Welcome to the NavList Message Boards.

NavList:

A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

Message:αβγ
Message:abc
Add Images & Files
    or...
       
    Reply
    Re: Still on LOP's
    From: Rodney Myrvaagnes
    Date: 2002 Apr 23, 17:13 -0500

    On Mon, 22 Apr 2002 19:06:42 +0100, Dr. Geoffrey Kolbe wrote:
    
    >
    >My "proof", as you were kind enough to call it, has nothing to say
    >regarding the size of the 'hat. All that is demonstrated is that the 'hat
    >will enclose the actual position 25% of the time.
    >
    Help me understand what you are saying here, speaking of normal
    distributions.
    
    Let us consider a location we are trying to determine, with three
    visible landmarks equidistant at 120 degrees apart, so our bearings
    have similar error distribution.
    
    Among the possible triangles we could get are equilateral triangles
    tangent (within a distance as small as we want to wait for) to 1-sigma,
    2-sigma, 3-sigma, and 4-sigma contours.
    
    Any one of these equilateral triangles will recur at locations not
    exactly on the center of our space if enough bearings are taken. They
    will (I suppose?) also have a normal distribution. Your statement is:
    
    1) that in a long enough run of observations, 25% of triangles of a
    given size will contain the true location.
    
    OR
    
    2) that in a long enough run of observations, not more than 25% of
    triangles of a given size will contain the true location.
    
    If 2 is the assertion, there must be some size of triangle that
    maximizes the function P(inside) or approaches most closely to 25%. I
    would be much happier with an analytic answer to this one, since I have
    not seen anything yet that doesn't appear to assume a flat, rather than
    normal, distribution. If I have missed something that does take care of
    this, perhaps someone will send it to me off list.
    
    Thanks,
    
    
    
    Rodney Myrvaagnes                                  J36 Gjo/a
    
    
    "Curse thee, thou quadrant. No longer will I guide my earthly way by thee."  Capt. Ahab
    
    
    

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Join NavList

    Name:
    (please, no nicknames or handles)
    Email:
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
    Email:

    Email Settings

    Posting Code:

    Custom Index

    Subject:
    Author:
    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site