An Efficient Algebraic Solution for Moving Source Localization from Quadruple Hybrid Measurements

This paper deals with the 3-D moving source localization using time difference of arrival (TDOA), frequency difference of arrival (FDOA), angle of arrival (AOA) and AOA rate measurements, gathered from a set of spatially distributed receivers. The TDOA, FDOA, AOA and AOA rate measurement equations were firstly established according to the space geometric relationship of the source relative to the receivers. Then an efficient closed-form algorithm for source position and velocity estimation from the quadruple hybrid measurements was proposed. The proposed algorithm converts the nonlinear measurement equations into a linear set of equations, which can then be used to estimate the source position and velocity applying weighted least square (WLS) minimization. In contrast to existing two-stage WLS algorithms, the proposed algorithm does not introduce any nuisance parameters and requires merely one-stage, which enables for source localization with the fewest receivers necessary. Theoretical accuracy analysis shows that the proposed algorithm reaches the Cramer-Rao lower bound, and simulation studies corroborate the efficiency and superiority of the proposed algorithm over other algorithms.