A Linear-correction Based on Time Difference of Arrival Localization Algorithm

A novel Time Differences Of Arrival (TDOA) localization algorithm based on linear-correction is proposed to address the nonlinear problem of TDOA positioning. Firstly, the proposed algorithm reformulates the highly nonlinear TDOA equations into a set of pseudo-linear ones and the Weighted Least Squares (WLS) estimator is used to obtain the initial emitter position estimation. Then a linear weighted least squares problem with respect to the estimation bias is formulated through utilizing first-order Taylor-series expansion to the pseudo-linear equations. The effectiveness of the proposed method is theoretically analyzed under small noise postulation. Finally, the extension to the general case of moving emitter with constant acceleration localization scenario is also presented and the corresponding estimation accuracy can achieve the Cramer-Rao Lower Bound (CRLB) as well. Computer simulation results demonstrate the effectiveness of the proposed algorithm.