This paper considers the problem of persistently monitoring a set of moving targets using a team of aerial vehicles. Each agent in the network is assumed equipped with a camera with limited range and Field of View (FoV) providing bearing measurements and it implements an Information Consensus Filter (ICF) to estimate the state of the target(s). The ICF can be proven to be uniformly globally exponentially stable under a Persistency of Excitation (PE) condition. We then propose a distributed control scheme that allows maintaining a prescribed minimum PE level so as to ensure filter convergence. At the same time, the agents in the group are also allowed to perform additional tasks of interest while maintaining a collective observability of the target(s). In order to enforce satisfaction of the observability constraint, we leverage two main tools: (i) the weighted Observability Gramian with a forgetting factor as a measure of the cumulative acquired information, and (ii) the use of High Order Control Barrier Functions (HOCBF) as a mean to maintain a minimum level of observability for the targets. Simulation results are reported to prove the effectiveness of this approach.