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    Re: Latitude by Lunar Distance
    From: Lars Bergman
    Date: 2006 Oct 18, 08:59 +0200

    Some comments on George's "adding together 14 numbers, each varying
    randomly in the range between -.05' and +.05' ", in [NavList 1433]. 
    
    As the variation in each number is due to rounding error, we can assume
    a uniform distribution for each variable. The standard deviation of a
    uniform distribution is the interval length divided by sqrt(12), i.e. in
    this case 0.1'/sqrt(12)=0.03'. Adding 14 such distributions results in a
    nearly normal distribution with standard deviation 0.03'*sqrt(14)=0.1'. 
    
    In such a normal distribution, the probability of an error in excess of
    0.19' is 6%, and 68% for an error less than 0.1'. This corresponds
    pretty well with George's brute-force simulations, as it should.
    
    With Frank's assumed distance measurements within 0.1', no timing errors
    and presumably negligible almanac data errors, furthermore assuming a
    "good cut" between the lines; we get a resulting standard deviation of
    say 0.08'. Using a "positional error multiplier" of 60 gives us a "less
    than 6 miles error" with about 80% probability, less than 9 miles with
    95%. So I think Frank's claim is reasonable, given the stated
    preconditions. 
    
    Frank could also claim that although there is 20% probability to have an
    error above 6 miles, there is as well a 20% probability that the error
    is less than 1.2 miles!
    
    Lars
    59N 18E
    
    
    
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