TDOA Localization Algorithm for Multiply Disjoint Sources without Extra Variables

This paper addresses the passive localization problem for multiple disjoint sources with sensor position errors. Although the previous closed-form solutions can achieve optimal performance at low noise levels, they may suffer from performance loss at high noise levels since they assume the unknown source position is independent of the extra parameters. To overcome this drawback, we first eliminate the nuisances by using a projection matrix and give the coarse position estimate. Then, the coarse estimate is improved by using the weighted least squares (WLS) technique. The proposed method can attain the Cramer-Rao lower bound (CRLB) in theory and simulations under mild measurement noise levels. Furthermore, numerical simulations indicate that the proposed method outperforms the existing methods.