A general approach to the optimization of the observation horizon of moving sensor trajectories for parameter estimation of distributed systems is presented. Two problems are formulated here. The first consists in maximizing the determinant of the information matrix for a specified duration of observations and an open initial time, and the other constitutes its generalization to the case where the elapsed observation time is minimized subject to a guaranteed D-efficiency of the experiment. The approach is to convert the problem to an optimal control one in Mayer form, in which both the control forces of the sensors and the initial sensor positions are optimized in addition to the limits of the observation horizon.