A TDOA-FDOA Passive Positioning Algorithm Based on the Semi-Definite Relaxation Technique

In the passive location of moving target, the closed-form solution can reach Cramer-Rao Lower Bound (CRLB) under the low noise level, but these algorithms often can not adapt to the large measurement noise condition. For this problem, this paper proposes a passive positioning algorithm based on the Semi-Definite Relaxation (SDR) using Time Difference Of Arrival (TDOA) and Frequency Difference Of Arrival (FDOA). Firstly, this method constructs the pseudo-linear equation of the typical closed-form solution. Secondly, the idea of Stochastic Robust Least Squares (SRLS) and the nonlinear relationship between the target parameters and the additional variables are used to transform the localization problem into the least squares problem with quadratic equality. Using Semi-Definite Programming (SDP) technique, constrained least squares problem is then converted into the SDP problem, which is finally solved by the optimization toolbox. The proposed method does not require an initial priori information and simulations show the effectiveness of the proposed method.