Direct Position Determination of Multiple Noncircular Sources with a Moving Array

Abstract

Compared with conventional two-step localization methods, direct position determination (DPD) is a promising technique that offers superior performance under low signal-to-noise ratio conditions. However, existing DPD methods mainly focus on complex circular sources without considering noncircular signals, which can be exploited to enhance the localization accuracy. This study proposes an improved subspace data fusion (SDF)-based DPD algorithm for multiple noncircular sources with a moving array. By constructing and decomposing the extended covariance matrices, extended noise subspaces are obtained for all positions of the moving array. The source positions are then directly estimated by fusing the extended noise subspaces without computing the intermediate parameters, thereby avoiding the data association problem inherent in two-step methods. Our proposed DPD algorithm combines the low complexity of SDF with the high robustness to noise and sensor errors that comes from exploiting signal noncircularity. Specifically, a closed-form expression for the localization mean square error (MSE) of the algorithm and the stochastic Cramer–Rao bound for strict-sense noncircular signals are derived. Simulation results validate our theoretical prediction for MSE and also demonstrate that the proposed algorithm outperforms other localization methods in terms of accuracy and capacity to resolve noncircular sources.