ABSTRACT This letter addresses the issue of mobile source localization using time of arrival (TOA) measurements in scenarios where the source and sensors are not synchronized, and the start transmission time is unknown. We propose a non-convex weighted least squares (WLS) minimization problem for estimating the source position, velocity and start transmission time from the distance measurement equation, without the need for Taylor approximation commonly used in traditional processing approaches. To effectively solve the non-convex WLS optimization problem, we use the semi-positive definite relaxation (SDR) technique to transform the original problem into a convex semi-positive definite programming (SDP) problem. Additionally, we further extend the proposed method to scenarios where the positions of sensors are uncertain. Computer simulation results demonstrate that the proposed method surpasses the existing methods, whether the positions of sensors are known or uncertain.
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