Navigation by inertial device and signals of opportunity

Inertial navigation systems are known to yield rather accurate measurements over short time intervals, while their error variance tends to increase with time. In order to keep the error within specification most systems use GPS signals. In the absence of GPS data, due to jamming or spoofing, it is desirable to use signals of opportunity instead. We examine the use of time of arrival measurements of signals of opportunity that have known structure. We propose a low complexity semi-definite relaxation algorithm by converting the maximum likelihood location estimator to a convex optimization problem. Simulation results demonstrate that the proposed algorithms converge to the Cramér–Rao lower bound under some geometrical and noise limitations.