Kalman filter variants in the closed skew normal setting

Rezaie, Javad; Eidsvik, Jo

doi:10.1016/j.csda.2014.01.014

Cited by 20 publications

(12 citation statements)

References 15 publications

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“…The skew-normal distribution [32] is modified from a normal distribution by multiplying with a function whose skewness parameter is α. Skew-normal noise is a class of noise that includes normal-distribution noise as a limiting case. Although this distribution is not widely used as noise, it arises in simulations of noise for filters and detectors [34,36].…”

Section: Skew-normal-distribution Noisementioning

confidence: 99%

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Robustness of quantum-enhanced adaptive phase estimation

Palittapongarnpim

Sanders

2019

Phys. Rev. A

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As all physical adaptive quantum-enhanced metrology schemes operate under noisy conditions with only partially understood noise characteristics, so a practical control policy must be robust even for unknown noise. We aim to devise a test to evaluate the robustness of AQEM policies and assess the resource used by the policies. The robustness test is performed on adaptive phase estimation by simulating the scheme under four phase noise models corresponding to the normal-distribution noise, the random telegraph noise, the skew-normal-distribution noise, and the log-normal-distribution noise. The control policies are devised either by a reinforcement-learning algorithm in the same noise condition, albeit ignorant of its properties, or a Bayesian-based feedback method that assumes no noise. Our robustness test and resource comparison can be used to determining the efficacy and selecting a suitable policy.

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Section: Skew-normal-distribution Noisementioning

confidence: 99%

“…Skew-normal and log-normal distributions represent asymmetric noise, which serve as distinct generalizations of the normal distribution. Both distributions are used to simulate noise in detectors and electronics [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Robustness of quantum-enhanced adaptive phase estimation

Palittapongarnpim

Sanders

2019

Phys. Rev. A

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“…The prior for the initial state vector is a selection-Gaussian distribution, but instead of sampling the initial ensemble directly from the selection-Gaussian distribution, the proposed approach takes advantage of the structure of the selection-Gaussian to sample from a Gaussian augmented state vector, thereby preventing unwanted regression towards the mean while keeping the computational cost to a minimum. A similar approach has been proposed for asymmetric priors using the closed skew Gaussian distribution (Naveau et al 2005;Rezaie and Eidsvik 2014).…”

Section: Introductionmentioning

confidence: 99%

Ensemble-Based Seismic and Production Data Assimilation Using Selection Kalman Model

Conjard¹,

Grana

2021

Math Geosci

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Data assimilation in reservoir modeling often involves model variables that are multimodal, such as porosity and permeability. Well established data assimilation methods such as ensemble Kalman filter and ensemble smoother approaches, are based on Gaussian assumptions that are not applicable to multimodal random variables. The selection ensemble smoother is introduced as an alternative to traditional ensemble methods. In the proposed method, the prior distribution of the model variables, for example the porosity field, is a selection-Gaussian distribution, which allows modeling of the multimodal behavior of the posterior ensemble. The proposed approach is applied for validation on a two-dimensional synthetic channelized reservoir. In the application, an unknown reservoir model of porosity and permeability is estimated from the measured data. Seismic and production data are assumed to be repeatedly measured in time and the reservoir model is updated every time new data are assimilated. The example shows that the selection ensemble Kalman model improves the characterisation of the bimodality of the model parameters compared to the results of the ensemble smoother.

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“…Citation: H. Nurminen, T. Ardeshiri, R. Piché, and F. Gustafsson with skewed marginals. The article [16] proposes filtering of independent skew measurement and process noises with the cost of increasing the filter state's dimension over time. In all the skew filters of [14]- [16], sequential processing requires numerical evaluation of multidimensional integrals.…”

Section: Introductionmentioning

confidence: 99%

“…The article [16] proposes filtering of independent skew measurement and process noises with the cost of increasing the filter state's dimension over time. In all the skew filters of [14]- [16], sequential processing requires numerical evaluation of multidimensional integrals. The inference problem with skew likelihood distributions can also be cast into an optimization problem; [3] proposes an approach to model the measurement noise in an ultra-wideband (UWB) based positioning problem using a tailored half-normal-half-Cauchy distribution.…”

Section: Introductionmentioning

confidence: 99%

Skew-$t$ Filter and Smoother With Improved Covariance Matrix Approximation

Nurminen

Ardeshiri

Piché

et al. 2018

IEEE Trans. Signal Process.

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Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness variables to reduce the error caused by the variational approximation. Although the variational update is done suboptimally using an expectation propagation algorithm, our simulations show that the proposed method gives a more accurate approximation of the posterior covariance matrix than an earlier proposed variational algorithm. Consequently, the novel filter and smoother outperform the earlier proposed robust filter and smoother and other existing low-complexity alternatives in accuracy and speed. We present both simulations and tests based on real-world navigation data, in particular GPS data in an urban area, to demonstrate the performance of the novel methods. Moreover, the extension of the proposed algorithms to cover the case where the distribution of the measurement noise is multivariate skew-t is outlined. Finally, the paper presents a study of theoretical performance bounds for the proposed algorithms.

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Kalman filter variants in the closed skew normal setting

Cited by 20 publications

References 15 publications

Robustness of quantum-enhanced adaptive phase estimation

Robustness of quantum-enhanced adaptive phase estimation

Ensemble-Based Seismic and Production Data Assimilation Using Selection Kalman Model

Skew-$t$ Filter and Smoother With Improved Covariance Matrix Approximation

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