Implicit Sampling, with Application to Data Assimilation

Alexandre, Stéphane; Chorin,; Matthias,; Morzfeld,; Xuemin,; Ту,

doi:10.1007/978-3-642-41401-5_6

Cited by 2 publications

(5 citation statements)

References 27 publications

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“…For comparison, the estimation results calculated by using our previous method [11] and standard method are also shown in Figure 5 and Figure 6. Since Kalman's filtering theory has been widely used in the field of stochastic system, the extended Kalman filter [5] was also applied to the observation data as a trail by using observation model shown in Equation (15). The results by our previous method show relatively good estimation.…”

Section: Application To Sound Environmentmentioning

confidence: 94%

“…Though the particle filter has been proposed as a state estimation method for nonlinear stochastic systems with non-Gaussian noise [12] [13] [14] [15], there remain a number of problems such as the complexity of calculation in resampling process and the tremendous calculation time based on Monte Carlo simulation. Furthermore, how to describe the likelihood function reflecting non-Gaussian properties for the observed data still remains in the process of realization of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

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State Estimation for Sound Environment System with Nonlinear Observation Characteristics by Introducing Wide-Sense Particle Filter

Orimoto¹,

Ikuta²,

Hasegawa³

2019

IIM

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In this study, a modified particle filter considering non-Gaussian properties of noises is proposed in a form applicable to real situation in sound environment system where the observation data are contaminated by the external noise (i.e., background noise) of arbitrary probability distribution and measured in decibel scale. More specifically, a nonlinear observation model in decibel scale with a quantized level is first paid considered by introducing the additive property of energy variables (i.e., sound intensity) in sound environment system. Next, a wide-sense particle filter of an expansion expression type is derived in a form suitable for the nonlinear observation characteristics and the signal processing considering higher-order correlation information between the specific signal and observation. Furthermore, the effectiveness of the proposed theory is confirmed by applying it to the observed data measured in real sound environment.

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Section: Application To Sound Environmentmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

State Estimation for Sound Environment System with Nonlinear Observation Characteristics by Introducing Wide-Sense Particle Filter

Orimoto¹,

Ikuta²,

Hasegawa³

2019

IIM

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“…The bias created by solving the quadratic equation ( 8) instead of ( 7) can be removed by the weights [2,9] w ∝ exp (F 0 (θ) − F (θ)) . (10) Note that the algorithm is mesh-independent in the sense of [6,28,37] due to the use of Hessian of F . Specifically, the eigenvectors associated with non-zero eigenvalues of the discrete Hessian span the same stochastic sub-space as the mesh is refined.…”

Section: Solving the Implicit Equations With Linear Mapsmentioning

confidence: 99%

“…The linear map method requires generating a sample using (9) and weighing it by (10). Evaluation of the weights thus requires one forward solve.…”

Section: Implementation Of the Random And Linear Mapsmentioning

confidence: 99%

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Parameter estimation by implicit sampling

Morzfeld

Wilkening

et al. 2015

Commun. Appl. Math. Comput. Sci.

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Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use implicit sampling in parameter estimation problems, where the goal is to find parameters of a numerical model, e.g. a partial differential equation (PDE), such that the output of the numerical model is compatible with (noisy) data. We use the Bayesian approach to parameter estimation, in which a posterior probability density describes the probability of the parameter conditioned on data and compute an empirical estimate of this posterior with implicit sampling. Our approach generates independent samples, so that some of the practical difficulties one encounters with Markov Chain Monte Carlo methods, e.g. burn-in time or correlations among dependent samples, are avoided. We describe a new implementation of implicit sampling for parameter estimation problems that makes use of multiple grids (coarse to fine) and BFGS optimization coupled to adjoint equations for the required gradient calculations. The implementation is "dimension independent", in the sense that a well-defined finite dimensional subspace is sampled as the mesh used for discretization of the PDE is refined. We illustrate the algorithm with an example where we estimate a diffusion coefficient in an elliptic equation from sparse and noisy pressure measurements. In the example, dimension/mesh-independence is achieved via Karhunen-Loève expansions.

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Implicit Sampling, with Application to Data Assimilation

Cited by 2 publications

References 27 publications

State Estimation for Sound Environment System with Nonlinear Observation Characteristics by Introducing Wide-Sense Particle Filter

State Estimation for Sound Environment System with Nonlinear Observation Characteristics by Introducing Wide-Sense Particle Filter

Parameter estimation by implicit sampling

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