# A GPS Uncertainty Calculation

1. Aug 23, 2016

### Robin64

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.

2. Aug 23, 2016

### Staff: Mentor

Hi Robin64, welcome to PF!

What do you mean by total uncertainty for the trip. The 15 m uncertainty is an uncertainty in position, but a trip isn't a position. Are you interested in the uncertainty of the final position or in the length of the path or what?

3. Aug 28, 2016

### Robin64

I should have been more clear, I'm speaking with respect to how a bicycle GPS computer calculates the total distance for a trip, wherein the total distance is the sum of the distances measured with a given sampling frequency (my computer records GPS data once per second.).