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    Re: A simple three-body fix puzzle
    From: Gary LaPook
    Date: 2010 Dec 19, 00:46 -0800

    I had written:

    Or, if you do get three stars, then just accept that the third line is mainly useful as a check of the two body fix to find gross errors so that you can have more confidence in your fix. Aircraft GPS units are required to have RAIM, Receiver Autonomous Integrity Monitoring, so that a pilot can be sure that the accuracy of the GPS position is within strict narrow limits to allow an instrument approach to a runway hidden in the clouds. It has to take you to the center line of the runway and you have to know that it is accurate enough to do that so that you don't go flying into a school. To do this you must have at least 5 satellites in view at good azimuths. This is one more than required for a three dimensional fix and the GPS checks the pseudorange expected from the extra satellite from the computed fix and if the pseudorange differs too much the unit flags the fault and you have to use a different navigation system to complete your flight. The third star LOP serves the same function as the fifth pseudorange confirming the accuracy of the two body fix.

    If you are sailing near to danger then don't use the center of the triangle as the fix, use the point closest to the danger and plan your course based on that while keeping in mind that you might be outside the triangle, and closer to the danger, by three sigmas. It is perfectly valid to use any of the corners of the triangle as your fix since each corner is a valid two body fix which you would be perfectly happy with if you had only been able to get two stars.

    I know that adding more LOPs to the solution will also mathematically improve the accuracy of the fix a bit but since a two body fix is accurate enough for practical navigation there is no compelling need to use the third (or fourth or fifth) LOP for this purpose, just use the extra LOP for confidence in the two body fix. There is no good reason to polish the cannonball.


    It's nice to find myself in good company, Bowditch agrees with ME!

    See attached.


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