A Code for Unscented Kalman Filtering on Manifolds (UKF-M)

Brossard, Martin; Barrau, Axel; Bonnabel, Silvère

doi:10.1109/icra40945.2020.9197489

Cited by 38 publications

(38 citation statements)

References 48 publications

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“…6], which would require an optimization procedure to find the mean Č on SO(3) [11]. However, as suggested by [12], and verified extensively through simulation in this paper, it is sufficient to simply obtain the nominal points (ρ, Č) by passing ř through the nonlinear model ( 2), (ρ, Č) = h(ř), without an apparent loss in accuracy. An example of the results of this sigma point procedure can be visualized in Figure 2.…”

Section: A Converting a Cartesian Gaussian Distribution To Directiona...mentioning

confidence: 86%

Localization with Directional Coordinates

Cossette¹,

Shalaby²,

Saussié³

et al. 2021

Preprint

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A coordinate system is proposed that replaces the usual three-dimensional Cartesian x, y, z position coordinates, for use in robotic localization applications. Range, azimuth, and elevation measurement models become greatly simplified, and, unlike spherical coordinates, the proposed coordinates do not suffer from the same kinematic singularities and angle wraparound. When compared to Cartesian coordinates, the proposed coordinate system results in a significantly enhanced ability to represent the true distribution of robot positions, ultimately leading to large improvements in state estimation consistency.

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Section: A Converting a Cartesian Gaussian Distribution To Directiona...mentioning

confidence: 86%

Localization with Directional Coordinates

Cossette¹,

Shalaby²,

Saussié³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The PF, ProgSE2BF, and S3F are part of the latest version of libDirectional [ 28 ]. For the UKF-M, we use the implementation of [ 13 ]. The UKF-M involves a parameter that can be tuned, which is called

in [ 29 ].…”

Section: Discussionmentioning

confidence: 99%

“…This parameter influences how far away from the mean the sigma points of the UKF [ 30 ] are placed. [ 13 ] recommends values in the range

. The implementation allows specifying different parameters for the state uncertainty, the uncertainty introduced in the prediction step, and the measurement uncertainty.…”

Section: Discussionmentioning

confidence: 99%

“…However, PFs suffer from particle degeneracy and impoverishment [ 10 ] and can be slow to converge [ 11 ]. Other general approaches that can be applied to

are the invariant extended and unscented Kalman filter [ 12 ] and the unscented Kalman filter on manifolds (UKF-M) [ 13 ]. An approach tailored explicitly to

that is based on dual quaternions was proposed in [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

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The State Space Subdivision Filter for Estimation on SE(2)

Pfaff

Hanebeck

2021

Sensors

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The SE(2) domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle. We present a novel filter that involves splitting up the joint density into a (marginalized) density for the periodic part and a conditional density for the linear part. We subdivide the state space along the periodic dimension and describe each part of the state space using the parameters of a Gaussian and a grid value, which is the function value of the marginalized density for the periodic part at the center of the respective area. By using the grid values as weighting factors for the Gaussians along the linear dimensions, we can approximate functions on the SE(2) domain with correlated position and orientation. Based on this representation, we interweave a grid filter with a Kalman filter to obtain a filter that can take different numbers of parameters and is in the same complexity class as a grid filter for circular domains. We thoroughly compared the filters with other state-of-the-art filters in a simulated tracking scenario. With only little run time, our filter outperformed an unscented Kalman filter for manifolds and a progressive filter based on dual quaternions. Our filter also yielded more accurate results than a particle filter using one million particles while being faster by over an order of magnitude.

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“…This can cause the covariance of the robot's state to become disproportionately small resulting in an overconfidence in the propagation and eventually a divergence to an incorrect solution [16]. As Manifold filters solve this problem, they have proven themselves to be more consistent, and more accurate on average, than other filters [17]. The Invariant filter formulation [1] [2] [3] is proven to solve the aforementioned problems by ensuring the Log-Linear property of the error, that is, the independence of the error dynamics from the state estimate.…”

Section: Related Workmentioning

confidence: 99%

Consistent State Estimation on Manifolds for Autonomous Metal Structure Inspection

Starbuck

Fornasier

Weiß

et al. 2021

2021 IEEE International Conference on Robotics and Automation (ICRA)

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This work presents the Manifold Invariant Extended Kalman Filter, a novel approach for better consistency and accuracy in state estimation on manifolds. The robustness of this filter allows for techniques with high noise potential like ultra-wideband localization to be used for a wider variety of applications like autonomous metal structure inspection. The filter is derived and its performance is evaluated by testing it on two different manifolds: a cylindrical one and a bivariate b-spline representation of a real vessel surface, showing its flexibility to being used on different types of surfaces. Its comparison with a standard EKF that uses virtual, noise-free measurements as manifold constraints proves that it outperforms standard approaches in consistency and accuracy. Further, an experiment using a real magnetic crawler robot on a curved metal surface with ultra-wideband localization shows that the proposed approach is viable in the real world application of autonomous metal structure inspection.

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A Code for Unscented Kalman Filtering on Manifolds (UKF-M)

Cited by 38 publications

References 48 publications

Localization with Directional Coordinates

Localization with Directional Coordinates

The State Space Subdivision Filter for Estimation on SE(2)

Consistent State Estimation on Manifolds for Autonomous Metal Structure Inspection

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