This paper investigates the estimation problem for a spatially distributed process described by a partial differential equation with missing measurements. The randomly missing measurements are introduced in order to better reflect the reality in the sensor network. To improve the estimation performance for the spatially distributed process, the network of sensors which are allowed to move within the spatial domain is used. We aim to design the estimator which is used to approximate the distributed process and the mobile trajectories for sensors such that, for all possible missing measure-ments, the estimation error system is globally asymptotically stable in the mean square sense. By constructing Lyapunov functionals and using inequality analysis, the guidance scheme of every sensor and the convergence of the estimation error system are obtained. Finally, a numerical example is given to verify the effectiveness of the proposed estimator utilizing both the proposed guidance scheme for sensors.