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    Re: Compare Methods: Lat/Lon Near Noon
    From: Antoine Couëtte
    Date: 2021 Oct 1, 22:26 -0700

    Good Morning Ed,

    Still referring to the Enclosure of my last post as a "Ref Document" here-after.

    In reply to your own last post , and in further reference to your last reply to Tony we all seem to fully agree that, for any initial "Quadratic curve" computation, you do not need specific individual Azimuths for any of the observations. Simply because this "Number crunching quadratic curve" process is the mere mathematical transcription of the hand drawn curve process.

    You now want to "refine" your approximation from your first LAN result ... That now seems to be your main concern, which actually had earlier escaped my attention.

    The only realistic way I know of "to attempt improving" your initial LAN fix result is to treat it as a "many body fix" using your LAN Fix as an "assumed position" exactly as Peter Hakel did it in his reply to Frank's Initial problem.

    In this way, yes, you treat each individual observation as a classical one and you do need to process each individual Azimuth. But, be aware that the effects of GDOP will be quite high since all Azimuths are extremely close over your entire Observations set. (See Ref Document 4.1.2.1) .

    Now your new end result may or may not differ from your "quadratic solution" LAN result.

    (1) - Restraining Regression to 2nd Order in T (i.e. restraining it to UT**2 terms) is not sufficient in this example to get the most of this entire data set because there are already in it some "hidden / concealed" non symmetrical effects which can be only partially "detected" by a 2nd order quadratic Regression. I am suspecting that this is the main reason which accounts for the difference between Peter's both positions here-after :

    UT of LAN (from both “noon_motion” and “transit”): 16:37:29

    Lat: N 37° 10’
    Lon: W 70° 11

    From the least-squares-based NA method ("many-body fix"):

    at 16:37:29 (LAN)
    Lat: N 37° 11’
    Lon: W 70° 12’

    There is a small difference of approximately 1 nm in his results, which is a quite minor and fully acceptable one. Still, we should consider the "many-body fix" to be slightly more reliable than the initial LAN fix, in spite of its quite significant Geometric Dilution of Position (GDOP).

    Peter, if you can bring your own view-point here, that would be great. :-)

    (2) - If you use a higher order fit with respect to UT (See Ref Document 4.4.3), then you can see that a "many-body fix" method does not improve at all the LAN Fix because this one is already "spot on" (See Ref Document 5.2) given the more powerful higher order regression used here.

    As a full summary : in the process of attempting to improve your initial LAN Fix, I know of no other method than running a plain traditional "Many-body fix" process starting with your first LAN result as an assumed position ( or more accurately an "assumed vertical"). And definitely Yes, if you use such a "Many-Body" Fix solution - (is it really necessary in the real world once you already have your "quadratic regression" LAN results?) then for each pair of observation data (UT , H) you now need an accurate knowledge of each individual Zn. Keep in mind though that such specific Zn's configuration is subject to quite significant and adverse GDOP here.

    Again, hope it helps,

    Best Regards

    Antoine

       
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