[anthrax]

The underwater log system could accurately measure "speed" and "distance" traveled. It measured "dynamic pressure" caused by movement of the submarine through water.

You are right that it didn't "take into account of currents" so this couldn't be used solely for long range navigation. The speed however was still useful information for navigational use.

As for its uses in fire control.
The "speed" measured by the "underwater log system" + the "course" measured with the gyrocompass were the only imputs that were automatically fed into the TDC.

The "Postion Keeper" constantly calculates the position of the target in relation to the submarine. So in effect, it was definately was capable "knowing where the own ship location was. The PK required at least the following 5 inputs.

2 automated imputs that were constant fed into the TDC.
ownship course from "gyro compass"
ownship speed from "underwater log"

4 inputs estimated or measured by the subs crew at least once.
Target course (AoB) = from estimation of plotting method.
Target speed from estimation or plotting method.
Target bearing = From observation on preriscope.
Target Range from Standimeter (which required a estimation on target height) or from radar.

2 outputs where constantly shown at the observation locations. (the other could be read of the TDC)
Caculated target range.
Caculated target Bearing.



Back to the original question, of whether you should know your exact location. For the purposes of Firecontrol, Yes, its reasonable to know and IRL i beleive there was device called the " Dead reckoning tracer" that could automatically plot ownship location onto paper.