Double Chi-Squared Distributions-Based Advanced RAIM for Air Transportation

Safety-critical dual-frequency and multi-constellation global navigation satellite system (GNSS) appli- cations are driving the development of advanced receiver autonomous integrity monitoring (ARAIM) to handle the effects of constellation faults, multi-satellite faults and nominal satellite biases. A Chi-squared residual-based ARAIM significantly differing from the traditional solution separation (SS) based ARAIM in principle is proposed for air transportation in this work. The proposed ARAIM expresses the integrity risk of each hypothesis as the product of the cumulative distribution functions of two Chi-squared distributions and the hypothesis occurrence probability. Based on the equivalence between the normalized solution separation and the residual Chi-square separation, an upper bound in terms of the worst Chi-squared distribution noncentrality parameter induced by GNSS faults is established for the integrity risk of each hypothesis. The log-concavity of the cumulative distribution function of Chi-squared distribution ensures that the protection level computation of the proposed ARAIM is theoretically convergent and conservative. A comparative analysis of the proposed ARAIM and SS-based ARAIM in civil aviation scenarios indicates that the proposed ARAIM can offer a competitive protection level.