A novel maximum likelihood trajectory estimation algorithm for targets in mixed stationary/moving conditions is presented. The proposed approach is able to estimate position and velocity of the target over arbitrary complex trajectories, while explicitly taking into account the possibility of stop\&go motion. Moreover, a novel trajectory reconstruction method based on the theory of B\'ezier curve is developed for online smoothing of the trajectory, which keeps the advantages of Bayesian smoothing while introducing only a fixed lag in the estimation process. The performance assessment, conducted on both simulated and real data, shows that the proposed approach can outperform classical Kalman filter and Rauch-Tung-Striebel smoother techniques.