This paper presents two extensions to robust model predictive control (MPC) involving imperfect information. Previous work developed a form of MPC guaranteeing feasibility and constraint satisfaction given an unknown but bounded disturbance and perfect state information. In the first extension, this controller is modified to account for an unknown but bounded state estimation error. As an example, a simple estimator is proposed and analyzed to provide the necessary error bounds. Furthermore, it is shown that delayed state information can be handled using the same method. These analyses depend on knowledge of bounds on the measurement and disturbance uncertainties. The second extension provides a method of estimating these bounds using available data, providing an adaptive form of the controller for cases where the error levels are poorly known a priori.