On Gaussian Optimal Smoothing of Non-Linear State Space Models

Author

Särkkä, Simo ; Hartikainen, Jouni

Author_Institution

Aalto Univ., Aalto, Finland

Volume

55

Issue

8

fYear

2010

Firstpage

1938

Lastpage

1941

Abstract

In this note we shall present a new Gaussian approximation based framework for approximate optimal smoothing of non-linear stochastic state space models. The approximation framework can be used for efficiently solving non-linear fixed-interval, fixed-point and fixed-lag optimal smoothing problems. We shall also numerically compare accuracies of approximations, which are based on Taylor series expansion, unscented transformation, central differences and Gauss-Hermite quadrature.

Keywords

Gaussian processes; approximation theory; smoothing methods; state-space methods; Gauss-Hermite quadrature; Gaussian approximation; Gaussian optimal smoothing; Taylor series expansion; approximate optimal smoothing; approximation framework; fixed-lag optimal smoothing; fixed-point optimal smoothing; nonlinear fixed-interval optimal smoothing; nonlinear state space models; nonlinear stochastic state space models; unscented transformation; Bayesian methods; Filtering; Gaussian approximation; Gaussian noise; Gaussian processes; Noise measurement; Nonlinear filters; Postal services; Smoothing methods; State-space methods; Stochastic processes; Taylor series; Time measurement; Bayesian smoothing; Gaussian assumed density smoothing; non-linear Rauch-Tung-Striebel smoothing; non-linear optimal smoothing;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2050017

Filename

5462954