We present an approach to control design for a mobile sensor network tasked with sampling a scalar field and providing optimal space-time measurements. The coverage metric is derived from the mapping error in objective analysis (OA), an assimilation scheme that provides a linear statistical estimation of a sampled field. OA mapping error is an example of a consumable density field: the error decreases dynamically at locations where agents move and sample. OA mapping error is also a regenerating density field if the sampled field is time-varying: error increases over time as measurement value decays. The resulting optimal coverage problem presents a challenge to traditional coverage methods. We prove a symmetric dynamic coverage solution that exploits the symmetry of the domain and yields symmetry-preserving coordinated motion of mobile sensors. Our results apply to symmetric sampling regions that are non-convex and non-simply connected.