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    Re: Ellipse of Confidence in position finding
    From: Andrés Ruiz
    Date: 2019 Mar 14, 14:57 +0100
    Fix IS inside EoC
    Fix = intersection of bisectors = CoG( cocked hat) = symmedian =...

    El mié., 13 mar. 2019 a las 15:33, Bill Lionheart (<NoReply_Lionheart@fer3.com>) escribió:
    Another important thing about ellipses. Remember my post with an example where the EoC, the symmedian point, and others give us the wrong position.
    Fix by bisectors

    I had a bit of a look at that thread and saw a lot of confusion.  You get a probability density function and that is correct given the assumptions. As navigators we have sometimes to choose a point estimate from the PDF, for example as departure point for our next dead reckoning. One should always understand a "fix" as just a point estimate of a probability distribution and so consider the risks to navigation of being at the "most dangerous" location within a probability contour.

    I think practically the common reason the symmedian is not a good point estimate is that the variances of the LoPs are different, eg they were obtained from linear regression fit for a different number of altitude observation of the same body. Then we need the weighted symmedian (weighted least squares solution) as our maximum likelihood estimate. It is still inside the cocked hat for three LoPs but it could be anywhere in the interior depending on the weights.

    Bill Lionheart

    fair winds!
    Andrés Ruiz
    Navigational Algorithms
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