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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: The Darn Old Cocked Hat - the sequel 1
From: Geoffrey Kolbe
Date: 2013 Mar 18, 14:28 +0000
Brad Morris wrote:
Well now Brad, it is of course intuitive common sense that the order in which you take the LOPs does not affect the final Most Probable Position. But as we have already seen, just because it is 'obvious' does not make it so.
It may well be that the order in which you take the LOPs does not matter. It may well be that when you do the sums, the Most Probable Position will be in the same place regardless of order you plot the LOPs. It may well be that the Bayesian approach gives exactly the same Most Probable Position as the Frequentist approach.
But I say to you that unless you can break the logic of what I wrote, and a consequence is that the Most Probable Position does depend on the order in which you plot the LOPs, then that is a mighty interesting discovery!
Geoffrey Kolbe
From: Geoffrey Kolbe
Date: 2013 Mar 18, 14:28 +0000
Brad Morris wrote:
Hi Geoffrey
I agree with the premise that there will be a bias when drawing the third LOP towards the intersection of the first two.
But which LOP comes last is arbitrary. Repeat the exercise 3 times, with a different LOP last.
All three biases are now towards the vertices of the opposing two LOPs.
Now where is the Most Probable Position?
Brad
Well now Brad, it is of course intuitive common sense that the order in which you take the LOPs does not affect the final Most Probable Position. But as we have already seen, just because it is 'obvious' does not make it so.
It may well be that the order in which you take the LOPs does not matter. It may well be that when you do the sums, the Most Probable Position will be in the same place regardless of order you plot the LOPs. It may well be that the Bayesian approach gives exactly the same Most Probable Position as the Frequentist approach.
But I say to you that unless you can break the logic of what I wrote, and a consequence is that the Most Probable Position does depend on the order in which you plot the LOPs, then that is a mighty interesting discovery!
Geoffrey Kolbe
