Computation and visualization of posterior densities in scalar nonlinear and non-Gaussian Bayesian filtering and smoothing problems

One-dimensional Bayesian filtering and smoothing problems can be solved numerically using a number of algorithms, even in nonlinear and non-Gaussian cases. In this educational paper we advocate for the benefits of visualizing the obtained posterior densities as complement to, e.g., estimation error analysis. In addition to a review of Bayesian filtering and smoothing and the respective point mass and particle solutions, we devise a novel algorithm for filtering when the likelihood cannot be evaluated. Several instructive examples are discussed and easily adjustable matlab code is provided as complement to this paper.