Optimal Estimation and Cramér-Rao Bounds for Partial Non-Gaussian State Space Models

被引：5

作者：

Niclas Bergman

Arnaud Doucet

Neil Gordon

机构：

[1] Linköping University,Division of Automatic Control

[2] University of Cambridge,Signal Processing Group, Department of Engineering

[3] Defence Evaluation and Research Agency,undefined

来源：

Annals of the Institute of Statistical Mathematics | 2001年 / 53卷

关键词：

Optimal estimation; Bayesian inference; sequential Monte Carlo methods; posterior Cramér-Rao bounds;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Partial non-Gaussian state-space models include many models of interest while keeping a convenient analytical structure. In this paper, two problems related to partial non-Gaussian models are addressed. First, we present an efficient sequential Monte Carlo method to perform Bayesian inference. Second, we derive simple recursions to compute posterior Cramér-Rao bounds (PCRB). An application to jump Markov linear systems (JMLS) is given.

引用

页码：97 / 112

页数：15

共 36 条

[1]

Bergman N.(1999)Terrain navigation using Bayesian statistics IEEE Control Systems Magazine 19 33-40

[2]

Ljung L.(1975)A lower bound on the estimation error for Markov processes IEEE Trans. Automat. Control 20 785-788

[3]

Gustafsson F.(1994)On Gibbs sampling for state space models Biometrika 81 541-553

[4]

Borobsky B. Z.(1996)Markov chain Monte Carlo methods in conditionally Gaussian state space models Biometrika 83 589-601

[5]

Zakai M.(1999)Discrete filtering using branching and interacting particle systems Markov Processes and Related Fields 5 293-318

[6]

Carter C. K.(1995)Cramér-Rao bounds for discrete-time nonlinear filtering problems IEEE Trans. Automat. Control 40 1465-1469

[7]

Kohn R.(2000)On sequential Monte Carlo sampling methods for Bayesian filtering Statist. Comput. 10 197-208

[8]

Carter C. K.(1994)Data augmentation and dynamic linear models J. Time Ser. Anal. 15 183-202

[9]

Kohn R.(1980)A Cramér-Rao bound for discrete-time nonlinear filtering problems IEEE Trans. Automat. Control 25 117-119

[10]

Crisan D.(1995)Applications of the Van Trees inequality: a Bayesian Cramér Rao bound Bernoulli 1 59-79

← 1 2 3 4 →