This paper addresses the problem of safely navigating a mobile robot with limited sensing capability and limited information about stationary and moving obstacles. We consider two sensing limitations: blind spots between sensors and limited sensing range. We study three notions of safety: (1) static safety, which ensures collision-freedom with respect to stationary obstacles, (2) passive safety, which ensures collision-freedom while the robot is moving, and (3) passive friendly safety, which ensures the robot leaves sufficient room for obstacles to avoid collisions. We present a runtime approach, based on the Simplex architecture, to ensure these safety properties. To obtain the switching logic for the Simplex architecture, we identify a set of constraints on the sensors' readings whose satisfaction at time t guarantees that the robot will still be able to ensure the safety property at time t+Δt, regardless of how it navigates during that time interval. Here, Δt is the period with which the switching logic is executed and is bounded by a function of the maximum velocity and braking power of the robot and the range of the sensors. To the best of our knowledge, this work is the first that provides runtime assurance that an autonomous mobile robot with limited sensing can navigate safely with limited information about obstacles. The limited information about obstacles is used to derive an over-approximation of the set of nearby obstacle points.