This paper presents methods for overbounding the missed-detection probability for monitors with nominally chi-square noise distributions. Such distributions occur commonly for integrity monitors in safety-critical applications, such as in Space-Based and Ground-Based Augmentation Systems for GNSS. Robust bounding methods are needed when noise parameters, such as the measurement covariance matrix, are not precisely known. Simple inflation of the covariance model for the input data does not, typically, ensure conservative bounding for all bias directions. To address this problem, conservative models of monitor-statistic noise are introduced, which ensure bounding for all covariance matrices in a specified range, between lower and upper bounds.
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