Why does the intersection of only two LOPs give an estimated position?

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Multiple Choice

Why does the intersection of only two LOPs give an estimated position?

A line of position defines all points where one observation is consistent with your location. When two independent observations are used, their lines intersect and you take that intersection as your estimated position. But every observation has some error, so the two lines may cross at a point that is not the true position. Without a third independent observation, you have no way to gauge how big that error is or how the two errors combine. The third line provides a redundancy check and a way to quantify uncertainty. With three observations, you can see whether the lines concur or form a small triangle; you can compute a best-fit position and an error estimate (an error ellipse) based on the known uncertainties of the measurements. So the intersection of just two LOPs gives an estimate, but the third LOP is needed to determine how accurate that estimate is.

A line of position defines all points where one observation is consistent with your location. When two independent observations are used, their lines intersect and you take that intersection as your estimated position. But every observation has some error, so the two lines may cross at a point that is not the true position. Without a third independent observation, you have no way to gauge how big that error is or how the two errors combine.

The third line provides a redundancy check and a way to quantify uncertainty. With three observations, you can see whether the lines concur or form a small triangle; you can compute a best-fit position and an error estimate (an error ellipse) based on the known uncertainties of the measurements. So the intersection of just two LOPs gives an estimate, but the third LOP is needed to determine how accurate that estimate is.

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