TDoA

Time Difference of Arrival (TDOA) is a localization method that estimates the position of a transmitter by measuring differences in signal arrival times at multiple spatially separated receivers with known locations. If t_i is the arrival time at receiver i and p_i is its position, the true transmitter location x and the signal speed c satisfy, approximately, ||x - p_i|| - ||x - p_j|| = c (t_i - t_j) for pairs (i, j). Each pair defines a hyperbola of possible transmitter positions; the intersection of several hyperbolae yields x. In two dimensions, three receivers (four for 3D) are typically required to obtain a unique solution. Practical implementations use time-difference measurements over time and apply least-squares or maximum-likelihood estimation to mitigate measurement noise.

A key feature is that TDOA does not require synchronized transmitters; only the receivers need coordinated timing references. This makes TDOA attractive for passive localization in networks where beacons are not directly controllable. Systems may synchronize receivers using GPS time, wired clocks, or distributed synchronization protocols.

Applications include locating cellular phones for emergency services (E911), Wi‑Fi and sensor-network localization, land-mobile radio, and underwater acoustics. Advantages include scalability and the ability to locate transmitters without knowing their emission time. Limitations include reliance on accurate synchronization among receivers, susceptibility to multipath and non-line-of-sight biases, and geometric dilution of precision depending on receiver geometry.

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