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

Michael Roth; Fredrik Gustafsson

ICASSP 2017accepted0 citations

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

Abstract

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.

BibTeX

@inproceedings{icassp2017_computationandvi,
  title = {Computation and visualization of posterior densities in scalar nonlinear and non-Gaussian Bayesian filtering and smoothing problems},
  author = {Michael Roth and Fredrik Gustafsson},
  booktitle = {ICASSP 2017},
  year = {2017}
}