Nonhomogeneous poisson sampling and reconstruction in clustered sensor networks

A bandlimited signal emitted by an object moving through a field of sensors is sampled by the sensors it passes during its transit. If the sensors' locations follow a spatial Poisson distribution, the temporal sampling of the signal can be considered to be Poisson with intensity lambda = (A + B). The clustered communication architecture of sensor networks, however, causes samples further from the clusterhead to be lost with a probability that increases with distance. This leads to sampling times that can be modeled as a non-homogeneous Poisson process with lambda(t) = A + B cos(omega t + theta). We investigate the effect of this sampling strategy on a Kalman-filter-based reconstruction of the sensed signal. Its average performance, when theta is uniformly distributed on [0,2 pi], is shown via numerical analysis to be essentially equivalent to Poisson sampling with intensity pi = A.