An Improved Grid-Search Method for the Identity-Test of Ionosphere-Layer Virtual Heights via TDOA Measurements

Sky-wave time-difference-of-arrival (TDOA) localization is a promising technique, which may enable surveillance over large-scale areas via passive radar systems. In a recently published paper, we have proposed a novel sky-wave TDOA localization method by introducing an assumption, i.e., the ionosphere-layer virtual heights (IVHs) for transmitting paths from a target to different closely spaced sensors are identical. In this paper, we further verify the assumption by testing the identity of the IVHs based on TDOA measurements of a known-position target. To realize this goal, the identity-test problem is converted into a coefficient retrieval problem. The current state-of-the-art method has to make an approximation to select the nearest grid-point (NGP) of coefficient vector, which induces a larger recovery error with the increase of dimension. To alleviate this, an improved grid-search method is proposed by training weights, which can build the proportional relationship between the weighed norm-2 cost functions and the norm-2 distances of grid-points and coefficients. Thus, the NGP can be selected freely from the aforementioned approximation error; and the coefficient recovery accuracy is improved. Additionally, the training phase of the proposed method is guaranteed to be feasible while that of the conventional method is not. The simulation results verify the superiority of the proposed method over the current state-of-the-art in terms of recovery accuracy and computational complexity.