What is the time difference of arrival technique for emitter geolocation?

Time difference of arrival (TDOA) is a passive geolocation technique that determines an emitter location by measuring the difference in signal arrival times at three or more geographically separated receivers: (1) Principle: an emitter at unknown position (x, y) transmits a signal. Receiver A receives the signal at time t_A. Receiver B receives the signal at time t_B. The time difference TDOA_AB = t_A - t_B corresponds to a constant range difference: Δd_AB = c × TDOA_AB. This range difference defines a hyperbola on the map (the locus of all points with the same range difference to A and B). A second pair (A and C, or B and C) produces a second hyperbola. The intersection of two or more hyperbolas gives the emitter location. (2) Implementation: the receivers must be precisely time-synchronized (using GPS timing: accuracy < 10 ns). Each receiver digitizes the received signal. The TDOA is measured by cross-correlating the signals from two receivers: the correlation peak occurs at the time lag corresponding to the TDOA. Cross-correlation accuracy: depends on the signal bandwidth. Wider bandwidth = sharper correlation peak = more accurate TDOA. TDOA accuracy: σ_TDOA ≈ 1 / (BW × √(2 × SNR)), where BW is the signal bandwidth. (3) Geolocation accuracy: depends on the TDOA measurement accuracy and the receiver geometry (baseline length and orientation relative to the emitter). Geometric dilution of precision (GDOP): the accuracy degrades when the emitter is along the baseline axis (poor crossing angle of hyperbolas). Best accuracy: when the emitter is roughly equidistant from all receivers and the baselines provide diverse crossing angles. (4) Example: three receivers separated by 50 km. Signal bandwidth = 10 MHz. SNR = 20 dB. σ_TDOA = 1/(10e6 × √200) = 7.1 ns → position error ≈ 2.1 m × GDOP. With GDOP = 5 (typical for a moderate geometry): position accuracy ≈ 10 m.