Time Difference of Arrival (TDOA)
Locating a transmitter from how much later its signal reaches one receiver than another. Each pair of synchronised receivers gives one hyperbola, and the crossing of several hyperbolas is the fix.
Time difference of arrival (TDOA) locates a transmitter by comparing when the same signal reached several receivers, rather than by measuring its direction or its strength. It needs no cooperation from the transmitter and no knowledge of when it sent anything, which is what makes it the workhorse technique for finding an uncooperative or unknown emitter.
What it is
Two receivers with synchronised clocks hear the same burst a few hundred nanoseconds apart. That delay converts directly to a difference of distances at the speed of light: 1 microsecond is about 300 metres. Because you do not know when the signal was transmitted, the measurement is not a distance to either receiver, only the difference between the two. Every point in the plane that shares one constant difference of distances lies on one hyperbola whose foci are the two receivers.
One pair therefore narrows the transmitter to a curve, not a point. Three receivers give two independent pairs, and their hyperbolas intersect at the position. Four or more give a three-dimensional fix and enough redundancy to check the answer. Solving for the position from several such measurements is called multilateration.
Why it matters
It is how an unknown transmitter is found in practice. Aircraft without a position source are tracked by multilateration of their transponder replies, jammers and unlicensed emitters are located by networks of cheap receivers, and a GNSS spoofer that looks flawless in every cryptographic check betrays itself in the geometry, because its signals all arrive from one direction with the same delay structure. On the defensive side, the same measurement validates that a signal really came from where its content claims.
TDOA versus its neighbours
| Technique | Measures | Needs | One measurement gives |
|---|---|---|---|
| TDOA | difference in arrival time | synchronised receivers | a hyperbola |
| Trilateration | absolute range | a known transmit time | a circle or a sphere |
| Angle of arrival | bearing | an array or a rotating antenna | a line |
| Received signal strength | level | a propagation model | a very fuzzy ring |
GNSS is the familiar hybrid: satellites transmit at a known time, but the receiver's own clock is unknown, so it solves for position plus clock offset from four satellites, which is trilateration with one extra unknown.
Geometry decides the accuracy
The same timing accuracy produces a good or a useless fix depending on where the receivers are. GDOP (geometric dilution of precision) is the multiplier from timing error to position error: receivers spread widely around the target make hyperbolas that cross at a sharp angle and a small timing error moves the crossing very little, while receivers bunched together or in a line make hyperbolas that cross at a shallow angle and the same error smears the fix over kilometres. Adding a receiver in a bad place adds almost nothing; moving one to a good place can be worth more than three new ones.
Pitfalls
- Synchronisation is the whole problem. A
100 nanosecondclock error is30 metresof position error, so receivers need a common clock discipline (GNSS-locked, or a shared reference signal), and a network built on unsynchronised hosts produces confident nonsense. - Correlate, do not timestamp. The time difference is measured by cross-correlating the two recordings, not by noting when each receiver "saw" the burst; a threshold-based timestamp is far too coarse and depends on level.
- Multipath biases the measurement. A reflected path arrives late and can dominate the correlation peak in urban terrain, pulling the fix towards the reflector.
- A fix without a geometry check is not a result. Always report the receiver layout and the resulting dilution alongside the position.