GPS is no longer distorted since decades, at least 15 years.
Sorry, I thought you were using a broad definition of distorted. Nominal accuracy of GPS is 1 - 10 m, depending on conditions, in my experience. I'm not sure where you're getting this idea that it's accurate to 20 cm. That's the kind of accuracy you'd expect with something like DGPS. If this were the case, competitors in the DARPA Urban Challenge wouldn't have needed DGPS and expensive inertial navigation systems. Would you care to offer a citation for this claim?
When I used the term "distorted", I was referring to multipath errors you will get from GPS signals reflecting off buildings. This, combined with low satellite visibility makes GPS-only localization a poor choice in urban environments.
With visible land marks you don't need GPS, or in other words it wont be helpfull.
Unless you have a map with absolute coordinates of those landmarks you still can't position yourself on the globe, only relative to those landmarks. With GPS you can create a map as you explore (SLAM), and refine the absolute locations of those landmarks over time using sensor fusion and filtering (GPS, LIDAR, INS). With survey results (as you say, millimeter level precision) as ground truth, we can say this method achieves sub-decimeter accuracy in global pose.
Sorry, but not being able to pinpoint your position in a city down to less than a centimeter is fail (for a robot).
Depends on what your goal is. If your only goal is to get a position, then there are better techniques. If your goal is a mobile robot that can move down a sidewalk without $60,000 worth in sensors, then sub decimeter is enough. With a wheel base of 0.6 m and an average sidewalk width of 1.5 m, a robot traveling down the center can easily be off 10 cm either way and still succeed in its operation. Typical error I've seen using the described system is around 6 cm with a minimum of 0.12 cm. This is enough to navigated sidewalks, crowds, and even through doors.
Hm, or you don't have access to accurate maps. Here in germany you buy them or even get them for free at the land-registry (and those maps are accurate below a milimeter level)
The robot makes the map itself, as I described.