Localizing moving targets in unknown harsh environments has always been a severe challenge. This letter investigates a novel localization system based on multi-agent networks, where multiple agents serve as mobile anchors broadcasting their time-space information to the targets. We study how the moving target can localize itself using the sequential time of arrival (TOA) of the one-way broadcast signals. An extended two-step weighted least squares (TSWLS) method is proposed to jointly estimate the position and velocity of the target in the presence of agent information uncertainties. We also address the large target clock offset (LTCO) problem for numerical stability. Analytical results reveal that our method reaches the Cramer-Rao lower bound (CRLB) under small noises. Numerical results show that the proposed method performs better than the existing algorithms.