Optimal smoothing of non-linear dynamic systems via Monte Carlo Markov chains

被引:8
作者
Pillonetto, Gianluigi [1 ]
Bell, Bradley M. [2 ]
机构
[1] Univ Padua, Dept Informat Engn, I-35100 Padua, Italy
[2] Univ Washington, Appl Phys Lab, Seattle, WA 98105 USA
关键词
Bayesian estimation; state estimation; nonlinear time series; stochastic processes; iterated Kalman smoothing filter; stochastic fed-batch bioreactor;
D O I
10.1016/j.automatica.2007.10.028
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 [计算机科学与技术];
摘要
We consider the smoothing problem of estimating a sequence of state vectors given a nonlinear state space model with additive white Gaussian noise, and measurements of the system output. The system output may also be nonlinearly related to the system state. Often, obtaining the minimum variance state estimates conditioned on output data is not analytically intractable. To tackle this difficulty, a Markov chain Monte Carlo technique is presented. The proposal density for this method efficiently draws samples from the Laplace approximation of the posterior distribution of the state sequence given the measurement sequence. This proposal density is combined with the Metropolis-Hastings algorithm to generate realizations of the state sequence that converges to the proper posterior distribution. The minimum variance estimate and confidence intervals are approximated using these realizations. Simulations of a fed-batch bioreactor model are used to demonstrate that the proposed method can obtain significantly better estimates than the iterated Kalman-Bucy smoother. (c) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1676 / 1685
页数:10
相关论文
共 22 条
[1]
[Anonymous], 1993, MATH OPERATIONS RES
[2]
The marginal likelihood for parameters in a discrete Gauss-Markov process [J].
Bell, BM .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2000, 48 (03) :870-873
[3]
BELL BM, 1994, SIAM J CONTROL OPTIM, V4, P156
[4]
CARTER CK, 1994, BIOMETRIKA, V81, P541
[5]
CRISAN D, 2001, PARTICLE FILTERS THE
[6]
Del Moral P, 1998, ANN APPL PROBAB, V8, P438
[7]
On sequential Monte Carlo sampling methods for Bayesian filtering [J].
Doucet, A ;
Godsill, S ;
Andrieu, C .
STATISTICS AND COMPUTING, 2000, 10 (03) :197-208
[8]
GILKS WR, 1996, M CHAIN M CARLO PRAC
[9]
Monte Carlo smoothing for nonlinear time series [J].
Godsill, SJ ;
Doucet, A ;
West, M .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2004, 99 (465) :156-168
[10]
NOVEL-APPROACH TO NONLINEAR NON-GAUSSIAN BAYESIAN STATE ESTIMATION [J].
GORDON, NJ ;
SALMOND, DJ ;
SMITH, AFM .
IEE PROCEEDINGS-F RADAR AND SIGNAL PROCESSING, 1993, 140 (02) :107-113