Simultaneous Localization and Mapping : Literature Survey

One of the initial solutions to the SLAM problem was proposed by Smith and Cheeseman who used the Extended Kalman Filter (EKF) to jointly represent the landmark position with the pose [38]. Guivant and Nebot [18] developed compressed EKF which performed mapping in local space using a reduced number of landmarks and only performed global update when the robot moved from one local map to another local map. The worst case complexity in this case is O(kn) required for full global update. Paskin [36] proposed thin junction tree filter (TJTF) to maintain manageable complexity. It is an assumed density filtering algorithm where the belief state is represented using a junction tree and proposed a thinning operation to maintain an ever-increasing tree width caused by filtering operations. Estimation in this case is performed in O(kn) time by passing marginalized distribution along the edges of the junction tree. According to Frese et al. [13] “From the perspective of “linear equation solving” this approach is complementary to the approach proposed in this paper. In the Gaussian case the junction tree algorithm is a direct, i.e., exact equation solver based on Schur-complements (corresponding to the marginalized distributions) and approximation is performed on the equation level. In contrast Multilevel Relaxation is an iterative, i.e., approximate equation solver but does not approximate the equations themselves.”