Field Guide · algorithm

Also known as: multilateration, MLAT, hyperbolic positioning, TDOA positioning

Multilateration (MLAT) computes the position of a signal source from the differences in arrival time of one transmission recorded at several receivers at known, surveyed locations.1 A single time-difference-of-arrival (TDOA) between two receivers constrains the emitter to a hyperbola (a hyperboloid in 3-D) — the locus of points whose range difference to that receiver pair is fixed — and the intersection of several such hyperbolas from multiple pairs pins down the location. Crucially it needs only relative timing, so the emitter itself carries no clock and need not cooperate.

hyperbola (RX1,RX2) hyperbola (RX2,RX3) emitter RX1 t₁RX2 t₂RX3 t₃ Δt₁₂, Δt₂₃, Δt₁₃ → intersection = position
Each receiver pair's time difference of arrival defines a hyperbola of constant range difference; the emitter sits where the hyperbolas from independent pairs cross.

How it works

Radio waves travel at a known speed, so a difference in arrival time maps directly to a difference in path length. With receivers at surveyed positions and a common time reference:

  • Measure TDOAs. Cross-correlate the same waveform captured at each receiver to get the time offset between every pair. Each Δt fixes a range difference, hence one hyperbola.
  • Solve the geometry. Two hyperbolas give a 2-D fix; a third (or receivers at differing heights) resolves altitude and the ambiguity of which branch. With more receivers than unknowns the system is overdetermined and solved by least squares, improving accuracy and detecting bad measurements.
  • Smooth over time. Because a target moves, successive fixes are usually fed to a Kalman filter that fuses them with a motion model to produce a clean track and reject outliers.

The hard engineering problem is time synchronisation: 1 nanosecond of timing error is about 30 cm of position error, so the receivers must share a common clock (GNSS-disciplined, or calibrated against a reference transmitter at a known location). Accuracy also depends on geometry — the dilution of precision is poor when the receivers and target are nearly collinear.

Relevance to SDR

The highest-profile use is aviation: Mode S and ADS-B MLAT networks locate aircraft from the arrival times of their 1090 MHz replies and squitters at multiple ground stations. This provides independent surveillance for aircraft that broadcast an identity but no position, and a cross-check on the GPS-derived positions that ADS-B aircraft self-report via compact position reporting. The same TDOA principle geolocates emitters generally — interference hunting, SIGINT, and wildlife tags — and is the mirror image of how a GPS receiver works (there the receiver solves its own position from many synchronised transmitters). GopherTrunk decodes the ADS-B/Mode S messages a single receiver can hear, but multilateration itself requires several time-synchronised receivers sharing captures, which is a network-level system beyond what a standalone GT node does.

Sources

  1. Multilateration — Wikipedia, on hyperbolic position estimation from time-difference-of-arrival measurements. ↩

See also