Optimally observable and minimal cardinality monocular SLAM

This paper utilizes system observability to guide monocular SLAM. Instead of providing all measured features then performing data-driven outlier rejection (such as with RANSAC), we propose to identify only the minimal subset of features which form an optimally observable SLAM subsystem for localization. Modeling the SLAM system as a discrete time system with piece-wise linear SE〈3〉 motion, complete observability conditions are derived and a means to test the observability conditioning of candidate feature point groupings is proposed. Based on the conditioning, an efficient algorithm for picking the optimally observable feature subset is derived by incorporating the image geometric measures. The proposed monocular SLAM algorithm, called Optimally Observable and Minimal Cardinality (OOMC) SLAM is formulated as an EKF process. OOMC SLAM is first validated using a 6-DOF localization experiment; the results demonstrate accuracy comparable to the state-of-art SLAM algorithm with significantly improved computational efficiency. A longer sequence on a 620-meter trajectory is also tested. The algorithm achieves 0.9178% relative error against the GPS ground truth.