Wavefront Orientation Estimation Based on Progressive Bingham Filtering

2021

Sensors

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In this work, we present a novel scheme for nonlinear hyperspherical estimation using the von Mises–Fisher distribution. Deterministic sample sets with an isotropic layout are exploited for the efficient and informative representation of the underlying distribution in a geometrically adaptive manner. The proposed deterministic sampling approach allows manually configurable sample sizes, considerably enhancing the filtering performance under strong nonlinearity. Furthermore, the progressive paradigm is applied to the fusing of measurements of non-identity models in conjunction with the isotropic sample sets. We evaluate the proposed filtering scheme in a nonlinear spherical tracking scenario based on simulations. Numerical results show the evidently superior performance of the proposed scheme over state-of-the-art von Mises–Fisher filters and the particle filter.

Section: Discussionmentioning

confidence: 99%

“…Consequently, deterministic samples of small sizes are less likely to degenerate and become more deployable for nonlinear estimation. Similar schemes have also been proposed for estimating angular systems [ 28 ] and Bingham-based hyperspherical filtering [ 29 ] with non-identity measurement models.…”

Section: Introductionmentioning

confidence: 99%

Progressive von Mises–Fisher Filtering Using Isotropic Sample Sets for Nonlinear Hyperspherical Estimation

2021

Sensors

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“…The proposed method could be enhanced in two ways: (1) For non-identity measurement models with a known likelihood function, the progressive update method [33], [34] could be used in conjunction with the proposed sampling scheme for further improvement on filtering performance.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear von Mises–Fisher Filtering Based on Isotropic Deterministic Sampling

2020 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI)

2020

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We present a novel deterministic sampling approach for von Mises-Fisher distributions of arbitrary dimensions. Following the idea of the unscented transform, samples of configurable size are drawn isotropically on the hypersphere while preserving the mean resultant vector of the underlying distribution. Based on these samples, a von Mises-Fisher filter is proposed for nonlinear estimation of hyperspherical states. Compared with existing von Mises-Fisher-based filtering schemes, the proposed filter exhibits superior hyperspherical tracking performance.

“…We compare the sample reduction-based filter (SRF) proposed in Sec. IV with a plain particle filter (PF) and the SE(2)-Bingham filter (SE2BF) with a progressive update step [14], [27]. As the SE2BF relies on the SE(2)-Bingham distribution [12], we exploit 10 5 random samples for fitting the parametric model offline.…”

Section: Discussionmentioning

confidence: 99%

Dual Quaternion Sample Reduction for SE(2) Estimation

2020 IEEE 23rd International Conference on Information Fusion (FUSION)

2020

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We present a novel sample reduction scheme for random variables belonging to the SE(2) group by means of Dirac mixture approximation. For this, dual quaternions are employed to represent uncertain planar transformations. The Cramér-von Mises distance is modified as a smooth metric to measure the statistical distance between Dirac mixtures on the manifold of planar dual quaternions. Samples of reduced size are then obtained by minimizing the probability divergence via Riemannian optimization while interpreting the correlation between rotation and translation. We further deploy the proposed scheme for nonparametric modeling of estimates for nonlinear SE(2) estimation. Simulations show superior tracking performance of the sample reduction-based filter compared with Monte Carlo-based as well as parametric model-based planar dual quaternion filters.