Four methods to calculate the Vertical Protection Level (VPL) can be used in Advanced Receiver Autonomous Integrity Monitoring (A-RAIM), among which the ideal method is the strictest one. To obtain the ideal VPL satisfying the exact required integrity risk, the worst case bias with the maximum integrity risk is searched for. This investigation has found that the correct worst case highly depends on the choice of the input VPL. To gain the correct result, the computation becomes complex and the accuracy of the result is compromised. Therefore, a new procedure is designed with a new search: the maximum VPL is searched to encompass all possible bias sizes. Since VPL is calculated with a given integrity risk for each bias size, the uncertainty of the arbitrary VPL input in the ideal method is avoided. Also, an optimisation algorithm is adopted to improve computational efficiency. It is shown that the new method is more reliable and efficient than the current best method. Simulation results worldwide also 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.

A method to compute the minimum Horizontal Protection Level (HPL) using the test statistic of normal distribution, which will exploit advances in computational power to meet the requirement of Time to Alert (TTA), is proposed to improve service availability. To obtain the minimum solution, two approximations used in traditional algorithms need exact solutions: the distribution of the horizontal position error and the determination of the worst case to ensure that the resulting HPL is able to accommodate all possible bias. This is validated with results such that the optimal solution is achieved with a pre-defined accuracy and sufficient computational efficiency. Also, the new HPL is used to determine if current approximated methods are conservative, where one of the methods does not meet the integrity requirement with given test statistics, error model and integrity risk definition.

This paper proposes a geometric-based method of the ground-point visibility from a satellite or satellite constellation in elliptical orbit considering the J ₂ perturbation. First, the field-element equations describing the relationship between the elliptical satellite orbit, field parameters, and ground point are introduced and can be solved semi-analytically. Also, using a two-dimensional map composed of the mean argument of latitude and geographic longitude of the ascending node, the problem of calculating visible intervals is transformed into a simple intersection problem of a group of parallel lines and a time-invariant region generated by the field-element equations. Furthermore, based on the geometric relationship between any two satellites, the relative field mapping and constellation field mapping are described, which can simplify the multi-satellite coverage problem to a single-satellite coverage problem and can be used to obtain the coverage performance of the constellation analytically and rapidly for the target. The simulation results demonstrate that the proposed method is rapid, efficient, intuitive, and accurate, suggesting its wide applications in constellation studies .

Train integrity resolution is an important part of a train operation control system. In current train operation control systems, train integrity resolution is achieved by using information on the track circuit or the wind pressure. However, both approaches have limitations; the utilization of the track circuits requires high construction and maintenance costs, and the wind pressure approach has to overcome the problem of low update rate and false alarm caused by the incident pipe leakage. In this paper a new train integrity resolution method based on double-differenced carrier phase relative positioning is proposed. To improve the system performance, an online integer ambiguity fixing method is applied to overcome the frequent integer ambiguity re-fixing problem caused by the high train speed and the complex operational environment. Moreover, the elevation angle constraint optimal distribution based reference satellite selection method is applied to guarantee optimal satellite geometry distribution during train operation. To evaluate the performance of the proposed train integrity resolution method, a real train test was carried out on the Beijing-Shenyang high speed railway. The experimental results show that the proposed train integrity resolution method can provide train integrity solutions with an accuracy of better than 0.5m, with STD and RMS of 0.15m and 0.17m respectively. Compared with the conventional GNSS single point positioning based train integrity method, the proposed method can achieve a much better performance, with an improvement, in this test, of 77%.