A comparison of simultaneous state and parameter estimation schemes for a continuous fermentor reactor

Chitralekha, Saneej B.; Prakash, J.; Raghavan, Harigopal; Gopaluni, R. Bhushan; Shah, Sirish L.

doi:10.1016/j.jprocont.2010.06.008

Cited by 39 publications

(18 citation statements)

References 13 publications

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“…The EM algorithm has also been used in conjunction with the EnKS and the Extended Kalman Smoother (EKS) to estimate physical parameters in chemical (Chitralekha et al , 2010) and neuroscience (Kulkarni and Paninski, 2007) applications relying on nonlinear dynamical models. (Ueno and Nakamura, 2014) used the EM algorithm to sequentially compute an approximation of the maximum likelihood estimate of the observation‐error covariance in a data assimilation scheme using the EnKF.…”

Section: Introductionmentioning

confidence: 99%

Estimating model‐error covariances in nonlinear state‐space models using Kalman smoothing and the expectation–maximization algorithm

Dreano

Tandeo

Pulido

et al. 2017

Quart J Royal Meteoro Soc

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Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation-maximisation (EM) algorithm to estimate the model error covariances using classical extended and ensemble versions of the Kalman smoother. We show that, for additive model errors, the estimate of the error covariance converges. We also investigate other forms of model error, such as parametric or multiplicative errors. We show that additive Gaussian model error is able to compensate for non additive sources of error in the algorithms wepropose. We also demonstrate the limitations of the extended version of the algorithm and recommend the use of the more robust and flexible ensemble version. This article is a proof of concept of the methodology with the Lorenz-63 attractor. We developed an open-source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models.

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Section: Introductionmentioning

confidence: 99%

Estimating model‐error covariances in nonlinear state‐space models using Kalman smoothing and the expectation–maximization algorithm

Dreano

Tandeo

Pulido

et al. 2017

Quart J Royal Meteoro Soc

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“…The EM algorithm for parameter estimation in nonlinear SSMs has been widely applied due to the asymptotic consistency and efficiency of the resulting estimates (Chitralekha et al, 2010). The EM algorithm includes two steps: (1) computing the expectation and (2) the maximization step (Wills et al, 2008).…”

Section: Smc-based Maximum Likelihood Estimationmentioning

confidence: 99%

“…In this study, we mainly describe the major procedures; and more details of this algorithm and its applications can be found in references such as Wills et al (2008), Gopaluni (2008), Chitralekha et al (2010) and Schön et al (2011).…”

Section: Smc-based Maximum Likelihood Estimationmentioning

confidence: 99%

Sequential Monte Carlo methods for parameter estimation in nonlinear state-space models

Gao

Zhang

2012

Computers & Geosciences

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“…Here we focus on inference in complex models that do not admit analytic solutions, for which sequential Monte Carlo (SMC) methods are widely used to approximate the expectation in the E-step. Generally, the use of Monte Carlo methods in the context of EM is known as stochastic approximation EM (SAEM; Delyon et al 1999) and this class of methods is favored in practice over gradient-based approaches due to their relative stability and computational efficiency when estimating high dimensional parameters (Chitralekha et al 2010;Kantas et al 2009).…”

Section: Introductionmentioning

confidence: 99%

Efficient inference in state-space models through adaptive learning in online Monte Carlo expectation maximization

Henderson

Lunter

2019

Comput Stat

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Expectation maximization (EM) is a technique for estimating maximum-likelihood parameters of a latent variable model given observed data by alternating between taking expectations of sufficient statistics, and maximizing the expected log likelihood. For situations where sufficient statistics are intractable, stochastic approximation EM (SAEM) is often used, which uses Monte Carlo techniques to approximate the expected log likelihood. Two common implementations of SAEM, Batch EM (BEM) and online EM (OEM), are parameterized by a "learning rate", and their efficiency depend strongly on this parameter. We propose an extension to the OEM algorithm, termed Introspective Online Expectation Maximization (IOEM), which removes the need for specifying this parameter by adapting the learning rate according to trends in the parameter updates. We show that our algorithm matches the efficiency of the optimal BEM and OEM algorithms in multiple models, and that the efficiency of IOEM can exceed that of BEM/OEM methods with optimal learning rates when the model has many parameters. A Python implementation is available at https://github.com/luntergroup/IOEM.git.

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A comparison of simultaneous state and parameter estimation schemes for a continuous fermentor reactor

Cited by 39 publications

References 13 publications

Estimating model‐error covariances in nonlinear state‐space models using Kalman smoothing and the expectation–maximization algorithm

Estimating model‐error covariances in nonlinear state‐space models using Kalman smoothing and the expectation–maximization algorithm

Sequential Monte Carlo methods for parameter estimation in nonlinear state-space models

Efficient inference in state-space models through adaptive learning in online Monte Carlo expectation maximization

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