  In this paper, we study stateless and stateful physics-based anomaly
detection scenarios via distributed estimation over sensor networks. In the
stateful case, the detector keeps track of the sensor residuals (i.e., the
difference of estimated and true outputs) and reports an alarm if certain
statistics of the recorded residuals deviate over a predefined threshold, e.g.,
\chi^2 (Chi-square) detector. Instead, only instantaneous deviation of the
residuals raises the alarm in the stateless case without considering the
history of the sensor outputs and estimation data. Given (approximate)
false-alarm rate for both cases, we propose a probabilistic threshold design
based on the noise statistics. We show by simulation that increasing the window
length in the stateful case may not necessarily reduce the false-alarm rate. On
the other hand, it adds unwanted delay to raise the alarm. The distributed
aspect of the proposed detection algorithm enables local isolation of the
faulty sensors with possible recovery solutions by adding redundant
observationally-equivalent sensors. We, then, offer a mechanism to design
Q-redundant distributed observers, robust to failure (or removal) of up to Q
sensors over the network.
