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Given a handheld GPS with an accuracy of roughly 2 meters (verified through field tests) and an observation with an HDOP of 1.2, the accuracy of that one observation should be within 2 meters X 1.2 of actual horizontal position, correct? Where can I find documentation of how this works? That is documentation that shows reported device accuracy multiplied by the HDOP yields horizontal accuracy.

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DOP relates the User Ranging Error (URE) to position coordinates error (PCE):

PCE = URE * DOP

It seems you already determined both PCE (2 m) and HDOP (1.2). The only unknown left is URE, which is this case equals URE = HPCE / HDOP = 1.67 m.

Now with that information at hand, you can assume the URE will not change, then predict the PCE of interest given DOP predictions, as given in GPS survey planning software.

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