Very broad question. One case for sure would be if the measurements have to be analyzed in non-real time. Another example would be if delivery latency of the measurement has to be taken into account. Another would be if the measurements have to be coordinated among many sensed devices, let's say in cases where you need multiple different measurements taken of the same event, and conditions are not perfectly static.
I would almost approach this from the other side. When do you not need timestamps in measurements? I'd say, only in cases where you are monitoring exclusively in real time, or in cases where the measurement is not time-variant (for practical purposes).
Yes, time stamps are needed for target tracking, although these time stamps might only consist of measuring a time delay (only measuring delta time, not actually time stamping with GPS time, let's say). A common target tracking technique is to use radar. The assumption is that motion of the target is essentially nil while the radar beam travels to the target and the reflection comes back. So the radar measures the delay between transmission of the pulse and arrival of the reflection, from which it calculates range, and the reflection arriving at a directional antenna also provides bearing. If you want to reconstruct the target's track, then you'll be plotting the returns on a screen, which in effect is time stamping the returning echoes. But this now becomes a historical record, not so much a real time measurement.
But on the other hand, if you want to know how fast you are driving your car, to make sure the police don't stop you, the speedometer simply provides the speed now. Depending how the speedometer works, there may be no need for timestamp. The assumption is that the speed of light delay, from the speedometer dial to your eyes, is insignificant, so the car is in fact going at that indicated speed right this instant. You would only need to timestamp these speeds if you were trying to reconstruct your trip, in non real time.
Same goes for sensing temperature or pressure. No need for timestamps, unless you are building a historical record.
So what about multisensor multitarget tracking problem?As you said there is no need to timestamps unless for hostorical record. But in all MS-MT tracking papers, timestamped measurements(GPS time) are used as I understood. Is it possible to use measurements without timestamps in this problem?
Any kind of sensor array used for target tracking will involve synchronized operation of the individual sensors, certainly. So I agree that this would be the functional equivalent of using timestamps,. even if in a particular case, actual timestamps aren't used.
For instance, even something as compact as a phased array antenna would qualify as multiple sensors used in tracking one or more targets simultaneously. In phased arrays, the phase between elements is very tightly controlled, even if this is not done with actual timestamps. So yes, this qualifies.
What about an example of multiple fire and smoke sensors used to monitor a building? For real time monitoring, all you really want to know is which sensors are being set off, as soon as the alarm condition occurs. And any time stamps would be needed mostly just to reconstruct the event.