  The problem of sequentially detecting a moving anomaly which affects
different parts of a sensor network with time is studied. Each network sensor
is characterized by a non-anomalous and anomalous distribution, governing the
generation of sensor data. Initially, the observations of each sensor are
generated according to the corresponding non-anomalous distribution. After some
unknown but deterministic time instant, a moving anomaly emerges, affecting
different sets of sensors as time progresses. As a result, the observations of
the affected sensors are generated according to the corresponding anomalous
distribution. Our goal is to design a stopping procedure to detect the
emergence of the anomaly as quickly as possible, subject to constraints on the
frequency of false alarms. The problem is studied in a quickest change
detection framework where it is assumed that the evolution of the anomaly is
unknown but deterministic. To this end, we propose a modification of Lorden's
worst average detection delay metric to account for the trajectory of the
anomaly that maximizes the detection delay of a candidate detection procedure.
We establish that a Cumulative Sum-type test solves the resulting sequential
detection problem exactly when the sensors are homogeneous. For the case of
heterogeneous sensors, the proposed detection scheme can be modified to provide
a first-order asymptotically optimal algorithm. We conclude by presenting
numerical simulations to validate our theoretical analysis.
