  Simultaneous localization and mapping (SLAM) is the task of building a map
representation of an unknown environment while at the same time using it for
positioning. A probabilistic interpretation of the SLAM task allows for
incorporating prior knowledge and for operation under uncertainty. Contrary to
the common practice of computing point estimates of the system states, we
capture the full posterior density through approximate Bayesian inference. This
dynamic learning task falls under state estimation, where the state-of-the-art
is in sequential Monte Carlo methods that tackle the forward filtering problem.
In this paper, we introduce a framework for probabilistic SLAM using particle
smoothing that does not only incorporate observed data in current state
estimates, but it also back-tracks the updated knowledge to correct for past
drift and ambiguities in both the map and in the states. Our solution can
efficiently handle both dense and sparse map representations by
Rao-Blackwellization of conditionally linear and conditionally linearized
models. We show through simulations and real-world experiments how the
principles apply to radio (BLE/Wi-Fi), magnetic field, and visual SLAM. The
proposed solution is general, efficient, and works well under confounding
noise.
