## Abstract

The increased number of redundant ranging signals in future multi-constellation GNSS will improve RAIM-based integrity monitoring performance, but will also increase the probability of satellite faults, thereby increasing the continuity risk. In response, in this paper, a solution separation (SS) approach to fault detection and exclusion (FDE) is developed. The first part of the paper proves that for single-measurement faults, SS detection test statistics are projections of the parity vector on failure mode lines. It follows that the SS detection boundary can be represented as a polytope in parity space. To further analyze this result, we design a method that provides a piecewise linear detection boundary, which minimizes the integrity risk while limiting the probability of false alarms. This optimal detection region varies with navigation system parameters, but for realistic, practical requirements, the optimal detection region approaches the SS polytope-shaped boundary. The second part of the paper introduces complete integrity risk and continuity risk equations for SS fault detection and exclusion. Probability bounds are developed, which express the reduction of continuity risk using exclusion at the cost of increased integrity risk. The integrity risk bound (also given in the form of protection levels) is designed to enable risk evaluation in practical applications where computation resources are limited. In parallel, a continuity risk bound is derived, which provides the means to determine detection and exclusion thresholds that satisfy the continuity risk requirement. Parity space representations reveal the shape of the SS exclusion zones, and reaffirm the convenience of using normally-distributed SS test statistics for risk evaluation, especially in high-dimensional parity space. Finally, the SS FDE integrity and continuity risk bounds are implemented to establish worldwide availability maps for an example aircraft approach application using Advanced RAIM (ARAM) based on GPS and Galileo measurements.

Original language | English (US) |
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Pages | 2702-2722 |

Number of pages | 21 |

State | Published - Jan 1 2013 |

Externally published | Yes |

Event | 26th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2013 - Nashville, TN, United States Duration: Sep 16 2013 → Sep 20 2013 |

### Conference

Conference | 26th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2013 |
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Country | United States |

City | Nashville, TN |

Period | 9/16/13 → 9/20/13 |

## ASJC Scopus subject areas

- Computer Networks and Communications
- Transportation