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    Combine DR and celestial LOP
    From: Frank Reed
    Date: 2013 Mar 26, 08:43 -0700

    This is an important prior topic in the discussion of John Karl's modified running fix (and by the way, John, your latest attempts at explaining your concept are a considerable improvement!).

    You have been sailing under cloudy skies with limited visibility for a couple of hours. You have been doing careful dead reckoning. You have a DR position which you believe to be reasonably accurate. You put your thumb down on a chart, and you say, "I believe I am here at this latitude and longitude with a roughly estimated probability of two-thirds of being within one nautical mile of this point". So what you have is a position and a standard 1 standard deviation error ellipse (let's make it circular for the first example). Next, the clouds break and you have a couple of minutes to shoot the Sun. You work the sight using the DR position, and you get an intercept of 1.2 nautical miles towards azimuth 090°. From previous experience with sights under these conditions, you believe that your celestial LOP has a probable one standard deviation error of about 1.0 nautical miles. Traditionally, you would not attempt to combine these two sources of information: the DR error ellipse and the celestial LOP do not play well together. But (and here I completely agree with John Karl, in principle) tradition is not sacred. So how WOULD you combine these two pieces of information? 1) An error circle with an estimated 1 s.d. radius of 1 n.m. centered on some point labeled "DR" and 2) a celestial LOP running north-south 1.2 n.m. east of that DR point? There IS a real answer to this that is both mathematically correct and practical, too. And it's almost so obvious that it will seem like no answer at all... Hint: an error ellipse (from any source!) is equivalent to... what?


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