Direct, prediction- and smoothing-based Kalman and particle filter algorithms

This paper considers the Bayesian filtering problem in high-dimensional nonlinear state-space systems. In such systems, classical particle filters (PFs) are impractical due to the prohibitive number of required particles to obtain reasonable performances. One approach that has been introduced to overcome this problem is the concept of multiple PFs (MPFs), where the state-space is split into low-dimensional subspaces and then a separate PF is applied to each subspace. Remarkable performances of MPF-like filters motivated our investigation here into a new strategy that combines the variational Bayesian approach to split the state-space with random sampling techniques, to derive a new computationally efficient MPF. The propagation of each particle in the prediction step of the resulting filter requires generating only a single particle in contrast with standard MPFs, for which a set of (children) particles is required. We present simulation results to evaluate the behavior of the proposed filter and compare its performances against standard PF and a MPF.

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“…We consider a vectorial version of a nonlinear system extensively used in the PF literature (see e.g. [6] [11] [12]):…”

Section: Simulationsmentioning

confidence: 99%

A Variational Bayesian Multiple Particle Filtering Scheme for Large-Dimensional Systems

Ait‐El‐Fquih

Hoteit

2016

IEEE Trans. Signal Process.

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“…One may indeed reverse the order of the time-and measurement-update steps by involving the OSA smoothing pdf, p(z n−1 |y 0:n ), between two successive analysis pdf's: p(z n−1 |y 0:n−1 ) and p(z n |y 0:n ). Desbouvries et al (2011) considered the OSA smoothing-based filtering problem in low-dimensional statespace systems to derive a class of KF-and PF-like algorithms for filtering the state. The more recent work of Lee and Farmer (2014) proposed a number of algorithms to estimate both the system state and the model noise based on a similar strategy.…”

Section: Probabilistic Formulationmentioning

confidence: 99%

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

Ait‐El‐Fquih

Gharamti

Hoteit

2016

Hydrol. Earth Syst. Sci.

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Abstract. Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The joint EnKF directly updates the augmented state-parameter vector, whereas the dual EnKF empirically employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. To develop a Bayesian consistent dual approach and improve the stateparameter estimates and their consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of the state-parameter Bayesian filtering problem from which we derive a new dual-type EnKF, the dual EnKF OSA . Compared with the standard dual EnKF, it imposes a new update step to the state, which is shown to enhance the performance of the dual approach with almost no increase in the computational cost. Numerical experiments are conducted with a twodimensional (2-D) synthetic groundwater aquifer model to investigate the performance and robustness of the proposed dual EnKF OSA , and to evaluate its results against those of the joint and dual EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, providing further reliable estimates of their uncertainties. Furthermore, it is found to be more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25 % more accurate state and parameter estimations than the joint and dual approaches.

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“…(12), (13), (15)) and independently one from the two UQ methods (Eqs. (4), (5) with n ′ = n+1) to construct a conventional filter.…”

Section: Construction Of Gaussian Smoothing Filtersmentioning

confidence: 99%

Data Assimilation by Conditioning of Driving Noise on Future Observations

Lee

Farmer

2014

IEEE Trans. Signal Process.

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Abstract-Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where the associated data is assimilated using Bayes' rule. In this paper we switch the order of the steps to: (i) one step ahead data assimilation followed by (ii) uncertainty propagation. This route leads to a class of filtering algorithms named smoothing filters. For a system driven by random noise, our proposed methods require the probability distribution of the driving noise after the assimilation to be biased by a nonzero mean. The system noise, conditioned on future observations, in turn pushes forward the filtering solution in time closer to the true state and indeed helps to find a more accurate approximate solution for the state estimation problem.

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Direct, prediction- and smoothing-based Kalman and particle filter algorithms

Cited by 25 publications

References 18 publications

A Variational Bayesian Multiple Particle Filtering Scheme for Large-Dimensional Systems

A Variational Bayesian Multiple Particle Filtering Scheme for Large-Dimensional Systems

A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology

Data Assimilation by Conditioning of Driving Noise on Future Observations

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