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    R: Problems with AstronavPC
    From: Federico Rossi
    Date: 2004 Feb 16, 08:17 +0100

    I don't have this book (though I've often read about it on the internet)
    but I'm very interested in the matter of error ellipse and even if I
    found the equation to plot it, I've never been able to find the formula
    giving its orientation with respect to xy axis.
    I would greatly appreciate if you wrote it down for me.
    -----Messaggio originale-----
    Da: Navigation Mailing List [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]
    Per conto di George Huxtable
    Inviato: domenica 15 febbraio 2004 16.16
    Oggetto: Problems with AstronavPC
    Problems with AstronavPC.
    Do any listmembers possess the book (with CD), "AstronavPC and compact
    data 2001-5" or an earlier edition? Or perhaps another version of the
    same thing, published in the UK as "NavPac and compact data 2001-2005".
    What follows will be of interest only to those that do.
    Even better, have any listmembers attempted to implement the procedures
    given, in the chapter "Compact Data-Explanation"; in sections 7.4,
    "Position from intercept and azimuth by calculation", and/or 7.5,
    "Estimated position error"? Better still, does anyone claims to
    understand those procedures?
    I'm not asking whether the built-in program gives the right answer when
    you ask it to "display : plot of position lines". I've no reason to
    think it doesn't, though unable to try it out because it doesn't work on
    my Mac. All I an questioning is the written explanation.
    1. Go to section 7.5, "Estimated position error". This shows how a
    "confidence ellipse" can be calculated, with major axis a, minor axis b,
    and orientation of the major axis "theta". Near the end of the section
    is stated "The ideal situation is to produce a circular distribution of
    errors, with A = B and C = 0, so that the errors are the same in all
    directions." This seems to me to be wrong: to produce a circular
    distribution of errors, I suggest that what's needed is instead for A =
    C and B = 0. Only then would the ellipse become a circle; (a = b, and
    theta becomes immaterial). Does anyone agree (or, more interesting,
    2. A few lines down from the start of 7.5 is stated "The standard
    deviations sigma(L) and sigma(B) in longitude and latitude are given
    by-" and so on. I don't question the value for latitude, but I suggest
    that for longitude, the value given is for standard deviation of the
    East-West displacement, in nautical miles (that is, the "departure"),
    rather than in longitude (which is always expressed in terms of angle).
    3. Toward the end of 7.4 is stated- "If d exceeds about 20 nautical
    miles set L(F) = L(I), B(F) = B(I) and repeat the calculation until d,
    the distance between the position of the previous estimate and the
    improved estimate, is less than about 20 nautical miles".
    In the sentence above, "repeat the calculation" must first require, for
    each body sighted, the following-
    [Using the newly updated values for B(F) and L(F) as Lat and Long,
    rework the calculated altitudes and azimuths, in 7.2.2, 7.2.3, and
    7.2.4, and obtain a new intercept p from (observed alt. - calculated
    alt.). For this to be possible, the original values for dec., GHA, and
    observed altitude of the body must have been retained.]
    It's a pity that there's no specific mention of that necessary part of
    the iteration procedure, given in square brackets
    Then the new values Z and p are collected together for all these bodies
    in the expressions for A to G in 7.4. This allows new values for dB and
    dL to be calculated for a further iteration.
    In 7.4 is the statement- "Additional observations may be included in the
    solution by simply adding the extra terms to the summations A,B,C,D,E,
    and F and calculating dL and dB again." To me, that seems to be rather
    futile, in that it would be impossible to work any further iterations
    using those added terms unless their original values for dec, GHA, and
    observed altitude had been preserved.
    I'm tempted to submit these as suggestions for the next revision of this
    publication by HM Nautical Almanac Office (which must be due soon), but
    before making a fool of myself in front of them by getting things wrong,
    I would rather risk making a fool of myself in front of Nav-L readers.
    Any comments would be most welcome.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone
    at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1
    Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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