Unscented von Mises–Fisher Filtering

Kurz, Gerhard; Gilitschenski, Igor; Hanebeck, Uwe D.

doi:10.1109/lsp.2016.2529854

Cited by 25 publications

(16 citation statements)

References 18 publications

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“…(2) When the noise term

is additive and von Mises–Fisher-distributed, we obtain a transition density in the form of a von Mises–Fisher distribution [ 15 ]; namely,

with

being a noise-invariant system function of arbitrary form and

denoting the concentration of the noise distribution. Then, the predicted density in Equation ( 6 ) can be expressed as

…”

Section: Progressive Unscented Von Mises–fisher Filteringmentioning

confidence: 99%

“…Therefore, deterministic sample sets are desired for an efficient and accurate representation of the underlying distribution. Reminiscent of the unscented Kalman filter (UKF) for linear domains, the so-called unscented von Mises–Fisher filter (UvMFF) was proposed in [ 15 ] on unit hyperspheres

. Following the idea of the unscented transform (UT),

deterministic samples are drawn in a way that preserves the mean resultant vector of the underlying von Mises–Fisher distribution.…”

Section: Introductionmentioning

confidence: 99%

“…There remains considerable space for improvement for state-of-the-art von Mises–Fisher filtering schemes in the area of high-performance hyperspherical estimation. The deterministic sampling method used in the current UvMFF [ 15 ] only allows fixed numbers of hyperspherical samples (i.e.,

samples on

) in accordance with the unscented transform. Moreover, the current UvMFF only allows identity measurement models with the measurement still confined to hyperspheres, and the measurement noise must be von Mises–Fisher-distributed.…”

Section: Introductionmentioning

confidence: 99%

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

Pfaff

Hanebeck

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.

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“…(2) When the noise term

is additive and von Mises–Fisher-distributed, we obtain a transition density in the form of a von Mises–Fisher distribution [ 15 ]; namely,

with

being a noise-invariant system function of arbitrary form and

denoting the concentration of the noise distribution. Then, the predicted density in Equation ( 6 ) can be expressed as

…”

Section: Progressive Unscented Von Mises–fisher Filteringmentioning

confidence: 99%

. Following the idea of the unscented transform (UT),

deterministic samples are drawn in a way that preserves the mean resultant vector of the underlying von Mises–Fisher distribution.…”

Section: Introductionmentioning

confidence: 99%

samples on

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Pfaff

Hanebeck

2021

Sensors

Self Cite

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“…Approaches to the Bayesian tracking of reference vectors have recently been developed on this principle. Discrete-time filters have been developed by using the von Mises-Fisher distribution, based on moment-matching [4], [5], [13], [14]. While another approach, based on score-matching [15], [16], was proposed in [17].…”

Section: Introductionmentioning

confidence: 99%

Continuous-Discrete von Mises-Fisher Filtering on S² for Reference Vector Tracking

Tronarp

Hostettler

Särkkä

2018

2018 21st International Conference on Information Fusion (FUSION)

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This paper is concerned with tracking of reference vectors in the continuous-discrete-time setting. For this end, an Itô stochastic differential equation, using the gyroscope as input, is formulated that explicitly accounts for the geometry of the problem. The filtering problem is solved by restricting the prediction and filtering distributions to the von Mises-Fisher class, resulting in ordinary differential equations for the parameters. A strategy for approximating Bayesian updates and marginal likelihoods is developed for the class of conditionally spherical measurement distributions, which is realistic for sensors such as accelerometers and magnetometers, and includes robust likelihoods. Furthermore, computationally efficient and numerically robust implementations are presented. The method is compared to other state-of-the-art filters in simulation experiments involving tracking of the local gravity vector. Additionally, the methodology is demonstrated in the calibration of a smartphone's accelerometer and magnetometer. Lastly, the method is compared to state-of-the-art in gravity vector tracking for smartphones in two use cases, where it is shown to be more robust to unmodeled accelerations.

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“…Our simulations show that the proposed positioning algorithms outperform the conventional algorithms in accuracy. VMF filters have also been proposed in [14][15][16][17], but in these filters both the state and measurements are VMF-distributed unit vectors.…”

Section: Introductionmentioning

confidence: 99%

3D Angle-of-Arrival Positioning Using von Mises-Fisher Distribution

Nurminen

Suomalainen

Ali-Löytty

et al. 2018

2018 21st International Conference on Information Fusion (FUSION)

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We propose modeling an angle-of-arrival (AOA) positioning measurement as a von Mises-Fisher (VMF) distributed unit vector instead of the conventional normally distributed azimuth and elevation measurements. Describing the 2dimensional AOA measurement with three numbers removes discontinuities and reduces nonlinearity at the poles of the azimuth-elevation coordinate system. Our computer simulations show that the proposed VMF measurement noise model based filters outperform the normal distribution based algorithms in accuracy in a scenario where close-to-pole measurements occur frequently.

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Unscented von Mises–Fisher Filtering

Cited by 25 publications

References 18 publications

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

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

Continuous-Discrete von Mises-Fisher Filtering on S² for Reference Vector Tracking

3D Angle-of-Arrival Positioning Using von Mises-Fisher Distribution

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Unscented von Mises–Fisher Filtering

Cited by 25 publications

References 18 publications

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

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

Continuous-Discrete von Mises-Fisher Filtering on S2 for Reference Vector Tracking

3D Angle-of-Arrival Positioning Using von Mises-Fisher Distribution

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Product

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Continuous-Discrete von Mises-Fisher Filtering on S² for Reference Vector Tracking