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Author

Akio Nakabayashi

Bio: Akio Nakabayashi is an academic researcher from Graduate University for Advanced Studies. The author has contributed to research in topics: Covariance matrix & Covariance function. The author has an hindex of 2, co-authored 2 publications receiving 14 citations.

Papers
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Journal ArticleDOI
TL;DR: This paper presents a new method for handling outliers in nonlinear filtering problems by extending the unscented Kalman filter that can estimate the system state better than existing methods for both datasets with and without outliers.
Abstract: This article considers a nonlinear filtering method for handling outliers. The presence of outliers that are gross observation errors can greatly reduce the accuracy of filtering methods that assume Gaussian distributed errors. There are some existing methods that assume a Gaussian observation error, and estimate the error covariance matrix at each time step to avoid overfitting to the outliers. However, the estimates of the covariance matrix under such methods can become unstable. This results in underfitting or overfitting to observations when filtering. This paper presents a new method for handling outliers in nonlinear filtering problems by extending the unscented Kalman filter. In this method, two Gaussian observation error models with distinct covariance matrices are used: one for observations with regular errors, and another with a larger variance specified by a scale parameter for outliers. In addition to the system state, this method estimates an indicator variable that switches between the two models and the scale parameter for outliers. With the inclusion of the indicator variable and scale parameter, the estimated error covariance matrix can handle both regular observations and outliers appropriately at each time step. Furthermore, by estimating the scale parameter, the proposed method can be applied to a dataset without additional tuning to account for outlier characteristics. Through numerical experiments, we find that our method can estimate the system state better than existing methods for both datasets with and without outliers.

10 citations

Journal ArticleDOI
TL;DR: In this paper, an extension of the EnKF that can simultaneously estimate the state vector and the observation error covariance matrix by using the variational Bayes (VB) method is presented.
Abstract: This paper presents an extension of the ensemble Kalman filter (EnKF) that can simultaneously estimate the state vector and the observation error covariance matrix by using the variational Bayes’s (VB) method. In numerical experiments, this capability is examined for a time-variant observation error covariance matrix, and it is noteworthy that this method works well even when the true observation error covariance matrix is nondiagonal. In addition, two complementary studies are presented. First, the stability of a long-run assimilation is demonstrated when there are unmodeled disturbances. Second, a maximum-likelihood (ML) method is derived and demonstrated for optimizing the hyperparameters used in this method.

8 citations


Cited by
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Journal ArticleDOI
TL;DR: The proposed hybrid EnKF‐N method of adaptive inflation is found to yield systematic accuracy improvements in comparison with the existing methods, albeit to a moderate degree.
Abstract: This paper studies multiplicative inflation: the complementary scaling of the state covariance in the ensemble Kalman filter (EnKF). Firstly, error sources in the EnKF are catalogued and discussed in relation to inflation; nonlinearity is given particular attention as a source of sampling error. In response, the “finite‐size” refinement known as the EnKF‐N is re‐derived via a Gaussian scale mixture, again demonstrating how it yields adaptive inflation. Existing methods for adaptive inflation estimation are reviewed, and several insights are gained from a comparative analysis. One such adaptive inflation method is selected to complement the EnKF‐N to make a hybrid that is suitable for contexts where model error is present and imperfectly parametrized. Benchmarks are obtained from experiments with the two‐scale Lorenz model and its slow‐scale truncation. The proposed hybrid EnKF‐N method of adaptive inflation is found to yield systematic accuracy improvements in comparison with the existing methods, albeit to a moderate degree.

40 citations

Journal ArticleDOI
TL;DR: In this article, the EnKF-based data assimilation method was used to estimate the true shape of the grain boundary energy cusp and the GB mobility peak in a 3D-MPF model.

33 citations

Journal ArticleDOI
TL;DR: The performance of different sigma-point update frameworks for CKF is analyzed by simulation on tightly coupled GNSS/INS, and observations missing during different maneuvers are simulated to evaluate the performance of resampling-free HCKF.

14 citations