Edge-device collaboration has the potential to facilitate compute-intensive device pose tracking for resource-constrained mobile augmented reality (MAR) devices. In this paper, we devise a 3D map management scheme for edge-assisted MAR, wherein an edge server constructs and updates a 3D map of the physical environment by using the camera frames uploaded from an MAR device, to support local device pose tracking. Our objective is to minimize the uncertainty of device pose tracking by periodically selecting a proper set of uploaded camera frames and updating the 3D map. To cope with the dynamics of the uplink data rate and the user's pose, we formulate a Bayes-adaptive Markov decision process problem and propose a digital twin (DT)-based approach to solve the problem. First, a DT is designed as a data model to capture the time-varying uplink data rate, thereby supporting 3D map management. Second, utilizing extensive generated data provided by the DT, a model-based reinforcement learning algorithm is developed to manage the 3D map while adapting to these dynamics. Numerical results demonstrate that the designed DT outperforms Markov models in accurately capturing the time-varying uplink data rate, and our devised DT-based 3D map management scheme surpasses benchmark schemes in reducing device pose tracking uncertainty.

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