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    Re: Combine DR and celestial LOP
    From: Greg Rudzinski
    Date: 2013 Mar 30, 14:33 -0700

    John,

    See the attached plot with given 1 sigma variables:

    1. Standard DR with circles of uncertainty.
    2. Bayesian DR with circles of uncertainty and LAN EP
    3. Running fix.
    4. Shaded areas of uncertainty (asymmetrical) which combines the Bayesian DR circle of uncertainties with the LAN LOP uncertainties.

    If the uncertainties are unknown then the Bayesian EP stands. If known then the center of the area of uncertainty should be the MPP. Right ?

    Greg Rudzinski

    Re: Combine DR and celestial LOP
    From: John Karl
    Date: 2013 Mar 30, 10:45 -0700
    In the 1960s and 70s the Bayesian theorists had the same trouble getting their ideas across -- don't assume info that you don't have. This is not an mathematical concept. It is one of rational reasoning.

    The point is that in the LOP/DR estimation problem, (unlike for altitude measurements) we do not have a knowledge of the probability distribution surrounding the EP. To have such a meaningful EP error distribution it would be necessary to make many measurements comparing the EP to the true position under exactly the same heading, distance, leeway, and current set & drift conditions. Moreover, during a long run, conditions change requiring time-dependent distribution.

    Because we don't have this probability distribution, it's not a probability problem. It's an estimation problem, making the best prediction possible, using all the info we have -- and no more than that.

    Frank's example (post#23098) is a probability solution to an estimation problem. And even there, he assumes nearly equal standard deviations for the LOP and the EP -- far from true in practice. (BTW, I've presented this case on post #22959.)

    Well for the irrelevant academic fun of it, I've attached MPP results for the LOP/EP probability problem. Just like Frank's example these assume EP distributions that don't exist. These are for those interested in math, not for the practical navigator.

    I'd be happy to run off other examples if anyone wishes,
    JK

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