# How to find the standard deviation in GPS measurement of latitude and longitude?

Let's say my GPS configuration is said to have a precision of 10 meters. I have taken this as the standard deviation in the GPS measurements. But the measurements that come from GPS are latitude, longitude, and height, whose units are radian, radian, and meter, respectively. Can anyone help me figure out the standard deviation for latitude and longitude in radians with the given accuracy of 10 m for GPS?

• "GPS is said to have a precision of 10 meters." do you have a source for that statement? It is down to number of Satellite fixes and chipset. New GPS chipsets are more precise but there are many factors including weather and surroundings.
– Mapperz
Commented Feb 8, 2023 at 15:53
• I have modified the question accordingly. I'm new to the area of GPS/INS navigation, I appreciate your valuable comment. Commented Feb 9, 2023 at 5:05

1- calculate standard deviation of latitude (sdLat)

2- calculate standard deviation of longitude (sdLon)

3- calculate DRMS = Square Root (sdLat^2 + sdLon^2)

DRMS is radius measure for the error from your point. It defines a circle around the point which should contain the actual value.

e.g. if my point is x,y then the circular distance deviation from the measured x,y will be found by calculating the DRMS

DRMS = sqrt(sdX^2 + sdY^2)

If your device truly does measure as 10 meter resolution, then the DRMS is likely to come out around 10m, but you will likely get a lower DRMS for several reasons.