  Rapid detection of spatial events that propagate across a sensor network is
of wide interest in many modern applications. In particular, in communications,
radar, environmental monitoring, and biosurveillance, we may observe
propagating fields or particles. In this paper, we propose Bayesian single and
multiple change-point detection procedures for the rapid detection of
propagating spatial events. It is assumed that the spatial event propagates
across a network of sensors according to the physical properties of the source
causing the event. The multisensor system configuration is arbitrary and
sensors may be mobile. We begin by considering a single spatial event and are
interested in detecting this event as quickly as possible, while statistically
controlling the probability of false alarm. Using a dynamic programming
framework we derive the structure of the optimal procedure, which minimizes the
average detection delay (ADD) subject to a false alarm probability upper bound.
In the rare event regime, the optimal procedure converges to a more practical
threshold test on the posterior probability of the change point. A convenient
recursive computation of this posterior probability is derived by using the
propagation pattern of the spatial event. The ADD of the posterior probability
threshold test is analyzed in the asymptotic regime. Then, we take a multiple
hypothesis testing (MHT) approach and develop a procedure for the detection of
multiple propagating spatial events in parallel. The proposed parallel
procedure controls the overall false discovery rate (FDR) under prespecified
upper bound. Simulations are conducted to verify the theoretical findings. It
is shown that exploiting the spatial properties of the event improves the ADD
compared to procedures that do not properly take advantage of the spatial
information.
