Ephemeris monitor with ambiguity resolution for CAT II/III GBAS

Abstract

In safety-critical applications, such as the Ground-Based Augmentation System for precision approaches in civil aviation, it is important to safeguard users under the case of ephemeris failures. For CAT II/III approaches, different ephemeris monitors with approaches for ambiguity resolution are proposed with the double differenced carrier phase as the test statistics. The continuity risks introduced by the ambiguity resolution are addressed by deriving the required averaging time for new, acquired, and re-acquired satellites. Since the ephemeris fault is closely related with the baseline length between ground stations, the minimum baseline length is derived to meet the probability of missed detection region. Current methods are compared with both the averaging time and the ground baseline length. It is demonstrated that a combination of two methods is able to achieve the best performance with 94 averaging epochs and 218 m ground baseline length.

Appendix: residual ambiguities

For the PC_ALT method under WA,

$$\hat{N}_{w}^{ij} - N_{w}^{ij} = \left| {\left[ {\frac{{\emptyset_{w}^{ij} - R_{n}^{ij} }}{{\lambda_{w} }}} \right]_{\text{round}} - N_{w}^{ij} } \right| \le 1$$

(a1)

the maximum residual N_w bounded by (9) is assumed to be 1. Similarly,

$$\left| {\left[ {\frac{{\emptyset_{1}^{ij} - \emptyset_{5}^{ij} - \lambda_{5} N_{w}^{ij} }}{{\lambda_{1} - \lambda_{5} }}} \right]_{\text{round}} - N_{1}^{ij} } \right| \le 1$$

(a2)

where the maximum residual N₁ is also 1 assuming the correct $N_{w}^{ij}$ input. Therefore, the residual ambiguity in the test statistics is 5N₁ with the PC_ALT method,

$$\begin{aligned} & \left| {\left[ {\frac{{\emptyset_{1}^{ij} - \emptyset_{5}^{ij} - \lambda_{5} \hat{N}_{w}^{ij} }}{{\lambda_{1} - \lambda_{5} }}} \right]_{\text{round}} - N_{1}^{ij} } \right| \le \left| {\left[ {\frac{{\emptyset_{1}^{ij} - \emptyset_{5}^{ij} - \lambda_{5} N_{w}^{ij} }}{{\lambda_{1} - \lambda_{5} }}} \right]_{\text{round}} \pm \left[ {\frac{{\lambda_{5} }}{{\lambda_{1} - \lambda_{5} }}} \right]_{\text{round}} - N_{1}^{ij} } \right| \\ & \quad \le \left| {\left[ {\frac{{\emptyset_{1}^{ij} - \emptyset_{5}^{ij} - \lambda_{5} N_{w}^{ij} }}{{\lambda_{1} - \lambda_{5} }}} \right]_{\text{round}} - N_{1}^{ij} } \right| \pm \left| {\left[ {\frac{{\lambda_{5} }}{{\lambda_{1} - \lambda_{5} }}} \right]_{\text{round}} } \right| \le 5 \\ \end{aligned}$$

(a3)