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    Re: Fix Maximum Probability Positions
    From: Hewitt Schlereth
    Date: 2013 Mar 24, 14:13 -0700

    John -
    
    You wrote, "But the traditional advancing of the previous LOP to the DR position, ..."
    
    This is a puzzling statement to me, and may not be what you mean.
    
    In what you term the 'traditional running fix,' (TRF) an LOP is not advanced 
    TO the DR. The earlier LOP is advanced the distance and direction run between 
    DRs. The earlier LOP virtually never lands on the DR plotted for the time of 
    the sight for the most recent LOP.
    
    Hewitt
    
    Sent from my iPad
    
    On Mar 24, 2013, at 12:52 PM, "John Karl"  wrote:
    
    > Geoffrey:  Thanks for your response.  Here's my answers:
    > 
    > From GK:
    > In figure 1 of your paper, you show a circular area of uncertainty around 
    your DR, which given no other information is reasonable enough.  But in 
    figure 5 you show an elliptical area of uncertainty, for which I can see no 
    justification.
    > 
    > From JK:
    > We’re assuming that with no other info, the DR uncertainty grows equally in 
    all directions.  After the first DR position with the circular symmetry,  
    Figure 2 starts with the oval narrow dark-blue line, its width uncertainty 
    determined by the LOP’s accuracy (for CN), and its length uncertainty formed 
    by the previous DR uncertainty’s size and shape (light blue).  It grows all 
    directions in size while retaining this the oval shape.
    > 
    > From GK:
    > Suppose, in figure 5, your course had been along the LOP1 so that DR1 was in 
    fact on LOP1. What would your area of uncertainty around DR1 look like then? 
    Since your original DR started out as a point (as shown in the figure) it 
    would be circular, just as in figure 1.
    > 
    > From JK:
    > It would still be oval, with it’s long axis parallel the LOP1, because it 
    grew from expanding equally it all directions from the oval narrow dark-blue 
    section on LOP1.  The uncertainty area would only be circular when the origin 
    of the DR run is a true fix of two or more LOPs.  So in Figure 3 all the DR 
    uncertainty areas are oval.
    > 
    > From GK:
    > The point about advancing an LOP along the vector of your course and 
    distance run is that it does not create a new DR position, as you attempt to 
    do. It retains the LOP as an LOP, but makes use of the estimated course and 
    distance run information in a reasonable way to re-locate the LOP.
    > 
    > From JK:
    > The estimation approach uses all available info, makes no unnecessary 
    assumptions, and no contradictions.  (This seems to be a difficult principle 
    accept.)  After a DR run with its associated uncertainties (in all 
    directions), we are indeed at a new DR location.
    > 
    > But the traditional advancing of the previous LOP to the DR position, and 
    placing RFIX at its intersection with the new LOP, makes a very unreasonable 
    assumption – it can even be viewed as a contradiction:  As I’ve written many 
    times this tradition assumes that our reckoning over the last run has a 
    perfectly accurate component perpendicular to the advanced LOP, while at the 
    same time, has a perfectly inaccurate component along that advanced LOP.  
    Furthermore, the selection of these components is entirely dependent on the 
    orientation of the advanced LOP, which obviously has no connection whatsoever 
    with DR errors along the run between LOPs.  Apparently, tradition has faith 
    that the stars know how to command the drift and currents to force perfection 
    on one component of our DR track, but not the other.
    > 
    > From GK:
    > Celestial navigation is not actually a method of navigation. "Celestial 
    navigation" is a misnomer. "Celestial navigation" does not give you course 
    steered, distance run, or your most probable current position, which is what 
    "navigation" is about - having a good idea where you are at any given moment 
    in time. Position fixes using celestial bodies are a way to get an 
    independent check on your DR position. The navigation method used is actually 
    dead reckoning first, last and always.
    > 
    > From JK:
    > Doesn’t “navigation” include all types, from GPS to depth contours, to spotting of land birds?
    > 
    > From GK:
    > It follows then that polluting your celestial fixes with where you 
    arrogantly think you are is a dangerous way to proceed. It throws out the 
    independent check.
    > 
    > In your figure 5, if your LOP2 is good, then that should give you cause for 
    concern that your course steered was not what you thought it was. There may 
    well be a current flowing to the East which you had not suspected. You, 
    however, are not treating CN as a check on your DR, you are using CN in 
    combination with estimated course and distance run to create a DR, which - I 
    respectfully submit - is dangerous.
    > 
    > From JK:
    > The EPRF does not pollute information, it uses all known info, and no more, 
    i.e., it doesn’t invent any info (like the TRF does with its perfect 
    perpendicular distance between the LOP and its advanced version).  In the 
    estimation approach when the DR is updated with a new LOP, it usually doesn’t 
    fall on the DR location (very unlike the TRF, where without justification the 
    advanced line is always plotted exactly through the DR location).  It’s the 
    EPRF that gets an indication of error (the distance between the new LOP and 
    the DR location).  In contrast, it’s the traditional running fix that ignores 
    this independent check – and with that advanced LOP drawn exactly through the 
    DR it’s certainly not independent of it!
    > 
    > Furthermore, since the RFIX distance-to-the-DR location is largely 
    determined by crossing angles of the LOPs, that measurement is pretty 
    irrelevant for evaluating the DR error.  So for these reasons, it’s the 
    traditional running fix that does a darn poor job revealing the DR error. 
    > 
    > IN SUMMARY:  The EPRF uses all available info, makes no unjustifiable 
    assumptions, and makes no contradictions.  The TRF makes assumptions that are 
    clearly false, and gives unrealistic estimations (some zero, some hundreds of 
    miles) in arbitrary directions of the dead reckoning errors (determined only 
    by the stars).
    > 
    > BTW, one traditional example of the EPRF is the old consecutive noon-sun 
    latitude sights.  They give consecutive parallel LOPs of latitude, with 
    longitudes determined by dead reckoning.  The updated ship’s position is 
    plotted by dropping a line from the previous DR position perpendicular to the 
    new latitude LOP.  Nobody’s ever complained about that.
    > 
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