Localization and Observability of Aircraft via Doppler Shifts

The linear trajectory of an airplane with constant velocity is obtained from Doppler shifts at stationary sensors, each yielding a corresponding time of closest approach, closest distance, and speed [3, 8]. Based on these inferences and on the sensors' locations, three sensors yield two candidate trajectories, and four sensors yield one - provided that the locations span R
²
and R
³
respectively: constituting observability for the problem at hand.