  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 (BBF). 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.
