Modified CRLB for Cooperative Geolocation of Two Devices Using Signals of Opportunity

We consider the problem of localizing two devices using signals of opportunity from beacons with known positions. Beacons and devices have asynchronous local clocks or oscillators with unknown clock skews and offsets. We model clock skews as random, and analyze the biases introduced by clock asynchronism in the received signals. By deriving the equivalent Fisher information matrix for the modified Bayesian Cram r-Rao lower bound (CRLB) of device position and velocity estimation, we quantify the errors caused by clock asynchronism. We propose an algorithm based on differential time-difference-of-arrival (DTDOA) and frequency-difference-of-arrival (FDOA) that mitigates the effects of clock asynchronism to estimate the device positions and velocities. Simulation results suggest that our proposed algorithm is robust and approaches the CRLB when clock skews have small standard deviations.