In this paper, by utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of a signal received at a number of receivers, an efficient constrained weighted least-squares (CWLS) algorithm for estimating the position and velocity of a moving source is proposed, which exploits the known relation between the intermediate variable and the source location coordinates explicitly. On basis of Newton's method, a numerical iterative solution can be obtained allowing real-time implementation and ensuring global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least squares (WLS) approach, which makes the Cramr-Rao lower bound (CRLB) at a sufficiently high noise level before the threshold effect occurs.