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    Re: Marq St. Hilaire - Altitude intercept method:
    From: Henry Halboth
    Date: 2007 Oct 29, 10:47 -0700

    Andres,
    
    Thank you for your most complete reply.
    
    We are in complete agreement as respects Marc St.
    Hillaire. Under yor comments on Latitude by Meridian
    Transit, I would add only the comment that Course is
    also relevant, which I feel sure you meant to include.
    
    Regards,
    
    Henry
    
    --- Andres Ruiz  wrote:
    
    > 
    > [NavList 3635] Re: Marq St. Hilaire - Altitude
    > intercept method:
    > An accurate position is determined by meridian
    > transit
    > Latitude and subsequent Longitude by Time Sight,
    > utilizing the accurate Latitude. In your opinion,
    > will
    > or will not an intercept determined by the Marc St.
    > Hillarie method, utilizing the so determined
    > accurate
    > position, be equal to zero, If not, why?
    > ------------------
    > 
    > Henry, if you know your exact position; Yes
    > 
    > The intercept is the great circle distance between
    > the CoP based on calculated altitude, Hc, and the
    > one based on the observed altitude, Ho. The
    > calculate altitude is a function of the position.
    > But Ho always has a little error, and the true CoP
    > and the observed one may be different. 
    > 
    > If you use the St-Hilarie in an iterative way, the
    > estimated position is not important, because you can
    > improve it. Only the accuracy of the star shootings
    > with the sextant is. And of course the knowledge of
    > the conditions: temperature, pressure, height of the
    > eye,
    > The accuracy deepens only on the bodies and the
    > measurements, not in the method. You can obtain a
    > fix by iterative St-hilaire, by sight reduction with
    > matrices, by T. Metcalf LS method or by Kaplan
    > STELLA method, and the final solution in the case of
    > two sights is the same. Also by Summer in an
    > iterative way.
    > If tree or more sights are involved, the solution
    > can be different because the technique to obtain the
    > most probable position is different.
    > Using St-Hilaire in the old traditional graphic way
    > to obtain the MMP, from a cooked hat, is the use of
    > bisectors of the azimuth angle.
    > 
    > Meridian sight has tree main problems:
    > 1. the maximum altitude
    > 2. the time of the LAN
    > 3. The speed of the vessel. (aboard a sailboat 4,8
    > kn are insignificance)
    > But taking a series of sight before and after the
    > local noon, and adjusting them by a least squares
    > method I usually get good results.
    > 
    > About accuracy, in coastal navigation is more
    > important that in blue water, because the shallow.
    > One friend of mine says: "Navigating, is not
    > important to know where you are, the important thing
    > is to know where you are not" (Is well expressed)
    > 
    > An example: some different AP and the effect of the
    > improvement by iteration
    > 
    > 25/08/2004
    > 22:00:00
    > Enif
    > GHA = 338.391817 � = 338� 23.5'
    > Dec = 9.896533 � =   9� 53.8'
    > Ho = 50.77
    > Schedar
    > GHA = 294.303014 � = 294� 18.2'
    > Dec = 56.560600 � =  56� 33.6'
    > Ho = 46.44
    > 
    > Result by exact 2 CoP solution, NA and Kaplan
    > algorithm:
    > B = 43.32162 =  43� 19.3' N
    > L = -2.00219 = 002�  0.1' W
    > 
    > For AP:
    > Be = 43.3166�
    > Le = -2.0000�
    > St-Hilaire:
    > BI = 43.3216 
    > LI = -2.0021
    > HC     Z   p 
    > 50.7749   141.4002    -0.0049
    > 46.4378   47.7147 0.0022
    > 
    > For AP:
    > Be = 41.5�
    > Le = -3.5�
    > St-Hilaire:
    > BI = 43.3614
    > LI = -2.0890
    > HC     Z   p 
    > 51.4421   137.8834    -0.6721
    > 44.3881   46.1244 2.0519
    > 
    > For AP:
    > Be = 30.0000 
    > Le = -10.0000
    > St-Hilaire:
    > BI = 45.0388 
    > LI = -5.5543
    > HC     Z   p 
    > 54.3421   117.6633    -3.5721
    > 32.353    39.2049 14.087
    > 
    > After five iterations:
    > HC     Z   p 
    > 50.7700   141.4011    -0.0000
    > 46.4400   47.7183 -0.0000
    > 43.321611 N
    > 2.002105  W
    > 
    > Best regards,
    > 
    > Andr�s Ruiz
    > Navigational Algorithms
    > http://www.geocities.com/andresruizgonzalez
    > 
    >
    > 
    > 
    
    
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