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Re: Still on LOP's (mea culpa)
From: Michael Wescott
Date: 2002 Apr 26, 00:48 -0400
From: Michael Wescott
Date: 2002 Apr 26, 00:48 -0400
I wrote:
> Sorry, but Steven Tripp's calculations don't find the MPP. They find
> the least squares point, a computationally more tractable exercise and
> in this case, they aren't the same.
And I was wrong.
So much for my credentials ...
Given that each observation comes from the same Gaussian distribution
the joint probability density is proportional to
exp( -(d1**2 + d2**2 + d3**2 ... ))
where dn is the distance from a point to LOP number n. So it's
a matter of minimizing d1**2 + d2**2 + d3**2 ... to get maximum
joint prob density or MPP. In other words it's a least squares problem.
So Steven Tripp, Trevor Kenchington et al. were correct that the MPP is
not the center of the inscribed circle.
I still wonder what the Nautical Almanac meant in that article ...
--
Mike Wescott
Wescott_Mike@EMC.COM
