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We propose a novel geometric Rao-Blackwellized particle filtering framework for monocular SLAM with locally planar landmarks. We represent the states for the camera pose and the landmark plane normal as SE(3) and SO(3), respectively, which are both Lie groups. The measurement error is also represented as another Lie group SL(3) corresponding to the space of homography matrices. We then formulate the unscented transformation on Lie groups for optimal importance sampling and landmark estimation via unscented Kalman filter. The feasibility of our framework is demonstrated via various experiments.