#### Dominik Nuss, Stephan Reuter, Markus Thom, Ting Yuan, Gunther Krehl, Michael Maile, Axel Gern, and Klaus Dietmayer, **A random finite set approach for dynamic occupancy grid maps with real-time application**, The International Journal of Robotics Research

Vol 37, Issue 8, pp. 841 – 866, DOI: 10.1177/0278364918775523.

Grid mapping is a well-established approach for environment perception in robotic and automotive applications. Early work suggests estimating the occupancy state of each grid cell in a robot’s environment using a Bayesian filter to recursively combine new measurements with the current posterior state estimate of each grid cell. This filter is often referred to as binary Bayes filter. A basic assumption of classical occupancy grid maps is a stationary environment. Recent publications describe bottom-up approaches using particles to represent the dynamic state of a grid cell and outline prediction-update recursions in a heuristic manner. This paper defines the state of multiple grid cells as a random finite set, which allows to model the environment as a stochastic, dynamic system with multiple obstacles, observed by a stochastic measurement system. It motivates an original filter called the probability hypothesis density / multi-instance Bernoulli (PHD/MIB) filter in a top-down manner. The paper presents a real-time application serving as a fusion layer for laser and radar sensor data and describes in detail a highly efficient parallel particle filter implementation. A quantitative evaluation shows that parameters of the stochastic process model affect the filter results as theoretically expected and that appropriate process and observation models provide consistent state estimation results.