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Keywords = Sinkhorn–Knopp algorithm

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17 pages, 2030 KB  
Article
Regularized Optimal Transport Based on an Adaptive Adjustment Method for Selecting the Scaling Parameters of Unscented Kalman Filters
by Chang Ho Kang and Sun Young Kim
Sensors 2022, 22(3), 1257; https://doi.org/10.3390/s22031257 - 7 Feb 2022
Viewed by 2560
Abstract
In this paper, an adaptation method for adjusting the scaling parameters of an unscented Kalman filter (UKF) is proposed to improve the estimation performance of the filter in dynamic conditions. The proposed adaptation method is based on a sequential algorithm that selects the [...] Read more.
In this paper, an adaptation method for adjusting the scaling parameters of an unscented Kalman filter (UKF) is proposed to improve the estimation performance of the filter in dynamic conditions. The proposed adaptation method is based on a sequential algorithm that selects the scaling parameter using the user-defined distribution of discrete sets to more effectively deal with the changing measurement distribution over time and avoid the additional process for training a filter model. The adaptation method employs regularized optimal transport (ROT), which compensates for the error of the predicted measurement with the current measurement values to select the proper scaling parameter. In addition, the Sinkhorn–Knopp algorithm is used to minimize the cost function of ROT due to its fast convergence rate, and the convergence of the proposed ROT-based adaptive adjustment method is also analyzed. According to the analysis results of Monte Carlo simulations, it is confirmed that the proposed algorithm shows better performance than the conventional algorithms in terms of the scaling parameter selection in the UKF. Full article
(This article belongs to the Section Optical Sensors)
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16 pages, 645 KB  
Article
Overrelaxed Sinkhorn–Knopp Algorithm for Regularized Optimal Transport
by Alexis Thibault, Lénaïc Chizat, Charles Dossal and Nicolas Papadakis
Algorithms 2021, 14(5), 143; https://doi.org/10.3390/a14050143 - 30 Apr 2021
Cited by 13 | Viewed by 7019
Abstract
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. [...] Read more.
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. In practice, such approaches lead to fast algorithms, but their global convergence is not ensured. Hence, we next proposed a new algorithm with convergence guarantees. The idea is to overrelax the Bregman projection operators, allowing for faster convergence. We proposed a simple method for establishing global convergence by ensuring the decrease of a Lyapunov function at each step. An adaptive choice of the overrelaxation parameter based on the Lyapunov function was constructed. We also suggested a heuristic to choose a suitable asymptotic overrelaxation parameter, based on a local convergence analysis. Our numerical experiments showed a gain in convergence speed by an order of magnitude in certain regimes. Full article
(This article belongs to the Special Issue Optimal Transport: Algorithms and Applications)
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