In this letter, an improved version of the popular two-stage weighted least squares (WLS) algorithm is presented to determine the position and velocity of a moving source using time difference of arrival and frequency difference of arrival measurements in a wireless sensor network. A closed-form solution is obtained from the minimization of the WLS criterion in each stage. The estimator accuracy is shown analytically to attain the Cramer-Rao lower bound under the small Gaussian noise assumption. Numerical simulations are included to support and corroborate the theoretical developments.