Navigation system technology
Regarding some of the posts on this thread, here is a quick background on how Nav systems work (thought it might help clear up some mysteries).
There are three positioning technologies inside a Nav system:
Gyroscope (so the vehicle knows which direction it is pointing)
Wheel sensor (so the vehicle knows how fast it is travelling and how far it has travelled)
GPS (so the vehicle knows it's absolute location and - only possible when moving - it's direction of travel, speed and distance covered).
Can't speak about the latest systems but certainly until recently, GPS was not necessarily the most important sensor (indeed, early nav systems worked before GPS became publicly available). This must still be true to an extent because the vehicle never "loses" itself even after passing through tunnels or when travelling around cities with lots of high-rise buildings (where you get what is known as the "canyon effect" in which the GPS receiver can no longer see enough satellites to compute a position). Furthermore, until 2000, GPS signals were deliberately skewed by the American govt using a system called SA (Selective accuracy, I think) so that the position could never be guaranteed to be accurate to more than 100m - and that's not very accurate. If your nav system software was designed before 2000 it just won't be paying much attention to the GPS signal, it will assume that the postion data is simply not very accurate. GPS will be used for initial fixing and periodic realignement (and, of course, accurate speed and direction data, which were largely unaffected by SA).
With this background (GPS deliberately made innacurate, high-rise buildings, tunnels, etc) two key technologies were developed that made Nav systems possible - and those technologies are still used today. The first is map matching. With this, the nav system is constantly collecting a profile of the road from the sensors and comparing it to the map data. For example, if you just drove through a 130 degree left bend, went 125 metres and then through a 45 degree right bend then you must be ... there .. because that's the only place on this road where those two bends occur in that geometric layout. Map matching is always re-aligning the nav system to your exact location by comparing sensor signals with the map data. If you have the incorrect tyre size entered in the nav system, then I could imagine that map matching would quickly break down leading to innacuracies.
The scond technology is very simple but very neat, it is called route snapping and all it does is say "Wherever you are, you have to be on a road if you are moving any distance". That is why you will see posts that say "my system thinks I am in the adjacent road" or "my nav system is about 300m behind my actual location on the road" but rarely "my system thinks I am in my back garden" or "my system shows me ploughing through the adjacent field". Of course, nav systems also recognise the concept of "off-road" but once you start moving any distance and at any speed, it assumes you are on a road and looks on the map for one that is most likely. It only shows "off-road" when there are no candidate roads that fit the vehicle's position. I expect that nav manufacturers rely much more on GPS than they used to to resolve vehicle positioning now that GPS is accurate to around 5 metres or even less.
Two other notes: The gyroscope is critical and one reason is because it is this that allows the system to tell you exactly which exit to take on the roundabout using the "Take the next exit" message - only possible because it knows the exact direction your vehicle is pointing. Blaupunkt systems used to (still?) do this brilliantly. My Becker system waits till I am already off the roundabout and heading down the road before it tells me to leave the roundabout with a confusing "Turn left now" instruction...
Secondly, sorry to contradict a previous post, but nav systems don't use differential GPS. Differential GPS is a combination of a GPS signal and a radio signal (typically broadcast on RDS) that allows the inherent innacuracies in GPS to be calculated out leaving you with a super-accurate position fix - down to a few centimetres on some systems. Before the US govt switched off SA in 2000 and allowed all GPS receivers to instantly achieve 5m or less accuracy, differential GPS was the only way of getting an accurate position. It is widely used for field surveying - and indeed is the technology that allows the map data to be so accurate. Accurate enough for the next great thing: Curevtronic. The ability for the car to swivel the headlights into approaching corners using the map data rather than the steering wheel postion, speed and yaw-sensor data. Whether this works remains to be seen....
Philip