A New Method for Generating Sigma Points and Weights for Nonlinear Filtering

Radhakrishnan, R.; Yadav, Ajay Kumar; Date, Paresh; Bhaumik, Shovan

doi:10.1109/lcsys.2018.2843184

Cited by 32 publications

(10 citation statements)

References 22 publications

(30 reference statements)

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“…which can be solved using the Lasserre's hierarchy. As the degree 2τ of the approximation polynomial increases, the solution of problem (15) converges to the solution of problem (14) in the sense of [34]. Alternatively, problem (12) can be shown to be equivalent to the following polynomial optimization problem:…”

Section: Polynomial Optimization Program To Compute Minimum Enclosingmentioning

confidence: 99%

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A robust unscented transformation for uncertain moments

Kussaba

Ishihara

Menezes

2019

Journal of the Franklin Institute

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This paper proposes a robust version of the unscented transform (UT) for one-dimensional random variables. It is assumed that the moments are not exactly known, but are known to lie in intervals. In this scenario, the moment matching equations are reformulated as a system of polynomial equations and inequalities, and it is proposed to use the Chebychev center of the solution set as a robust UT. This method yields a parametrized polynomial optimization problem, which in spite of being NP-Hard, can be relaxed by some algorithms that are proposed in this paper.

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Section: Polynomial Optimization Program To Compute Minimum Enclosingmentioning

confidence: 99%

“…In fact, many solutions are possible, and the choice of an adequate set of sigma points has been investigated thoroughly in the literature [6,15].…”

Section: Unscented Transformmentioning

confidence: 99%

A robust unscented transformation for uncertain moments

Kussaba

Ishihara

Menezes

2019

Journal of the Franklin Institute

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“…In the standard formulation of UT, the n dimensional ellipsoid is estimated by one sigma point at the expected value and further 2n sigma points selected symmetrically around it. There are other methods where more (e.g., 4n + 1) sigma points are used to achieve a better approximation of the uncertainty [15]. These sigma points are computed via Cholesky-factorization [16] of the covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

Computationally Relaxed Unscented Kalman Filter

Kuti

Rudas

Gao

et al. 2023

IEEE Trans. Cybern.

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Advanced robotics and autonomous vehicles rely on filtering and sensor fusion techniques to a large extent. These mobile applications need to handle the computations onboard at high rates while the computing capacities are limited. Therefore, any improvement that lowers the CPU time of the filtering leads to more accurate control or longer battery operation. This article introduces a generic computational relaxation for the unscented transformation (UT) that is the key operation of the Unscented Kalman filter-based applications. The central idea behind the relaxation is to pull out the linear part of the filtering model and avoid the calculations for the kernel of the nonlinear part. The practical merit of the proposed relaxation is demonstrated through a simultaneous localization and mapping (SLAM) implementation that underpins the superior performance of the algorithm in the practically relevant cases, where the nonlinear dependencies influence only an affine subspace of the image space. The numerical examples show that the computational demand can be mitigated below 50% without decreasing the accuracy of the approximation. The method described in this article is implemented and published as an open-source C++ library RelaxedUnscentedTransformation on GitHub.

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“…Based on the density approximation method presented in [8,9], reduced forms of the unscented Kalman filter (UKF), including minimal skew simplex UKF (MSS-UKF) [14] and spherical simplex UKF (SS-UKF) [15], are developed to reduce the computational cost by decreasing the number of sample points. Based on the literature, a couple of other new methods have also been proposed to generate sigma-points [16,17].…”

Section: Introductionmentioning

confidence: 99%