A cross reality system enables portable devices to access stored maps and efficiently and accurately render virtual content specified in relation to those maps. The system may process images acquired with a portable device to quickly and accurately localize the portable device to the persisted maps by constraining the result of localization based on the estimated direction of gravity of a persisted map and the coordinate frame in which data in a localization request is posed. The system may actively align the data in the localization request with an estimated direction of gravity during the localization processing, and/or a portable device may establish a coordinate frame in which the data in the localization request is posed aligned with an estimated direction of gravity such that the subsequently acquired data for inclusion in a localization request, when posed in that coordinate frame, is passively aligned with the estimated direction of gravity.