Bagging (i.e., bootstrap aggregating) involves combining an ensemble of bootstrap estimators. We consider bagging for inference from noisy or incomplete measurements on a collection of interacting stochastic dynamic systems. Each system is called a unit, and each unit is associated with a spatial location. A motivating example arises in epidemiology, where each unit is a city: the majority of transmission occurs within a city, with smaller yet epidemiologically important interactions arising from disease transmission between cities. Monte Carlo filtering methods used for inference on nonlinear non-Gaussian systems can suffer from a curse of dimensionality (COD) as the number of units increases. We introduce bagged filter (BF) methodology which combines an ensemble of Monte Carlo filters, using spatiotemporally localized weights to select successful filters at each unit and time. We obtain conditions under which likelihood evaluation using a BF algorithm can beat a COD, and we demonstrate applicability even when these conditions do not hold. BF can out-perform an ensemble Kalman filter on a coupled population dynamics model describing infectious disease transmission. A block particle filter (BPF) also performs well on this task, though the bagged filter respects smoothness and conservation laws that a BPF can violate. Supplementary materials for this article are available online.