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Abstract
The accuracy of the navigation solutions can be greatly improved by using modernized GNSS with more visible satellites and multiple civilian frequencies. Another important performance criterion is integrity, which is defined to guarantee the safety of the navigation solution for such applications as civil aviation in which safety is of paramount issue. Integrity is used to quantify the risky situation when the position error is at a hazardous level with faults in the observations, but the user is not aware of it. Integrity faults can be a consequence of clock anomalies, cycle slips, multipath, etc. One of the popular integrity monitoring methods in civil aviation is Receiver Autonomous Integrity Monitoring (RAIM), which is essentially a consistency check on the GNSS observations by the aircraft. The output is the integrity indicators, such as Vertical Protection Level (VPL) and Horizontal Protection Level (HPL), which is a statistical bound on the position domain with given integrity risk.
With the forthcoming of the modernized GPS system, new constellations and augmentation systems, the number of satellites will be increased and the multiple frequency signals will be available. Therefore, RAIM can be applied in more stringent procedures, such as LPV-200 for vertical guidance on a global scale. Two major RAIM architectures are recognized as feasible choices: Advanced RAIM (A-RAIM) and Relative RAIM (R-RAIM). Currently, there are two positioning methods (the range domain method and the position domain method) available in R-RAIM and two RAIM algorithms (the classic method and the multiple hypothesis solution separation (MHSS) method) available for both A-RAIM and R-RAIM. Based on different implementation methods, all these current choices are analysed by comparing the results within a generalized framework.
The algorithms to calculate VPLs and HPLs are critically important in deciding the final integrity results for both A-RAIM and R-RAIM, which is the focus of this thesis. With the notion that all current algorithms are expected to be conservative at different levels, the exact Protection Level (PL) value within pre-defined accuracy and computational efficiency is pursued to improve the service availability and promoting RAIM in more stringent services in civil aviation.
There are mainly four methods to calculate VPL in literature, among which the ideal VPL method is the least conservative one with the exact value as the ultimate goal. To calculate the ideal VPL with given integrity risk, the bias with the maximum integrity risk, which is a function of the input VPL value, is searched in a boundary. To make sure the maximum integrity risk is equal with the given one, another VPL search loop is added upon the bias search. In this way, the computation becomes complex and the precision of the result is compromised. Therefore, a new procedure is designed with a new worst case search: the maximum VPL is searched among a range to encompass all possible sizes of the bias. VPL is calculated with a given integrity risk for each possible bias size in the search, so that the uncertainty of the arbitrary VPL input in the previous method is avoided. In this way, the calculation is simplified and the computation is faster, but the accuracy is still uncertain. With the inequality constrained maximization problem defined as the criterion, an optimization method can be applied to obtain a solution with a pre-defined accuracy as well as improved the computational efficiency. It is demonstrated that the new method to calculate the exact VPL is more reliable and efficient than the ideal VPL method. Worldwide simulation results show that the new approach has improved A-RAIM availability from 32%-38% to 74% with GPS and from 44%-43% to 85% with Galileo. With the exact VPL, the conservativeness of all current algorithms can be analyzed and conclusions are provided in this thesis.
Similarly, the same approach can be applied to obtain the worst case bias when calculating HPL. Besides the bias search, the calculation of HPL is more complex with another approximation on the distribution of the two-dimensional position error. There are two types of approximations among current methods: the normal approximation and the chi-squared approximation. Both approximated distributions are analyzed with the exact distribution to determine conservativeness. An approach to calculate the exact distribution with high computational sufficiency is adopted. Together with the optimization method to obtain the worst case bias, the exact HPL is obtained within required accuracy and computational efficiency. In the same way, the conservativeness of current approximated HPLs is also concluded. RAIM is then generalized with a higher dimensional PL, where an example of three-dimensional PL is provided. Results show that the improvement of the service availability is from 50%~62% to around 87% with GPS.
Furthermore, as a component of RAIM, Fault Detection and Exclusion (FDE) is investigated in the background of the classic reliability theory. After analyzing the performance of current FDE methods, theoretical proof on the optimality of test statistics in regard of detectability and separability is made. Plus, the current separability measure is found to be not applicable in one of the test statistics used in navigation, and a new measure is proposed without loss of generality. Results show that the new measure is more consistent with the performance of FDE. Lastly, RAIM is expanded from PL with fault detection only to PL with fault exclusion using the new separability measure. Consequently, a comprehensive framework for RAIM is established here with theoretical and numerical results.