We study the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and incomplete state information. Given a suitable choice of causal control policies, we first present a slight extension of the Kalman filter to estimate the state optimally in mean-square sense.We then showhowto augment the underlying optimization problemwith a negative drift-like constraint,yielding a second-order cone programto be solved periodically online.We prove that the receding horizon implementation of the resulting control policies renders the state of the overall system mean-square bounded under mild assumptions. We also discuss how some quantities required by the finite-horizon
optimization problem can be computed off-line, thus reducing the on-line computation.