Let's say I have a GPS unit that reports an "accuracy" (this is what the GPS device reports as the uncertainty in the measurement of position) of 15ft. I travel some distance, with the GPS reporting a position every second. At the end of 1000 seconds I arrive at my destination. For the sake of the analysis I'm going to assume that the "accuracy" is constant and restricted to a plane (I'm not concerned about elevation changes and uncertainty associated with elevation measurement). I'm also going to assume that uncertainty is a function of radius, and angle, where angle is measured as the angle between my actual path and the segment between my current reported position and my last. I'm assuming that uncertainty in angle is uniformly distributed over 2π radians. My last assumption is that the correct way to calculate the total uncertainty for my trip is through quadrature; however I'm not quite sure what form each term in the quadrature takes. Can someone give me some insight? Note that I'm not concerned about the other sources of GPS error.