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A cognitive approach is proposed to detect unknown beacons of terrestrial signals of opportunity (SOPs). Two scenarios are considered in the paper: (i) detection of unknown beacons with integer constraints (IC) and (ii) detection of unknown beacons with no integer constraint (NIC). An example of beacons with IC is the pseudo-noise (PN) sequences in cellular code division multiple access (CDMA) signals. On the other hand, the reference signals (RSs) in orthogonal frequency-division multiplexing (OFDM)-based systems can be considered as beacons signals with NIC. Matched subspace detectors are proposed for both scenarios, and it is shown experimentally that the proposed matched subspace detectors are capable of detecting cellular third-generation (3G) cdma2000 signals and fifth-generation (5G) OFDM signals. A low complexity method is derived to simplify the matched subspace detector with IC for M -ary phase shift keying ( M PSK) modulation. The effect of symbol errors in the estimated beacon signal on the carrier to noise ratio (CNR) is characterized analytically. Closed-form expressions for the asymptotic probability of detection and false alarm are derived. Experimental results are presented showing an application of the proposed cognitive approach by enabling an unmanned aerial vehicle (UAV) to detect and exploit terrestrial cellular signals for navigation purposes. In one experiment, the UAV achieved submeter-level accurate navigation over a trajectory of 1.72 km, by exploiting signals from four 3G cdma2000 transmitters. In another experiment, the UAV achieves a position root mean-squared error (RMSE) of 4.63 m over a trajectory of 416 m, by exploiting signals from two 5G transmitters.