NavList:

Geoffrey, you wrote:

"In conclusion, I was able to get reliable fixes
far more quickly by moving away from the
traditional fix using three objects about 120°
apart with its resultant cocked hat, and adopting
a strategy of taking sightings on four objects,
each near one of the Cardinal points. I know that
if the box formed by the position lines is
substantially square, the errors are far more
likely to be dominated by systematic rather than
random errors. With a tradition
three-position-fix you never know if random or
systematic errors are dominating, so you can
never be sure just how accurate your fix is."

 

Very nice. A few months ago, I wondered in a message on the list about the statistics of this. Clearly, with three sights you can't eliminate systematic error unless you know in advance somehow that it is present. Your method with four sights at cardinal points makes it obvious graphically that we're dealing with systematic error. I think it's probably true (and probably obvious) that you would get even better results with more sights, but I haven't looked into the statistical details. In the general case, I think the approach would be to vary the fixed correction until the box surrounding the crossing points of the various LOPs is as small as possible. This should work even in cases at arbitrary azimuths and with random errors, too.