Abstract: In the Three-Dimension (3D) moving target passive positioning scenario, the minimum number of stations required for unambiguous localization is four. However, the traditional Two-Step Weighted Least Squares (TSWLS) and its improved closed-form algorithms require at least five stations. When reducing one station, these closed-form methods often cannot provide available solution. To solve this problem, a Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) based positioning algorithm which minimizes the number of stations is proposed in this paper. This algorithm is a closed-form solution and can locate the source with only four stations in the 3D scenario. This method has two steps:in the first step, a new set of equations is established by separating the unknown parameter space of the TSWLS from the known parameters, and the initial values of the source position and velocity are obtained by Weight Least Squares (WLS). In the second step, using taylor series expansion technique, the intermediates are linearized to further correct the initial values. Theoretical analysis proves that the proposed method can reach the Cramér-Rao Lower Bound (CRLB) at the appropriate noise level. In addition, simulations prove that both the far field and the near field parameter estimation accuracy of proposed method can achieve the CRLB at low noise level when only four stations are used.It also shows the positioning performance of the proposed algorithm can better adapt to large measurement noise than TSWLS or its improved algorithms when using five stations.

Key words: passive localization, Time Difference of Arrival (TDOA), Frequency Difference of Arrival (FDOA), number of stations, weighted least square