Fault detection algorithms (such as advanced RAIM) developed for aviation can be applied in situations where the probabilities of fault are arbitrarily high. However, with large probabilities, the user receiver needs to protect against a large number of fault modes (which results from the combination of simultaneous independent faults). In baseline ARAIM algorithms, the user receiver must compute a fault-tolerant position solution for each fault mode (computed using the subset of the available measurements that would not be affected by the fault mode), or at least its error covariance. After showing how to use a solution separation algorithm without computing the fault-tolerant position solutions, we present a technique to obtain upper bounds on the subset error covariance for a given subset size. This upper bound does not require the computation of every subset error covariance and can be computed without additional matrix inversions. We evaluate the potential of this technique by applying it to ARAIM scenarios.

中文翻译：

---

故障检测的快速保护级别及其在高级RAIM中的应用

为航空开发的故障检测算法（例如高级RAIM）可以应用于故障概率非常高的情况。但是，由于概率较大，因此用户接收器需要防止出现大量故障模式（这是由同时发生的独立故障组合而成）。在基线ARAIM算法中，用户接收器必须为每种故障模式（至少使用不会受故障模式影响的可用测量子集进行计算）计算容错位置解。在展示了如何在不计算容错位置解的情况下使用解决方案分离算法之后，我们提出了一种获取给定子集大小的子集误差协方差上限的技术。该上限不需要计算每个子集误差协方差，并且可以在没有附加矩阵求逆的情况下进行计算。我们通过将其应用于ARAIM方案来评估该技术的潜力。