  In this paper, we study Stochastic Control Barrier Functions (SCBFs) to
enable the design of probabilistic safe real-time controllers in presence of
uncertainties and based on noisy measurements. Our goal is to design
controllers that bound the probability of a system failure in finite-time to a
given desired value. To that end, we first estimate the system states from the
noisy measurements using an Extended Kalman filter, and compute confidence
intervals on the filtering errors. Then, we account for filtering errors and
derive sufficient conditions on the control input based on the estimated states
to bound the probability that the real states of the system enter an unsafe
region within a finite time interval. We show that these sufficient conditions
are linear constraints on the control input, and, hence, they can be used in
tractable optimization problems to achieve safety, in addition to other
properties like reachability, and stability. Our approach is evaluated using a
simulation of a lane-changing scenario on a highway with dense traffic.
