A navigation system for a host vehicle may include a processor programmed to: receive, from an entity remotely located relative to the host vehicle, a sparse map associated with at least one road segment to be traversed by the host vehicle; receive point cloud information from a LIDAR system onboard the host vehicle, the point cloud information being representative of distances to various objects in an environment of the host vehicle; compare the received point cloud information with at least one of the plurality of mapped navigational landmarks in the sparse map to provide a LIDAR-based localization of the host vehicle relative to at least one target trajectory; determine an navigational action for the host vehicle based on the LIDAR-based localization of the host vehicle relative to the at least one target trajectory; and cause the at least one navigational action to be taken by the host vehicle.