Java implementation of https://gist.github.com/amites/3718961

gistfile1.txt

private GPSPoint gpsCentre(Collection<GPSPoint> points) {
	float x = 0;
	float y = 0;
	float z = 0;

	for(GPSPoint pt : points) {
		final float lat = (float) pt.getLatitude();
		final float lon = (float) pt.getLongitude();

		x += Math.cos(lat) * Math.cos(lon);
		y += Math.cos(lat) * Math.sin(lon);
		z += Math.sin(lat);
	}

	x = (float) (x / points.size());
	y = (float) (y / points.size());
	z = (float) (z / points.size());

	return new GPSPoint(Math.atan2(y, x), Math.atan2(z, Math.sqrt(x * x + y * y)));
}