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
    Name or NavList Code:
    Email:
       
    Reply
    Re: Taking four stars for checking accuracy of fix - and "Cocked Hats"
    From: Paul Hirose
    Date: 2008 Aug 03, 22:14 -0700

    George Huxtable wrote:
    > 34º 16.7', 34º 21.0, 34º 25.4, 34º 32.0, 34º 38.6, 34º 46.3, 34º 49.9, 34º 
    > 58.3, 34º 58.8.
    
    I did a least squares solution for altitude at T0 and rate of change
    with my HP 49G. Like many calculators nowadays, it can solve systems of
    equations. Here, we have are nine equations of y = xm + b, where y is 
    the observed altitude, x the time offset of the observation from the 
    nominal time T0, m the unknown rate of altitude change, and b the 
    unknown "best fit" altitude at T0. For example, for the first two 
    observations, the equations are:
    
    34º16.7' = -4 * m + b
    34º21.0' = -3 * m + b
    
    After setting up all nine equations and solving by the method of least 
    squares, the first data set gives:
    
    5.727'/minute, 34°38.56' at T0 (38.56)
    
    
    > 76º 29.7, 76º 39.2, 76º 42.8, 76º 48.2, 76º 57.8, 77º 03.1, 77º 05.9, 77º 
    > 12.8, 77º 19.5.
    
    6.018'/minute, 76°55.44' at T0 (55.44)
    
    
    > 42º 47.3, 42º 53.3, 42º 54.9, 43º 05.8, 43º 12.4, 43º 16.9, 43º 24.4, 43º 
    > 29.2, 43º 37.9.
    
    6.337'/minute, 43°11.34' at T0 (11.34)
    
    
    > 11º 18.0 , 11º 25.9, 11º 30.8, 11º 39.8, 11º 42.7, 11º 44.1, 11º 51.3, 11º 
    > 58.6, 12º 05.3.
    
    5.543'/minute, 11°41.83' at T0 (41.83)
    
    
    > Yes, it's better to calculate the slope thanc trying to determine the 
    slope
    > of the fitted straight line from the data points themselves; no question
    > about that.
    
    Are you sure? My results fail to confirm that. The procedure above is
    equivalent to plotting the points, then drawing the straight line that 
    best fits the points. Both the slope and the vertical position of the 
    line are adjusted to achieve that fit.
    
    What you seem to be saying is that if the slope is constrained to the
    known correct value of 6'/minute, and I'm only free to move the best fit
    line up or down, the result is more accurate. So I tried it.
    Substituting 6'/minute for m, the first two equations in the first data
    set become:
    
    34º16.7' = -4 * 6.0 + b
    34º21.0' = -3 * 6.0 + b
    
    Continuing in that manner, we get nine such equations for each data
    set. Each one gives a value for b. Finding the "best fit" simply
    requires taking a mean. What I get, for all four data sets, are
    altitudes identical to the previous ones! (By "identical" I mean they
    agree to the .01'; I didn't write down the values any more precisely.)
    At least in this case, it seems that knowing the correct slope of the 
    line is no benefit.
    
    
    > And it's better than simply averaging those changing altitudes
    > over the time period, if the observations were unequally-spaced in 
    time. (If
    > they were equally spaced, you would arrive at exactly the same answer).
    
    These observations are equally spaced, and I verified that a simple mean 
    gives the same result as a least squares fit.
    
    -- 
    I block messages that contain attachments or HTML.
    
    --~--~---------~--~----~------------~-------~--~----~
    Navigation List archive: www.fer3.com/arc
    To post, email NavList@fer3.com
    To , email NavList-@fer3.com
    -~----------~----~----~----~------~----~------~--~---
    

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Get a NavList ID Code

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

    A NavList ID Code guarantees your identity in NavList posts and allows faster posting of messages.

    Retrieve a NavList ID Code

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

    Email Settings

    NavList ID 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