Global Positioning System Reference
In-Depth Information
FIGURE 7.6.
The cocked hat. (a) If three LoPs are drawn on a chart, they will intersect
only at a single point for the case of zero measurement errors. In general, they
intersect as shown; the central triangle is called a cocked hat. The probability for the
ship's being inside each area is shown, assuming unbiased, random measurement
errors. (b) A known systematic error can be corrected as shown. The new cocked hat
(defined by dotted lines) is much smaller, and in this case is outside the original
cocked hat (shaded). (c) For four LoPs, the probability of the ship's being inside the
shaded area is 50%.
smaller cocked hat, so that our captain has reduced the size of the most
likely location of the ship—he has reduced his position estimation error.
If a fourth measurement is made and a fourth LoP added to the chart,
then the same type of statistical analysis as before (assuming zero system-
atic error and no bias) leads to the conclusion that the probability of the
