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    Re: Navigational Algorithms - 3 COPs analytical solution
    From: Wolfgang K�berer
    Date: 2006 Oct 18, 11:35 -0700

    Dear Andres Ruiz,
    
    by chance I have a copy of Navigation, Vol. 25, No. 4, with the article
    by Watkins and Janiczek. I' ll send you a scan off-list tomorrow.
    
    And there is a french book on "La navigation astronomique" by Philippe
    Bourbon published by the Institut oc�anographique (Paris 2000), which
    makes use of matrices for reduction of multiple sights. It costs about
    40 � and may be ordered via Amazon  or directly from the Institut
    oc�anographique. I haven't had the time to try to follow the math,
    though, so I cannot comment on its merits ot faults.
    
    By the way - it may interest other list members - I bought the copy of
    "Navigation"  26 years ago because it contained an article by D.W.Kerst
    on "Longitude by lunar observations and the pocket calculator". It is
    based on the Chauvenet (direct) method and I wrote a program at that
    time which solved the formulae on a HP 41. Never tried it in the real
    world, though. I just owned a Davis Mark III then and did'nt think that
    could be accurate enough for lunar observations.
    
    Regards,
    
    Wolfgang K�berer
    
    Andres Ruiz schrieb:
    
    > [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
    >
    >
    >
    >
    > ------_=_NextPart_002_01C6F29C.75CAF27F
    > Content-Type: text/html; charset=iso-8859-1
    > Content-Transfer-Encoding: quoted-printable
    > X-Google-AttachSize: 24915
    >
    > 
    >
    > 
    > 
    > 
    >
    > 
    >
    > 
    >
    > 
    >
    > 
    > >

    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="http://fer3.com/arc/feed.aspx?m2=1&cid=img/101441.image001-jpg-01C6F2AA-04F86E70">

    > >

    > >

    > >

    Fix: BF LF

    > >

    > >
    > >

    > >

    Manual > Solution

    > >
    > >

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

    src="http://fer3.com/arc/feed.aspx?m2=1&cid=img/101441.image010-gif-01C6F2A9-46607840">

    >
    >

    src="http://fer3.com/arc/feed.aspx?m2=1&cid=img/101441.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-- --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---

       
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