The Bayes optimal detector is derived for a class of linear‐period‐modulated (LPM) signals whose velocities and times of arrival are uncertain. All terms necessary for claculating theaposterioriprobability‐density function of the uncertain parameters are shown to be available as a natural by‐product of the optimal detector computations. The processor structure derived is general in thataprioriknowledge of velocity and time of arrival other than complete uncertainty can be taken into account.