This paper addresses the problem of creating a geometric map with a mobile robot in a dynamic indoor environment. To form an accurate model of the environment

we present a novel map representation called the ‘grid vector’

which combines each vector that represents a directed line segment with a slender occupancy grid map. A modified expectation maximization (EM) based approach is proposed to evaluate the dynamic objects and simultaneously estimate the robot path and the map of the environment. The probability of each grid vector is evaluated in the expectation step and then used to distinguish the vector into static and dynamic ones. The robot path and map are estimated in the maximization step with a graph-based simultaneous localization and mapping (SLAM) method. The representation we introduce provides advantages on making the SLAM method strictly statistic

reducing memory cost

identifying the dynamic objects

and improving the accuracy of the data associations. The SLAM algorithm we present is efficient in computation and convergence. Experiments on three different kinds of data sets show that our representation and algorithm can generate an accurate static map in a dynamic indoor environment.