On Particle Methods for Parameter Estimation in State-Space Models

Kantas, Nikolas; Doucet, Arnaud; Singh, Sumeetpal S.; Maciejowski, Jan M.; Chopin, Nicolás

doi:10.1214/14-sts511

Cited by 410 publications

(368 citation statements)

References 95 publications

(199 reference statements)

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“…Usually, marginalization is implemented in an off-line manner. Data augmentation estimates the unknown parameters together with the states [11,18]. In other words, the data augmentation performs parameter estimation by extending the state with the unknown parameters and transforming the problem into an optimal filtering problem.…”

Section: Parameter Estimationmentioning

confidence: 99%

Random Finite Set Based Parameter Estimation Algorithm for Identifying Stochastic Systems

Wang

Peng

et al. 2018

Entropy

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Parameter estimation is one of the key technologies for system identification. The Bayesian parameter estimation algorithms are very important for identifying stochastic systems. In this paper, a random finite set based algorithm is proposed to overcome the disadvantages of the existing Bayesian parameter estimation algorithms. It can estimate the unknown parameters of the stochastic system which consists of a varying number of constituent elements by using the measurements disturbed by false detections, missed detections and noises. The models used for parameter estimation are constructed by using random finite set. Based on the proposed system model and measurement model, the key principles and formula derivation of the proposed algorithm are detailed. Then, the implementation of the algorithm is presented by using sequential Monte Carlo based Probability Hypothesis Density (PHD) filter and simulated tempering based importance sampling. Finally, the experiments of systematic errors estimation of multiple sensors are provided to prove the main advantages of the proposed algorithm. The sensitivity analysis is carried out to further study the mechanism of the algorithm. The experimental results verify the superiority of the proposed algorithm.

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Section: Parameter Estimationmentioning

confidence: 99%

Random Finite Set Based Parameter Estimation Algorithm for Identifying Stochastic Systems

Wang

Peng

et al. 2018

Entropy

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“…We present the auxiliary particle filter (APF) (Pitt and Shephard, 1999) here, as it covers a class of particle filter algorithms (Kantas et al, 2015) and is widely used in parameter and state estimation (Liu and West, 2001;Flury and Shephard, 2011). Let the proposal be q(x t , y t |x t−1 , ϕ) = q(x t |y t , x t−1 , ϕ)q(y t |x t−1 , ϕ), where q(x t |y t , x t−1 , ϕ) is a probability density function which is easy to sample from and q(y t |x t−1 , ϕ) is a nonnegative function that can be evaluated.…”

Section: Problem Statement and Particle Filter Algorithmmentioning

confidence: 99%

“…As studied by Liu and West (2001), they use a shrinkage strategy for kernel locations and variances estimation in order to removes the over-dispersion of the variances. Although this method works satisfactorily with a careful chosen shrinkage strategy, more efficient approach are still worth for further exploration (Kantas et al, 2015).…”

Section: Problem Statement and Particle Filter Algorithmmentioning

confidence: 99%

“…However, this naive approach has been recognized not to be efficient, because the parameter space is not well explored (Kitagawa, 1998;Liu and West, 2001). Consequently, various improve methods has been developed over the past fifteen years (Refer to Kantas et al (2015) for thoroughly review): maximum likelihood methods have been developed with different Monte Carlo evaluations of the likelihood of the model parameter (Hürzeler and Künsch, 2001;DeJong et al 2013), and gradient based optimization (Ionides et al, 2006;Ionides et al, 2011) or expectation maximization methods (Andrieu et al, 2005;Cappé, 2009) have been introduced for an on-line or off-line estimation of the model parameter. The maximum likelihood approach generally converges rather slowly, but it may be a good choice for large data sets because of its low complexity; Bayesian methods apply directly to the augmented states and Markov chain Monte Carlo steps are utilized to improve the inference/estimation of the model parameter ( Gilks and Berzuini, 2001;Fearnhead, 2002;Andrieu et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

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On Sequential Learning for Parameter Estimation in Particle Algorithms for State-Space Models

Ji¹

2016

IJSP

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Particle methods, also known as Sequential Monte Carlo, have been ubiquitous for Bayesian inference for state-space models, particulary when dealing with nonlinear non-Gaussian scenarios. However, in many practical situations, the state-space model contains unknown model parameters that need to be estimated simultaneously with the state. In this paper, We discuss a sequential analysis for combined parameter and state estimation. An online learning method is proposed to approach the distribution of the model parameter by tuning a flexible proposal mixture distribution to minimize their Kullback-Leibler divergence. We derive the sequential learning method by using a truncated Dirichlet processes normal mixture and present a general algorithm under a framework of the auxiliary particle filtering. The proposed algorithm is verified in a blind deconvolution problem, which is a typical state-space model with unknown model parameters. Furthermore, in a more challenging application that we call meta-modulation, which is a more complex blind deconvolution problem with sophisticated system evolution equations, the proposed method performs satisfactorily and achieves an exciting result for high efficiency communication.

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“…A recent overview of methods available to address this problem is provided by Kantas et al (2015). Here we focus upon the particular approach of Particle Markov chain Monte Carlo (PMCMC), developed by Andrieu et al (2010) PMCMC employs particle methods within MCMC to update the latent state sequence (either using MetropolisHastings or Gibbs-Sampler type updates).…”

Section: Introductionmentioning

confidence: 99%

On Blocks, Tempering and Particle MCMC for Systems Identification

Johansen

2015

IFAC-PapersOnLine

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The widespread use of particle methods for addressing the filtering and smoothing problems in state-space models has, in recent years, been complemented by the development of particle Markov Chain Monte Carlo (PMCMC) methods. PMCMC uses particle filters within offline systems-identification settings. We develop a modified particle filter, based around block sampling and tempering, intended to improve their exploration of the state space and the associated estimation of the marginal likelihood. The aim is to develop particle methods with improved robustness properties, particularly for parameter values which are not able to explain observed data well, for use within PMCMC algorithms. The proposed strategies do not require a substantial analytic understanding of the model structure, unlike most techniques for improving particle-filter performance.

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On Particle Methods for Parameter Estimation in State-Space Models

Cited by 410 publications

References 95 publications

Random Finite Set Based Parameter Estimation Algorithm for Identifying Stochastic Systems

Random Finite Set Based Parameter Estimation Algorithm for Identifying Stochastic Systems

On Sequential Learning for Parameter Estimation in Particle Algorithms for State-Space Models

On Blocks, Tempering and Particle MCMC for Systems Identification

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