ML-based single-step estimation of the locations of strictly noncircular sources

This paper concentrates on the location methods for strictly noncircular sources by widely separated arrays. The conventional two-step methods extract measurement parameters and then, estimate the positions from them. Compared with the conventional two-step methods, direct position determination (DPD) is a promising technique, which locates transmitters directly from original sensor outputs without estimating intermediate parameters in a single step, and thus, improves the location accuracy and avoids the data association problem. However, existing DPD methods mainly focus on complex circular sources without considering noncircular signals, which can be exploited to enhance the localization accuracy. This paper proposes a maximum likelihood (ML)-based DPD algorithm for strictly noncircular sources whose waveforms are unknown. By exploiting the noncircularity of sources, we establish an ML-based function in time domain under the constraint on the waveforms of signals. A decoupled iterative method is developed to solve the prescribed ML estimator with a moderate complexity. In addition, we derive the deterministic Cramér-Rao Bound (CRB) for strictly noncircular sources, and prove that this CRB is upper bounded by the associated CRB for circular signals. Simulation results demonstrate that the proposed algorithm has a fast convergence rate, and outperforms the other location methods in a wide range of scenarios.