In this paper, we study the target tracking problem in wireless sensor
networks (WSNs) using quantized sensor measurements under limited bandwidth
availability. At each time step of tracking, the available bandwidth $R$ needs
to be distributed among the $N$ sensors in the WSN for the next time step. The
optimal solution for the bandwidth allocation problem can be obtained by using
a combinatorial search which may become computationally prohibitive for large
$N$ and $R$.
Among the various procedures used to detect potential changes in a stochastic
process the moving sum algorithms are very popular due to their intuitive
appeal and good statistical performance. One of the important design parameters
of a change detection algorithm is the expected interval between false
positives, also known as the average run length (ARL). Computation of the ARL
usually involves numerical procedures but in some cases it can be approximated
using a series involving multivariate probabilities.