The Bingham-Gauss Mixture Filter for Pose Estimation

Darling, Jacob E.; DeMars, Kyle J.

doi:10.2514/6.2016-5631

Cited by 2 publications

(9 citation statements)

References 9 publications

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“…angular velocities) and the attitude on its manifold. Some of these implementations are the Partially-Conditioned Gaussian Mixtures (PCGM) [34], the Gauss-Bingham (GaBi) [10] and the Bingham-Gauss (BiGa) [7] distributions. These approaches allow us to capture the covariance between the attitude and angular velocity uncertainties.…”

Section: B Pose Trackingmentioning

confidence: 99%

“…whereq 7 is the sample located on the pole (identity quaternion). The canonical distribution will be employed since it simplifies the needed mathematical approach because the parameters will be dimensionless.…”

Section: Appendix C Bingham Filter Sigma Points Creationmentioning

confidence: 99%

“…Is possible to use the definition of conditional probability to construct a distribution that consists in the product of a Bi distribution and a Gaussian distribution conditioned on the Bi distributed random variables. The BiGa PDF is given by [7]:…”

Section: Appendix D Bingham-gaussmentioning

confidence: 99%

“…We have to guarantee that this distribution is antipodally symmetric with q and −q representing the same attitude. The PDF described in (58) needs to be divided into two hemispheres of the unit hypersphere to guarantee that condition [7]. The BiGa PDF becomes represented as: P BG = P BG q, ω; m ω , P ω , P q , P qω q ∈ S + P BG q, ω; m ω , P ω , P q , −P qω q ∈ S − (64) where S + and S − represent the hemispheres.…”

Section: A Distribution Parametersmentioning

confidence: 99%

“…Some examples of data that may be considered as directional statistics are orientations, compass directions and time of day. The BiGa distribution (Appendix D), consists in the product of a Bi distribution and a Gaussian distribution conditioned on the Bi distributed random variables [7]. This distribution allows us to capture dependencies between the angular velocity and the UAV attitude.…”

Section: Introductionmentioning

confidence: 99%

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Directional Statistics for 3D Model-Based UAV Tracking

2020

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We present a vision system based on a monocular camera to track the 3D position and orientation of an Unmanned Aerial Vehicle (UAV) during the landing process aboard a ship. The proposed method uses a 3D model-based approach based on a Particle Filter (PF) with proposal distributions given by an Unscented Kalman Filter (UKF) for the translational motion and filters based on directional statistics for the rotational motion. Our main contributions are (i) the development of a novel 3D model-based tracking architecture based on directional statistics that can be easily adapted to other tracking problems, and (ii) the development of the Unscented Bingham-Gauss Filter (UBiGaF) for rotation estimation. We show the advantages of using directional statistics based filters on 3D model-based tracking in a series of quantitative tests in a challenging simulation scenario with real video data. The obtained position and angular error are compatible with the automatic landing system requirements when using directional statistics. We obtain lower error when using the UBiGaF scheme for the vast majority of the tested combinations. INDEX TERMS Unmanned aerial vehicles, computer vision, motion estimation, algorithm design and analysis, military vehicles.

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Section: B Pose Trackingmentioning

confidence: 99%

Section: Appendix C Bingham Filter Sigma Points Creationmentioning

confidence: 99%

Section: Appendix D Bingham-gaussmentioning

confidence: 99%

Section: A Distribution Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Directional Statistics for 3D Model-Based UAV Tracking

2020

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Fixed-Wing Unmanned Aerial Vehicle 3D-Model-Based Tracking for Autonomous Landing

Santos

Lobo

Bernardino

2023

Drones

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The vast increase in the available computational capability has allowed the application of Particle-Filter (PF)-based approaches for monocular 3D-model-based tracking. These filters depend on the computation of a likelihood function that is usually unavailable and can be approximated using a similarity metric. We can use temporal filtering techniques between filter iterations to achieve better results when dealing with this suboptimal approximation, which is particularly important when dealing with the Unmanned Aerial Vehicle (UAV) model symmetry. The similarity metric evaluation time is another critical concern since we usually want a real-time implementation. We explored, tested, and compared with the same dataset two different types of PFs, (i) an Unscented Bingham Filter (UBiF) and (ii) an Unscented Bingham–Gauss Filter (UBiGaF), using pose optimization in both implementations. Using optimization steps between iterations increases the convergence capability of the filter and decreases the obtained error. A new tree-based similarity metric approach is also explored based on the Distance Transform (DT), allowing a faster evaluation of the possibilities without losing accuracy. The results showed that the obtained pose estimation error is compatible with the automatic landing requirements.

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The Bingham-Gauss Mixture Filter for Pose Estimation

Cited by 2 publications

References 9 publications

Directional Statistics for 3D Model-Based UAV Tracking

Directional Statistics for 3D Model-Based UAV Tracking

Fixed-Wing Unmanned Aerial Vehicle 3D-Model-Based Tracking for Autonomous Landing

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