NavList:

George writes:

Take an anchored vessel at a precisely known location, say
by GPS.

Measuring the altitude of a star does not alter that location. The probability of the observation being towards or away depends only on the random scatter of the observation itself, being precisely 50:50. Instead of actually measuring it, me might just as well simulate the observation by tossing a coin. And we could simulate the observations of the other two stars in exactly the same way.

In which case the probability of the three observations being in the same direction, TTT or AAA, is exactly the same as the probability of getting three coins the same (all-heads or all-tails), which is 1 in 4.
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Ah, Ha, that’s what I thought and suggested in my [14746] post.
George is knowingly at the exact fix location acquiring many LOPs, and plotting many cocked hats from them. Thus he’s computing the in/out statistics of the exact known position relative to the plotted cocked-hat locations. (This is very similar to simply measuring the random error distribution of his LOP measuring gadget.) In short, he’s doing the opposite of what navigators do:

He’s using his known position to measure the cocked-hat probability distribution. Navigators measure one cocked hat and estimate the MPP from a priori knowledge of the gadget’s error distribution.

These are very, very, different things. And this highlights the significance of the Bayesian approach to estimation theory. It may seem subtle, but the difference is rational thinking -- which isn’t always easy for many of us (including me).

JK

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