Associating Uncertainty With Three-Dimensional Poses for Use in Estimation Problems

Barfoot, Timothy D.; Furgale, Paul

doi:10.1109/tro.2014.2298059

Cited by 270 publications

(357 citation statements)

References 20 publications

Supporting

Mentioning

348

Contrasting

Order By: Relevance

“…A fairly natural definition of uncertainty in SO(3) is to define a distribution in the tangent space, and then map it to SO(3) via the exponential map (6) [32][33][34]:…”

Section: B Uncertainty Description In So(3)mentioning

confidence: 99%

See 1 more Smart Citation

IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation

Förster

Carlone

Dellaert

et al. 2015

Robotics: Science and Systems XI

415

368

View full text Add to dashboard Cite

Recent results in monocular visual-inertial navigation (VIN) have shown that optimizationbased approaches outperform filtering methods in terms of accuracy due to their capability to relinearize past states. However, the improvement comes at the cost of increased computational complexity. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes. The preintegration allows us to accurately summarize hundreds of inertial measurements into a single relative motion constraint. Our first contribution is a preintegration theory that properly addresses the manifold structure of the rotation group and carefully deals with uncertainty propagation. The measurements are integrated in a local frame, which eliminates the need to repeat the integration when the linearization point changes while leaving the opportunity for belated bias corrections. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated in a visual-inertial pipeline under the unifying framework of factor graphs. This enables the use of a structureless model for visual measurements, further accelerating the computation. The third contribution is an extensive evaluation of our monocular VIN pipeline: experimental results confirm that our system is very fast and demonstrates superior accuracy with respect to competitive state-of-the-art filtering and optimization algorithms, including off-the-shelf systems such as Google Tango. Abstract-Recent results in monocular visual-inertial navigation (VIN) have shown that optimization-based approaches outperform filtering methods in terms of accuracy due to their capability to relinearize past states. However, the improvement comes at the cost of increased computational complexity. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes. The preintegration allows us to accurately summarize hundreds of inertial measurements into a single relative motion constraint. Our first contribution is a preintegration theory that properly addresses the manifold structure of the rotation group and carefully deals with uncertainty propagation. The measurements are integrated in a local frame, which eliminates the need to repeat the integration when the linearization point changes while leaving the opportunity for belated bias corrections. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated in a visual-inertial pipeline under the unifying framework of factor graphs. This enables the use of a structureless model for visual measurements, further accelerating the computation. The third contribution is an extensive evaluation of our monocular VIN pipeline: experimental results confirm that our system is very fast and demonstrates superior accuracy with respect to competitive state-of-the-art filtering and optimization algorithms, including off-the-shelf systems such as Google Tango [1].

show abstract

“…A fairly natural definition of uncertainty in SO(3) is to define a distribution in the tangent space, and then map it to SO(3) via the exponential map (6) [32][33][34]:…”

Section: B Uncertainty Description In So(3)mentioning

confidence: 99%

“…The distribution of the random variableR ∈ SO(3) can be computed explicitly, as shown in [33], leading to:…”

Section: B Uncertainty Description In So(3)mentioning

confidence: 99%

IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation

Förster

Carlone

Dellaert

et al. 2015

Robotics: Science and Systems XI

415

368

View full text Add to dashboard Cite

show abstract

“…For many common groups used in engineering and physical sciences closed form expressions for ϕ G (·) and Φ G (·) can be found [17], [24]; otherwise, a truncated series expansion is used.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

“…In [16] it has been observed that the distribution of the pose of a differential drive mobile robot is not a Gaussian distribution in Cartesian coordinates, but rather a distribution on the special Euclidean group SE (2). Similarly, [17] discussed the uncertainty association with 3D pose employing the SE(3) group. Furthermore, attitude estimation arises naturally on the SO(3) group [15].…”

Section: Introductionmentioning

confidence: 99%

Mixture Reduction on Matrix Lie Groups

Ćesić

Marković

2017

IEEE Signal Process. Lett.

View full text Add to dashboard Cite

Abstract-Many physical systems evolve on matrix Lie groups and mixture filtering designed for such manifolds represent an inevitable tool for challenging estimation problems. However, mixture filtering faces the issue of a constantly growing number of components, hence require appropriate mixture reduction techniques. In this letter we propose a mixture reduction approach for distributions on matrix Lie groups, called the concentrated Gaussian distributions (CGDs). This entails appropriate reparametrization of CGD parameters to compute the KL divergence, pick and merge the mixture components. Furthermore, we also introduce a multitarget tracking filter on Lie groups as a mixture filtering study example for the proposed reduction method. In particular, we implemented the probability hypothesis density filter on matrix Lie groups. We validate the filter performance using the optimal subpattern assignment metric on a synthetic dataset consisting of 100 randomly generated multitarget scenarios.

show abstract

“…Λ o , Λ L and Λ LC are the information matrices of the odometry, landmark and loop closure measurements respectively, and ⊕ and are standard pose composition operators [15]. 2 The cost function in Eq.…”

Section: A Graph-based Slammentioning

confidence: 99%

Robust incremental SLAM with consistency-checking

Graham

How

Gustafson

2015

2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

View full text Add to dashboard Cite

Abstract-Both landmark measurements and loop closures are used to correct for odometry drift in SLAM solutions. However, if any of the measurements are incorrect (e.g. due to perceptual aliasing) standard SLAM algorithms fail catastrophically and can not return an accurate map. A number of algorithms have been proposed that are robust to loop closure errors, but it is shown in this paper that they can not provide robust solutions when landmark measurement errors occur. The root cause of the problem is that most robust SLAM algorithms only focus on creating a locally consistent map (by evaluating whether measurements appear correct individually) rather than a globally consistent map. This paper proposes a new formulation of the robust SLAM problem that explicitly requires finding a globally consistent solution. Motivated by the new cost function, a novel incremental SLAM algorithm is developed that provides accurate solutions for datasets with landmark or loop closure measurement errors. Simulated and experimental results of the new algorithm, called incremental SLAM with consistency-checking, show that the new algorithm provides significantly more accurate results than state-of-theart robust SLAM methods for datasets with incorrect landmark measurements and can match the performance of current robust SLAM methods for datasets with incorrect loop closures.

show abstract

Associating Uncertainty With Three-Dimensional Poses for Use in Estimation Problems

Cited by 270 publications

References 20 publications

IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation

IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation

Mixture Reduction on Matrix Lie Groups

Robust incremental SLAM with consistency-checking

Contact Info

Product

Resources

About