Reliability (or integrity) is an important performance metric of Global Navigation Satellite Systems (GNSS) for aviation applications. To this end, a reliable Kalman filter (KF)-based GNSS positioning algorithm is developed in this paper for aircraft navigation. More precisely, a novel receiver autonomous integrity monitoring (RAIM) algorithm with a KF is developed in the range domain to ensure reliable aircraft position estimation with GNSS. A major challenge with the range-based approach to KF RAIM is as follows. Its protection level (PL) computation should account for the contributions of all past measurements in an efficient way without growing computational burden over time. In this context, a computationally efficient RAIM algorithm is proposed under the assumption of a single satellite failure. It judiciously forms three simultaneous fault detection tests and appropriately modifies PL calculation. It is shown that the proposed method can address the problem of increasing computational burden over time. Thus, it holds promise for real time implementation on avionics, where processing capacity is generally limited. It also provides faster fault detection and lower PLs than that obtained with a single fault detection test. Performance of the proposed method is compared with two existing RAIM algorithms for an application of an unmanned aerial vehicle.