Where the Sound Actually Came From TDOA

The recorders, and when each heard it

The times only have to be on one clock — everything here is differences, so a clock wrong by a constant changes nothing at all. One recorder wrong relative to the others moves the answer and cannot be seen in the result, so reconcile the clocks first if they came off separate devices.

How fast it travelled, and how well you know the times

Sound in air is about 343 m/s at 20°C and changes by roughly 0.6 m/s per degree, so summer speed used on a winter night is two per cent out — four metres on a two hundred metre baseline, before any timing error at all. Radio is a different problem and takes its own speed. The timing figure is what the band below is computed from, so guessing it low is how a tool comes to promise a precision it does not have.

Where it came from

Squares are the recorders, the cross is the answer, and the faint cloud is every position consistent with your times at the accuracy you declared. The cloud is the point of the drawing: if it is a long smear rather than a blob, the array shape is doing that, not the arithmetic.

Do the times agree with each other

“Out by” is the gap between when a recorder actually heard it and when the answer says it should have. With more than three recorders these cannot all be zero, and a row that is out by far more than your stated accuracy means no single source produced all of these arrivals — a wrong position, a wrong sign, a mis-clocked recorder, or more than one event.

The working