  We investigate the problem of persistent monitoring, where a mobile agent has
to survey multiple targets in an environment in order to estimate their
internal states. These internal states evolve with linear stochastic dynamics
and the agent can observe them with a linear observation model. However, the
signal to noise ratio is a monotonically decreasing function of the distance
between the agent and the target. The goal is to minimize the uncertainty in
the state estimates over the infinite horizon. We show that, for a periodic
trajectory with fixed cycle length, the problem can be formulated as a set of
semidefinite programs. We design a scheme that leverages the spatial
configuration of the targets to guide the search over this set of optimization
problems in order to provide efficient trajectories. Results are compared to a
state of the art approach and we obtain improvements of up to 91% in terms of
cost in a simple scenario, with much lower computational time.
