Impact of Time-Correlation of Monitor Statistic on Continuity of Safety-Critical Operations

Abstract

Integrity monitors are an essential component of ensuring the quality of navigation measurements for safety‐critical GNSS augmentation systems. The sensitivity of these monitors is closely related to requirements limiting monitor false alarms. This paper shows that the risk of false alarms interrupting safety critical operations (loss of continuity) is closely tied to monitor‐noise correlation. Analysis shows that specific continuity risk may be as high as 50% for conventional monitor implementations, when time correlation is considered. This paper presents an alternate two‐threshold monitor implementation, which features both a subcritical threshold and a critical threshold, only the latter of which triggers a loss of continuity. Using this two‐threshold implementation, we introduce methods to compute specific continuity risk in the presence of time‐correlated noise. Subsequently, through simulation, we quantify how specific continuity risk is influenced by varying levels of time‐correlation, which may be present in the raw monitor data or introduced by smoothing. Copyright © 2012 Institute of Navigation.

The Effect of Uncertain Covariance on a Chi-Square Integrity Monitor

“…An important aspect of the CDFs illustrated in the lower plot of Figure 1 is that they are meant to apply to a wide range of different bias values with the same fixed magnitude (b = 7). As mentioned earlier, the bias direction matters for the true CDF, which is generalized chi-square as described by (10), but not for the proposed overbound, which is conventional chi-square as described by (5). The distinction is that the conventional chi-square CDF is symmetric about all axes of y, whereas the true CDF is compressed along one axis (the y 2 -axis) such that the bias "appears" to be larger in certain directions and smaller in others.…”

“…As indicated, the value of the generalized chi-square distribution inside any threshold T is dependent on two parameters: the vector mean μ y and matrix covariance Q for the input vector y. The generalized chi-square distribution represents a large set of distributions that includes conventional chi-square distributions, a term which will be used in this paper both to refer to chi-squared distributions, defined by (3), and when a bias is present to noncentral chi-square distributions, defined by (5). Specifically, the generalized chi-square distribution becomes a conventional chi-square distribution if the covariance matrix Q is the identity matrix I.…”

“…This overbounding approach is advantageous in that it is easy and efficient to compute using existing mathematical libraries (e.g., Matlab TM ) that evaluate the noncentral chi-square distribution P ncx , as defined by (5) .…”

“…Although continuity interruptions due to monitor alerts may sometimes be a mere annoyance, alerts may also trigger emergency contingency operations (such as a balked aircraft landing) that introduce additional safety risk and disrupt the flow of airport traffic. Clearly, specifications for new aviation‐sensor monitoring systems must place strict limits on integrity and continuity risks in order to ensure safe, efficient operations .…”

Applying sensor integrity concepts to detect intermittent bugs in aviation software

“…Because such alarm events suspend use of the primary automation software, they might be labeled continuity breaks, a term frequently used to describe alarm events in other aviation applications. 28…”