The use of the global navigation satellite systems in civil aviation is a safety-of-life application that requires optimized performance in terms of system reliability, accuracy, availability and integrity. The paper discusses a technique for evaluation of positioning reliability and detection of systematic errors in the airborne environment. The presented technique monitors and corrects main error sources affecting quality of GNSS measurements such as cycle slips and receiver clock jumps. An efficient statistical testing methodology is proposed using a series of tests. Stochastic modeling of observations needed to perform statistical testing is based on an adaptive technique where the residuals collected from the previous segment of positioning results were used to estimate the covariance matrices of the measurement noise and process noise for the epoch of computation. The use of two antennae on board the aircraft is proposed to improve reliability of the system as well as to provide attitude information (heading and pitch) of the aircraft. Data from a test utilizing a fixed-wing airplane were used. Results of the testing show that main error sources were mostly detected and repaired. The use of two antennae improves reliability of the system. Results also show that variation of the stochastic model can affect reliability performance.