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    Re: Raw data for bubble
    From: Bill B
    Date: 2007 Mar 08, 23:24 -0500

    > Bill wrote:
    >> ... my preference is to plot the observations against
    >> time and use the actual Hc line from the beginning and end to establish a
    >> slope to fit the points to and identify outliers.
    Peter responded:
    > Where does this slope comes from? It sounds as though you are taking
    > the first and last observations and establishing a line between them?
    > If so, why would these sights have any authority to be used to compare
    > others with? Why would this slope have any relationship with the
    > actual slope, apart from when the sights are without fault, the nature
    > of the thing we are trying to find?
    > Or do you mean that you establish the body's actual apparent rise or
    > fall and use this slope to compare the pattern of sights with - this
    > is the method I understand and use.
    The second paragraph is what I mean. Take the Hc (calculated elevation, not
    Ho--observed elevation) from your AP every 4 to 5 minutes and plot that
    slope. Fit that slope to the observations.  Then you are working against a
    known and can more easily detect outliers.
    >> Far better than linear regression IMHO.
    > Using the actual slope should be more useful than using the pattern of
    > sights to create a line of best fit to suit that data. With few sights
    > even one outlier can significantly skew the results of linear
    > regression. Using the actual slope enables such an outlier to be
    > identified and discarded.
    Exactly. I have used Excel to compare the the slopes of calculated altitude
    (Hc) versus  Ho (observed altitude).  When comparing the observations to the
    Hc slope, the stray sheep often stick out like a sore thumb.  They are much
    harder to identify compared to the linear regression slope for obvious
    reasons.  The two slopes can be significantly different.
    >> On the other hand, when I had horrible horizons on Lake Michigan but guessed
    >> at the hidden horizon line, then averaged and posted the results (very close
    >> to Hc) you quipped it was luck, one could not trust results with a sigma
    >> that large. 
    > Such a 'horrible horizon' could lead to a systematic error. This would
    > not be resolved via methods such as comparison of slope with sights,
    > but could be amenable to correction via methods to resolve systematic
    > error.
    Agreed.  In this case, the horizon had a white streak perhaps < 4 minutes in
    height obscuring it day one, over 10 minutes height and against dunes day
    two.  At first I thought it was a waste of time, but then reasoned in the
    real world (sans GPS. Loran etc.) one might have to work with that.  I then
    tried to figure proportions between the real horizon and upper and lower
    limits of what I could observe and eyeball the lower limb to that spot.  The
    horizon to the north was clear, so I followed that into the white band.  I
    also used seat-of-the pants dip short for craft where I could see the hull
    and waterline to establish a ratio.  For reasons unknown (glare vs
    backlighting) there were times I could grab a horizon from masts or hulls
    cut off by the horizon and swing it over.  A guessing game.  All results are
    compared to GPS locations.
    Results of day one:
    All observations:
    Mean error, 1.7' away
    Sigma 1.1'
    1 outlier removed:
    Mean 1.35 away
    Sigma 0.8'
    Results of day two:
    Mean error 0.9' away
    Sigma 8.3'
    Day two I would class as better lucky than good.  Not much confidence in the
    location with that sigma, especially if coupled with another like LOP to get
    a fix. But in the land of the blind, the one-eyed man is king.
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