  We investigate the problem of monitoring multiple targets using a single
mobile sensor, with the goal of minimizing the maximum estimation error among
all the targets over long time horizons. The sensor can move in a
network-constrained structure, where it has to plan which targets to visit and
for how long to dwell at each node. We prove that in an optimal observation
time allocation, the peak uncertainty is the same among all the targets. By
further restricting the agent policy to only visit each target once every
cycle, we develop a scheme to optimize the agent's behavior that is
significantly simpler computationally when compared to previous approaches for
similar problems.
