Exactly Sparse Extended Information Filters for Feature-based SLAM

Recent research concerning the Gaussian canonical form for Simultaneous Localization and Mapping (SLAM) has given rise to a handful of algorithms that attempt to solve the SLAM scalability problem for arbitrarily large environments. One such estimator that has received due attention is the Sparse Extended Information Filter (SEIF) proposed by Thrun et al., which is reported to be nearly constant time, irrespective of the size of the map. The key to the SEIF's scalability is to prune weak links in what is a dense information (inverse covariance) matrix to achieve a sparse approximation that allows for efficient, scalable SLAM. We demonstrate that the SEIF sparsification strategy yields error estimates that are overconfident when expressed in the global reference frame, while empirical results show that relative map consistency is maintained. In this paper, we propose an alternative scalable estimator based on an information form that maintains sparsity while preserving consistency. The paper describes a method for controlling the population of the information matrix, whereby we track a modified version of the SLAM posterior, essentially by ignoring a small fraction of temporal measurements. In this manner, the Exactly Sparse Extended Information Filter (ESEIF) performs inference over a model that is conservative relative to the standard Gaussian distribution. We compare our algorithm to the SEIF and standard EKF both in simulation as well as on two nonlinear datasets. The results convincingly show that our method yields conservative estimates for the robot pose and map that are nearly identical to those of the EKF.