NavList:

Hi Frank,

I'm not sure anyone ever answered your question below, so just in case...

The best fix is just a weighted average of the DR position and the LOP, where the weight is one over the error squared of the measurement. For the DR position the error ellipse is symmetric so the error along the line which is perpendicular to the LOP is 6 nm and the weight is 1/36. For the LOP the error is 2 nm and the weight is 1/4. Then their weighted average gives an estimated position which is 2.7 nm from the DR position along the line perpendicular to the LOP, or only 0.3 nm from the LOP.

The error ellipse of the estimated point has a half width of 6 nm parallel to the LOP since the only information in this direction comes from the DR position. The half width in the direction perpendicular is the square root of the variance of the above weighted average (which is given by one over the sum of the weights). This gives sqrt(3.6) = 1.9 nm, which is a small improvement over the error on the LOP.

Cheers,
George B

p.s. I confess to looking up the formula for the weighted average variance in Wikipedia.

p.p.s This gives me an idea for finding the MPP of the cocked hat without resorting to a least squares fit...
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