Modified CRB for Location and Velocity Estimation using Signals of Opportunity

We consider the problem of localizing two agents using signals of opportunity from beacons with known positions. Beacons and agents 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 CramérRao lower bound (CRLB) of agent position and velocity estimation, we quantify the errors caused by clock asynchronism. We propose an algorithm based on differential time-difference-of-arrival and frequencydifference-of-arrival that mitigates the effects of clock asynchronism to estimate the agent positions and velocities. Simulation results suggest that our proposed algorithm is robust and approaches the CRLB when clock skews have small standard deviations.