Stationary GPS is a little bit different. The receiver is planted in a location whose coordinates can be very carefully determined via more traditional survey methods. Combine this with some other technologies, and you can get very precise and accurate results. For example, one of the factors that degrades the accuracy of GPS is atmospheric effects. With a network of carefully surveyed stationary GPS units, we can correct for atmospheric effects by seeing how 'off' the various units are compared to normal, and to each other. There are other sources of error, but the point is that GPS error can be greatly reduced when you already know where you are.
Now, in this case, the 'stationary' GPS units are actually moving at a very slow rate. With the error corrections described above, once all the other errors are accounted for, what remains is error due to actual movement of the GPS. I can't see the full text of the paper, but probably what they have is a statistical model that says the GPS units are moving by a certain amount each year, and a confidence level, and all of that.
So, to your last point: if you want to improve the GPS accuracy of your lawn bot, you need only to install a stationary GPS receiver on your house, survey its location very carefully, and attach a transmitter to turn it into a 'GPS base station' that your robot's GPS will use as a local reference to improve its GPS fix. (You can buy a GPS base station from someone like Trimble; they're often used for construction and the like.)