A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Bill Lionheart
Date: 2019 Feb 4, 04:49 -0800
I was looking back over this discussion from October of the MPP started by Dave Pike, as I am revising my paper on the Cocked Hat. It is the "mode", that is the maximum of the probability distribution, sometimes called a Maximum Likelihood Estimate. The probability of any point is zero, so MPP is perhaps a misnomer.
In the conctext of three position lines with independent errors with zero mean, the Gauss-Markov theorem (see eg Åke Björck. Numerical methods in matrix computations, volume 59.
Springer, 2015. Thm 2.1.1) tells us this least squares point is the "best linear unbiased estimate" of the position.
One can say a little more than that in the case where one can assume the errors are Gaussian (that is Normally distributed). For example if each altitude is the mean of a series of sights and you can envoke the central limit theorem.