Overbounding integrity parameters for ARAIM with BDS-3 and Kalman filter

Abstract

The modernization of GPS along with the emergence of BDS-3 brings the satellite-based navigation into a new era of multi-constellation, which opens opportunities to develop Advanced Receiver Autonomous Integrity Monitoring (ARAIM). However, as the indicator that relates directly to safety of aircraft, the integrity is threatened by two significant challenges in implementing ARAIM. Since BDS-3, a new constellation during its initial deployment, may not offer same Integrity Support Message as GPS and the measurement error model designed for GPS may not be applicable to BDS-3, the first challenge relates to the characterization of measurement error for BDS-3 from the perspective of integrity. Additionally, since the utilization of Kalman filter (KF) in ARAIM does not consider the model uncertainty in the time-correlated error, which may result in a loss of integrity, the second challenge relates to the model uncertainty. Therefore, this research focuses on addressing these two challenges, which guarantees bounding of integrity risk for ARAIM. For the first challenge, this dissertation firstly undertakes a detailed study on satellite fault probabilities for BDS-3. The Signal-In-Space Range Error (SISRE) is characterized for all medium earth orbit and inclined geosynchronous orbit satellites during the first fully operational year, based on which ten single satellite faults are identified with no constellation fault found. Further, error components of SISRE are analyzed and root causes of faults are investigated in depth. The result reveals that BDS-3 meets latest accuracy criteria and the nominal SISRE is conservatively described by the broadcast user range accuracy. Additionally, probabilities of single satellite fault and constellation fault can be set as 8 × 10-5 and 1 × 10-3, respectively. After determining above two probability parameters, this dissertation then builds a Gaussian model to bound the Time Group Delay (TGD) error for BDS-3 across different combinations of frequencies. Additionally, two types of abnormal changes of TGD parameters are identified and analyzed. Based on the annual data, the result shows that the smallest bounding standard deviation of 0.78 m is obtained from the combination of B1C and B2a signals. Further, the bias component of TGD error is also evaluated and its value is 0.71m for the above frequency combination. For the second challenge, this dissertation proposes an efficient method to overbound the integrity risk for KF-based ARAIM given that the uncertainty in the model of time-correlated error is considered. To establish a mathematical expression to link the integrity risk and the time-correlated error, a new recursive equation for two variances is derived. Based on the obtained expression, a min-max model is built to bound the integrity risk and reduce the conservatism simultaneously. To rapidly solve this min-max optimization problem, a hybrid evolutionary algorithm is proposed. The simulation results demonstrate this algorithm outperforms other conventional algorithms in rapidly obtaining the minimum upper bound on the integrity risk. In summary, this dissertation is to overbound integrity parameters associated with measurement errors and the error model, which supports the determination of satellite fault probabilities, the TGD error modeling, and the consideration of model uncertainty.