arial>115.277
>   

>   
   face=Arial>38.758
>   

>   
3
>   

>   
Dubhe
>   

>   
   face=Arial>20.35
>   

>   
   face=Arial>226.98
>   

>   
   face=Arial>61.909
>   
>
> 
 
>
> 
 style='font-size:12.0pt;font-family:"Courier New"'> 
>
> 
 style='font-size:12.0pt;font-family:"Courier New"'>| -2.432  0.569 
> 0.876 | | 0.006|   | 1 |
>
> 
 style='font-size:12.0pt;font-family:"Courier New"'>| -0.354  0.750 
> 0.666 | | 0.731| = | 1 |
>
> 
 style='font-size:12.0pt;font-family:"Courier New"'>| -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.
>
> 
 
>
> 
Andr�s
>
> 
http://www.geocities.com/andresruizgonzalez
>
> 
 
>
> 
> 
> 
> 
> 
> 
> ------_=_NextPart_002_01C6F29C.75CAF27F--


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