My Audi A4 (2003, 1.9 TDI AVF engine, manual) sometimes decides to stall while driving, so far four times this winter. Engine will start successfully after a minute or two, otherwise I can hear it try but it kinda sounds like it gets no fuel. Once it starts it works just fine until it decides to stall again. This only seems to be happening in colder temperatures (5 and below degrees celsius) and once it starts the smoke coming out of exhaust is darker for a second, then returning to normal - though I've only seen the smoke once. It seems to stall only while driving between 10-~70km/h and right before it stalls it will sort of shake a little.
The ECU does not seem to be reporting any errors. I have checked it (Engine, Cent. Electrics, Immobiliser just in case as well) after it has started up and worked for a few as well as immediately after it stalls, without turning the engine on.
It has stalled one time last winter, however me and others believed it would just have been bad quality fuel.
So far replaced the fuel filter, but it has not helped. A few local mechanics have had a look at the fuel lines and they have not confirmed any air bubbles or similar. Next on my to-do list is to replace the crank shaft position sensor, as it seems that some people (on the Internet) have reported it to be causing similar issues.
What could possibly be the problem? Would there be a checklist of what to inspect in cases like this?