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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