A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Brad Morris
Date: 2013 Mar 18, 10:50 -0400
In your logic, you assume that the intersection of the first two LOPs will not be affected by the addition of a third LOP.
Indeed, the probability distribution from that intersection must also be biased towards the third LOP, just as the probability distribution of the third LOP is biased towards the intersection.
I think you will find that the final MPP ends up in the same location, independent of which LOP comes last.
Brad Morris wrote:
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.Â 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?
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!
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