On Gaussian Optimal Smoothing of Non-Linear State Space Models

被引：73

作者：

Sarkka, Simo ^{[1
]}

Hartikainen, Jouni ^{[1
]}

机构：

[1] Aalto Univ, FI-00076 Aalto, Finland

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2010年 / 55卷 / 08期

关键词：

Bayesian smoothing; Gaussian assumed density smoothing; non-linear optimal smoothing; non-linear Rauch-Tung-Striebel smoothing; FILTERS; ALGORITHMS;

D O I：

10.1109/TAC.2010.2050017

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：1938 / 1941

页数：4

共 50 条

[41] Optimal estimating equations for state vectors in non-Gaussian and nonlinear state space time series models
Durbin, J
[J]. SELECTED PROCEEDINGS OF THE SYMPOSIUM ON ESTIMATING FUNCTIONS, 1997, 32 : 285 - 291
[42] Recursive nonlinear estimation of non-linear/non-Gaussian dynamic models
Kulhavy, R
[J]. COMPUTER-INTENSIVE METHODS IN CONTROL AND SIGNAL PROCESSING: THE CURSE OF DIMENSIONALITY, 1997, : 141 - 167
[43] EQUIVALENCE OF GAUSSIAN MEASURES AT NON-LINEAR TRANSFORMATIONS IN HILBERT-SPACE
SOKHADZE, GA
SHATASHVILI, AD
[J]. DOKLADY AKADEMII NAUK SSSR, 1978, 240 (04): : 790 - 793
[44] Asymptotic quasi-likelihood based on kernel smoothing for nonlinear and non-Gaussian state-space models
Alzghool, Raed
Lin, Yan-Xia
[J]. WORLD CONGRESS ON ENGINEERING 2007, VOLS 1 AND 2, 2007, : 926 - +
[45] Valuation of financial models with non-linear state spaces
Webber, N
[J]. DISORDERED AND COMPLEX SYSTEMS, 2001, 553 : 315 - 320
[46] Smoothing algorithms for state–space models
Mark Briers
Arnaud Doucet
Simon Maskell
[J]. Annals of the Institute of Statistical Mathematics, 2010, 62 : 61 - 89
[47] An efficient two-stage algorithm for parameter identification of non-linear state-space models-based on Gaussian process regression
Li, Xiaonan
Ma, Ping
Wu, Zehua
Chao, Tao
Yang, Ming
[J]. IET CONTROL THEORY AND APPLICATIONS, 2023, 17 (08): : 985 - 1001
[48] Lifting high-dimensional non-linear models with Gaussian regressors
Thrampoulidis, Christos
Rawat, Ankit Singh
[J]. 22ND INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 89, 2019, 89
[49] Iterative statistical linear regression for Gaussian smoothing in continuous-time non-linear stochastic dynamic systems
Tronarp, Filip
Sarkka, Simo
[J]. SIGNAL PROCESSING, 2019, 159 : 1 - 12
[50] Impact of edge-preserved Non-Linear Gaussian smoothing for attenuation correction in PET.
Kitamura, K
Kuwamura, S
Shidahara, M
Iida, I
Miura, S
Kanno, I
[J]. JOURNAL OF NUCLEAR MEDICINE, 2000, 41 (05) : 197P - 197P

← 1 2 3 4 5 →