Classic approaches to tackle simultaneously localization and mapping (SLAM) are based on estimation problem. That is, robots try to estimate it position as well as landmark concurrently where both positions are modeled as random variables.

A series of works formulate SLAM differently by modeling the landmark positions as unknown parameters, and try to solve SLAM by EM algorithm [1,2]. To the best of our knowledge, [1] is the first EM formulation for SLAM problem. While observation data keep accumulating in SLAM problem, this work uses hidden Markov model (HMM), and calculates the sufficient statistics of the HMM by a particle method.

In [2], SLAM is proposed to avoid particle-based algorithm which is computationally intensive. Instead, the E-step in [2] is performed by extended Rauch-Tung-Striebel (E-RTS) smoother. However, the method proposed in [2] is based on batch EM. Therefore, it can only calculate the whole trajectory but not suitable for incoming data, which is the common scenario for SLAM problem.

[1] S. L. Corff, G. Fort, and E. Moulines, “Online Expectation Maximization algorithm to solve the SLAM problem,” in 2011 IEEE Statistical Signal Processing Workshop (SSP), Jun. 2011, pp. 225–228.

[2] Z. Sjanic, M. A. Skoglund, and F. Gustafsson, “EM-SLAM with inertial/visual applications,” IEEE Transactions on Aerospace and Electronic Systems, vol. 53, no. 1, pp. 273–285, Feb. 2017.