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    Re: running fix + lunar
    From: Andrés Ruiz
    Date: 2010 Nov 18, 20:03 +0100

    Hi Frank,
    The "practical circumstance", is: one is sailing with known course and
    speed and to obtain a fix uses two altitudes with a sextant and a
    lunar distance at different times ant the chronometer or on-board
    watch has an error. Please Paul, correct me if I have not
    misunderstood your example.
    If the unknowns are: time, latitude and longitude,
    the general differential equation is: dF = ∂F/∂t dt + ∂F/∂B dB + ∂F/∂L dL
    and one can combine navigational data from different sources, this is,
    F could be:
    - Altitude
    - Lunar distance
    - Star-star distance
    - Azimuth (measured on land with an astronomical instrument)
    - Bearing
    - Distance
    - Horizontal angle
    - Radio-bearing
    dF = Fobserved - Fcalculated and the partial derivatives are obtained
    with finite differences.
    The easier way to obtain a confidence ellipse is using the covariance
    matrix of the system of equations.
    Metcalf (see IoN journal) use celestial and coastal lines of position
    to obtain a fix, and a program is available for free at my web site.
    Andrés Ruiz
    Navigational Algorithms

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