Abstract: The existing time difference of arrival (TDOA) localization algorithms usually need to add the distance as an auxiliary variable to get the linear localization equation, which causes a two-step target state calculation and the unavailability for continuous localization when the auxiliary variable varies. Therefore, a linear localization equation is deduced relating only to the target state. Based on it, a constrained total least squares (CTLS) algorithm suitable for the continuous localization is proposed without dealing any auxiliary variable. expresses Each column of the measurement matrix and vector is expressed as the product of a matrix and the TDOA measurement error vector by the proposed algorithm. Then, the TDOA localization problem is transformed into a CTLS problem, which can be solved by the Newton method. Simulation results show that the proposed algorithm can achieve the Cramer-Rao lower bound and has better performance than existing typical continuous localization algorithms.