  Previously, we derived exact relationships between the properties of a linear
time-invariant control system and properties of an anomaly detector that
quantified the impact an attacker can have on the system if that attacker aims
to remain stealthy to the detector. A necessary first step in this process is
to be able to precisely tune the detector to a desired level of performance
(false alarm rate) under normal operation, typically through the selection of a
threshold parameter. To-date efforts have only considered Gaussian noises. Here
we generalize the approach to tune a chi-squared anomaly detector for noises
with non-Gaussian distributions. Our method leverages a Gaussian Mixture Model
to represent the arbitrary noise distributions, which preserves analytic
tractability and provides an informative interpretation in terms of a
collection of chi-squared detectors and multiple Gaussian disturbances.
