Long-Time Stability and Accuracy of the Ensemble Kalman--Bucy Filter for Fully Observed Processes and Small Measurement Noise

Wiljes, Jana de; Reich, Sebastian; Stannat, Wilhelm

doi:10.1137/17m1119056

Cited by 76 publications

(147 citation statements)

References 27 publications

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“…If ESS n (1) > J thresh , then then we can simply set φ n = 1 as no further tempering is thus required. Once the tempering parameter φ n has been computed via (23), normalised weights (20) can be computed. Since some of these can be very low, resampling with replacement according to these weights is then required to discard particles associated with those low weights.…”

Section: Selection-resamplingmentioning

confidence: 99%

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Transform-based particle filtering for elliptic Bayesian inverse problems

Ruchi¹,

Dubinkina²,

Iglesias³

2019

Inverse Problems

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We introduce optimal transport based resampling in adaptive SMC. We consider elliptic inverse problems of inferring hydraulic conductivity from pressure measurements. We consider two parametrizations of hydraulic conductivity: by Gaussian random field, and by a set of scalar (non-)Gaussian distributed parameters and Gaussian random fields. We show that for scalar parameters optimal transport based SMC performs comparably to monomial based SMC but for Gaussian highdimensional random fields optimal transport based SMC outperforms monomial based SMC. When comparing to ensemble Kalman inversion with mutation (EKI), we observe that for Gaussian random fields, optimal transport based SMC gives comparable or worse performance than EKI depending on the complexity of the parametrization. For non-Gaussian distributed parameters optimal transport based SMC outperforms EKI.

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Section: Selection-resamplingmentioning

confidence: 99%

“…There also exists a second-order accurate ETPF [23], which however does not satisfy T * ij ≥ 0. The main difference between resampling based on optimal transport and monomial resampling is that the former one is optimal in the sense of the Monge-Kantorovitch problem, while the latter one is non-optimal in that sense.…”

Section: Optimal Transport Within Smcmentioning

confidence: 99%

Transform-based particle filtering for elliptic Bayesian inverse problems

Ruchi¹,

Dubinkina²,

Iglesias³

2019

Inverse Problems

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“…The sde (3) represents the mean-field limit of the interacting particle system (5). These models are referred to as McKean-Vlasov SDEs [17] and their analysis is referred to as propagation of chaos [22].…”

Section: Finite-n Systemmentioning

confidence: 99%

“…For the linear Gaussian setting, it is shown that (i) the empirical distribution converges to the mean-field limit for any finite time; (ii) and even for a finite number of particles, the long term error converges to zero [25]. The convergence and long term stability results are shown for the nonlinear setting as well, where it is assumed that drift function is Lipschitz and the system is fully observed with small measurement noise [5].…”

Section: Introductionmentioning

confidence: 96%

Error Analysis of the Stochastic Linear Feedback Particle Filter

Taghvaei

Mehta

2018

2018 IEEE Conference on Decision and Control (CDC)

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This paper is concerned with the convergence and long-term stability analysis of the feedback particle filter (FPF) algorithm. The FPF is an interacting system of N particles where the interaction is designed such that the empirical distribution of the particles approximates the posterior distribution. It is known that in the mean-field limit (N = ∞), the distribution of the particles is equal to the posterior distribution. However little is known about the convergence to the mean-field limit. In this paper, we consider the FPF algorithm for the linear Gaussian setting. In this setting, the algorithm is similar to the ensemble Kalman-Bucy filter algorithm. Although these algorithms have been numerically evaluated and widely used in applications, their convergence and long-term stability analysis remains an active area of research. In this paper, we show that, (i) the mean-field limit is well-defined with a unique strong solution; (ii) the mean-field process is stable with respect to the initial condition; (iii) we provide conditions such that the finite-N system is long term stable and we obtain some mean-squared error estimates that are uniform in time.

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“…The constant gain approximation formula has been used in nonlinear extensions of the EnKF algorithm [21]. The connection to the Poisson equation provides a justification for this formula.…”

mentioning

confidence: 99%

Gain function approximation in the feedback particle filter

Taghvaei

Mehta

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-This paper is concerned with numerical algorithms for gain function approximation in the feedback particle filter. The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The problem is to approximate this solution using only particles sampled from the probability distribution. Two algorithms are presented: a Galerkin algorithm and a kernel-based algorithm. Both the algorithms are adapted to the samples and do not require approximation of the probability distribution as an intermediate step. The paper contains error analysis for the algorithms as well as some comparative numerical results for a non-Gaussian distribution. These algorithms are also applied and illustrated for a simple nonlinear filtering example.

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Long-Time Stability and Accuracy of the Ensemble Kalman--Bucy Filter for Fully Observed Processes and Small Measurement Noise

Cited by 76 publications

References 27 publications

Transform-based particle filtering for elliptic Bayesian inverse problems

Transform-based particle filtering for elliptic Bayesian inverse problems

Error Analysis of the Stochastic Linear Feedback Particle Filter

Gain function approximation in the feedback particle filter

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