Grid mapping is a well established approach for environment perception in\nrobotic and automotive applications. Early work suggests estimating the\noccupancy state of each grid cell in a robot's environment using a Bayesian\nfilter to recursively combine new measurements with the current posterior state\nestimate of each grid cell. This filter is often referred to as binary Bayes\nfilter (BBF). A basic assumption of classical occupancy grid maps is a\nstationary environment. Recent publications describe bottom-up approaches using\nparticles to represent the dynamic state of a grid cell and outline\nprediction-update recursions in a heuristic manner. This paper defines the\nstate of multiple grid cells as a random finite set, which allows to model the\nenvironment as a stochastic, dynamic system with multiple obstacles, observed\nby a stochastic measurement system. It motivates an original filter called the\nprobability hypothesis density / multi-instance Bernoulli (PHD/MIB) filter in a\ntop-down manner. The paper presents a real-time application serving as a fusion\nlayer for laser and radar sensor data and describes in detail a highly\nefficient parallel particle filter implementation. A quantitative evaluation\nshows that parameters of the stochastic process model affect the filter results\nas theoretically expected and that appropriate process and observation models\nprovide consistent state estimation results.\n