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Is it possible to understand what commands had been given to an aircraft if you look at its track containing information about lat, lon, altitude, speed and course? Is there anyone who has already tried to do this thing?

What do you think can be a problem? I suppose it may be ambiguous sometimes. For example, heading command and proceed to a fix command can both result in changing heading.

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No - there are just simply far too many permeation's of instructions.

For example - an aircraft climbs 1000ft. This could be because:

  1. It has just received an instruction to do so
  2. It previously received an instruction to do so at a certain point
  3. It is operating within a block clearance and chose to do so
  4. It experienced an emergency or TCAS resolution instruction and did so without instruction
  5. It made a mistake/pilot deviation and incorrectly did so

And that's just one minor change, with one aircraft. You can certainly take a guess on some of them but even ignoring unusual situations the first three possibilities are common and normal practice.

And that's just traffic presumed to be operating IFR within controlled airspace - add in VFR traffic in uncontrolled airspace (And bear in mind that they can be still be receiving instructions and clearances at that point - for example, entry into controlled airspace or landing at an airport in uncontrolled airspace) and you've got, essentially, no chance.

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