Triangulating GPS coordinates

Question

Say you have n GPS coordinates how could you work out the central GPS point between them?

Answer 1

In case it helps anyone now or in the future, here's an algorithm that's valid even for points near the poles (if it's valid at all, i.e. if I haven't made a silly math mistake ;-):

1. Convert the latitude/longitude coordinates to 3D Cartesian coordinates:

   x = cos(lat) * cos(lon)
   y = cos(lat) * sin(lon)
   z = sin(lat)
   

2. Compute the average of x, the average of y, and the average of z:

   x_avg = sum(x) / count(x)
   y_avg = sum(y) / count(y)
   z_avg = sum(z) / count(z)
   

3. Convert that direction back to latitude and longitude:

   lat_avg = arctan(z_avg / sqrt(x_avg ** 2 + y_avg ** 2))
   lon_avg = arctan(y_avg / x_avg)