In this article, we investigate the joint estimation of the position and velocity of a moving target in distributed networks of moving radars using Time Of Arrival (TOA) and Doppler Shift (DS) measurements. In contrast to most of the existing/recent methods, we avoid the use of Nuisance Variables (NVs) by employing algebraic manipulations. We reformulate a new set of equations that are linear with respect to the target's position and velocity, resulting in a significant performance improvement. Subsequently, we propose a Two-Stage Weighted Least Squares (TSWLS) estimator and recommend two alternative algorithms to reduce computational complexity while preserving the accuracy by selecting either a transmitter or receiver as the reference sensor. We implement the proposed method over fully and partially connected networks. Our theoretical derivations and numerical simulations reveal that the proposed estimators are asymptotically efficient, i.e., they attain the CRLB, at relatively high noise levels. Moreover, the simulation results show that the proposed methods outperform state-of-the-art algorithms.