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.