  This paper introduces a Poisson multi-Bernoulli mixture (PMBM) filter in
which the intensities of target birth and undetected targets are grid-based. A
simplified version of the Rao-Blackwellized point mass filter is used to
predict the intensity of undetected targets, and the density of targets
detected for the first time are approximated as Gaussian. Whereas conventional
PMBM filter implementations typically use Gaussian mixtures to model the
intensity of undetected targets, the proposed representation allows the
intensity to vary over the region of interest with sharp edges around the
sensor's field of view, without using a large number of Gaussian mixture
components. This reduces the computational complexity compared to the
conventional approach. The proposed method is illustrated in a sensor
management setting where trajectories of sensors with limited fields of view
are controlled to search for and track the targets in a region of interest.
