The coverage control problem of a circle by a mobile sensor network affected by bounded measurement errors is addressed in this paper. The mobile sensors are assumed to have different maximum velocities. Our main objective is to study the effect of measurement errors on the coverage cost function, which is defined as the largest time for the sensor network to arrive at any point on the circle. Coverage control laws with input constraints are developed based on the noisy position measurements among sensors, under which the mobile sensor network converges to a neighborhood of the optimal configuration. Furthermore, the conditions for the sensors to preserve their spatial order on the circle are derived in order to avoid collision among sensors. An upper bound on the limit of the coverage cost function as time goes to infinity is also given.