A novel grid selection method for sky-wave time difference of arrival localisation

This paper studies sky-wave time-difference-of-arrival (TDOA) localisation in passive-radar systems, and the focus is on two-dimensional localisation on the earth surface. Signals are reflected by the ionosphere layer before arriving at sensors, making the localisation problem very complicated. Parametric methods are found to be inefficient in this case; therefore, grid-based methods are studied. However, conventional grid-based methods are not guaranteed to find the nearest grid point (NGP) of target, even when the grid map is dense and the measurements are noise-free. Hence, this paper derives the sufficient condition for NGP selection in noiseless environments. Based on it, an ellipsoid-norm method (ENM) is proposed to promise optimal results with noise-free measurements, which consists of a test phase and a search phase. If a given grid map passes the offline test phase, the search phase produces a close-form estimate at a low computational complexity. The impact of noise on ENM is also theoretically analysed. Additionally, ENM is extended to handle cases with inaccurately known ionosphere layer heights. Numerical results show that for different sensor networks, the test phase is feasible by adjusting grid densities; and ENM is superior to the current state-of-the-art in terms of estimation accuracy and computational complexity.