In this paper, a new approach to the observability of dynamical systems with uncertain sensors is developed. This approach is based on the redefinition of indistinguishability to consider measurement uncertainty and on the definition of a set called the final indiscernible set, which is directly related to state estimation accuracy and whose size is a quantitative observability index. Making use of this index, an observability-oriented controller, which attempts to drive the system through a high-observability trajectory to reduce estimation error, is proposed. Finally, this controller is illustrated through its application to the model of a CSTR, showing that the proposed method enhances the accuracy of state estimation when compared with a similar control scheme that does not consider observability and with a another kind of controller that employs a different observability index. (C) 2019 Elsevier Ltd. All rights reserved.