In reality, a single sensor will probably not be accurate enough to do what you want. Most of what I know is related to AGVs (Ground Vehicles), but I think that some of the same principles apply.
You probably want to use a combination of sensors to get the accuracy that you need. Some of these can be quite expensive.
GPS: A standard GPS module should be able to get you down to about 1m +/- accuracy. If you step up to a differential setup (one station on the ground, one on the plane), then you should be able to get significantly more accuracy, but at a much higher cost. Something like 10cm or even 1cm should be possible (with velocity data), but with a significantly higher cost.
INS: You can supplement your GPS system with intertial measurements. The boom in MEMS devices has made relatively decent solid-state sensors available at consumer prices. Adding accelerometer, gyrometer, and magnetometer data to the GPS data should make the signal more accurate, and account for possible "glitches" in you GPS readings.
Radio-assisted navigation: I'm not entirely up on this, but many airports use a radio-assist to help land the planes. You may be able to research how these systems actually work and implement your own (legally, of course).
For a more detailed look at some of these considerations, I would check out DIYDrones. They have put together some pretty tightly-integrated systems using GPS, INS, Barometers, and a large array of other sensors. They have also tackled some of the difficult filtering challenges that come with multiple sources of data in an airborne system.