An integrated fault detection and exclusion scheme to support aviation navigation

Abstract

This paper proposes a novel integrity monitoring scheme against global navigation satellite systems (GNSS) fault for civil aviation navigation. The main contributions are (a) developing an efficient user algorithm that integrates fault detection and exclusion (FDE) functions, and (b) deriving the analytical methods to quantify its corresponding integrity risk. The intended application of the new scheme is advanced receiver autonomous integrity monitoring (ARAIM), which is proposed by the United States (U.S.) and European Union (E.U.), and will serve as the next generation of the main aviation navigation means. In this new approach, the exclusion decision-making process is unified into the first layer detection step, thereby dramatically improving efficiency. The principle of this method is utilizing the multi-dimensional parity vector projections in parity space to extract the information of faults. In this work, we derive the projection matrix for single satellite failure modes, establish the mechanism for determining exclusion subset based on the projection magnitudes, and rigorously account for the false exclusion probabilities in the integrity risk quantification. The feasibility of the algorithm is verified and validated using Monte-Carlo simulations, and the performance is analyzed by evaluating the integrity risk. It is shown that the new FDE scheme can efficiently and effectively exclude the faulty satellites as desired, while achieving promising navigation performance.

Appendix

This appendix develops the correlations among the variables in Eq. (23). In the following derivations, the mean values of the variables are implicitly removed:

$$ \sigma_{{jq_{j} }}^{2} = E\left\{ {\varepsilon_{j} ,q_{j} } \right\} = \left( {{\varvec{\upalpha}}_{r} {\mathbf{S}}_{j} {\mathbf{VS}}_{0}^{\text{T}} {\varvec{\upalpha}}_{r}^{\text{T}} - {\varvec{\upalpha}}_{r} {\mathbf{S}}_{j} {\mathbf{VS}}_{j}^{\text{T}} {\varvec{\upalpha}}_{r}^{\text{T}} } \right) \cdot \frac{1}{{\sigma_{{\Delta_{j} }} }} = {\varvec{\upalpha}}_{r} \left( {{\mathbf{P}}_{0} - {\mathbf{P}}_{j} } \right){\varvec{\upalpha}}_{r}^{\text{T}} \cdot \frac{1}{{\sigma_{{\Delta_{j} }} }} $$

(26)

$$ \sigma_{{jq_{i} }}^{2} = E\left\{ {\varepsilon_{j} ,q_{i} } \right\} = {\varvec{\upalpha}}_{r} \left( {{\mathbf{P}}_{0} - {\mathbf{P}}_{j} {\mathbf{P}}_{j,i}^{ - 1} {\mathbf{P}}_{i} } \right){\varvec{\upalpha}}_{r}^{\text{T}} \cdot \frac{1}{{\sigma_{{\Delta_{i} }} }}. $$

(27)

The elements in the covariance matrices of Eq. (24) are obtained using the following linear combinations:

$$ \sigma_{{jR_{1} }}^{2} = {\mathbf{n}}_{1} \left[ {\begin{array}{*{20}c} {\sigma_{{jq_{j} }}^{2} } & {\sigma_{{jq_{i} }}^{2} } \\ \end{array} } \right]^{\text{T}} \quad {\text{and}}\quad \sigma_{{jR_{2} }}^{2} = {\mathbf{n}}_{2} \left[ {\begin{array}{*{20}c} {\sigma_{{jq_{j} }}^{2} } & {\sigma_{{jq_{i} }}^{2} } \\ \end{array} } \right]^{\text{T}} . $$

(28)