Fundamental limits for location and velocity estimation using asynchronous beacons

We consider the problem of localizing two sensors using signals-of-opportunity from beacons with known positions. Beacons and sensors have asynchronous local clocks or oscillators with unknown clock skews and offsets. We analyze the biases introduced by clock asynchronism in the received signals, and derive the Cramér-Rao lower bound (CRLB) for sensor position and velocity estimation errors. We quantify the error caused by beacon clock asynchronism. We also propose an algorithm that mitigates the effects of clock asynchronism to estimate the sensor positions and velocities. Simulation results suggest that our proposed algorithm is robust and approaches the CRLB when sensor clock skews have small standard deviations.