An optimal one-impulse correction in a model

A rectilinear and uniform motion with an unknown random initial velocity is considered. The observer exactifies the trajectory of the motion by a finite set of trajectory measurements containing random errors. The terminal coordinates may be influenced by one and only one corrective impulse. We say that there is a success if the terminal coordinates of the trajectory belong to a fixed domain. A strategy is a rule which prescribes the time and the value of a corrective impulse to every sample of the trajectory measurements. A probability of “success” corresponds to every strategy. A strategy is constructed which maximizes this probability. There is a numerical example in the paper.