Eliminating conditionally independent sets in factor graphs: A unifying perspective based on smart factors

Carlone, Luca; Kira, Zsolt; Beall, Chris; Indelman, Vadim; Dellaert, Frank

doi:10.1109/icra.2014.6907483

Cited by 77 publications

(58 citation statements)

References 27 publications

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“…Similarly, substituting (28) in the expression of ∆p ij in (26), and using the first-order approximation (4), we obtain:…”

Section: Imu Preintegration On Manifoldmentioning

confidence: 99%

“…Substituting (28) back into the expression of ∆v ij in (26), using the approximation (4) for Exp −δφ ij , and dropping higher-order noise terms, we obtain:…”

Section: Imu Preintegration On Manifoldmentioning

confidence: 99%

“…Inspired by [20,28], we adopt a structureless model for visual measurements, which allows one to eliminate large numbers of variables (i.e., all 3D points) during incremental smoothing, further accelerating the computation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Förster

Carlone

Dellaert

et al. 2015

Robotics: Science and Systems XI

Self Cite

416

368

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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

“…Similarly, substituting (28) in the expression of ∆p ij in (26), and using the first-order approximation (4), we obtain:…”

Section: Imu Preintegration On Manifoldmentioning

confidence: 99%

“…Substituting (28) back into the expression of ∆v ij in (26), using the approximation (4) for Exp −δφ ij , and dropping higher-order noise terms, we obtain:…”

Section: Imu Preintegration On Manifoldmentioning

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

Self Cite

416

368

View full text Add to dashboard Cite

show abstract

“…We use IMU factors with preintegrated measurements as implemented in GTSAM 1 (based on [23], [24], [25]), as they have been used in [17], [16]. Note that poses in this subsection are in the metric world, so in practice they have to be calculated from the non-metric camera poses using the current estimate for T WmWf .…”

Section: B Visual-inertial Factorsmentioning

confidence: 99%

Rolling-Shutter Modelling for Direct Visual-Inertial Odometry

Schubert

Demmel

Stumberg

et al. 2019

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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We present a direct visual-inertial odometry (VIO) method which estimates the motion of the sensor setup and sparse 3D geometry of the environment based on measurements from a rolling-shutter camera and an inertial measurement unit (IMU).The visual part of the system performs a photometric bundle adjustment on a sparse set of points. This direct approach does not extract feature points and is able to track not only corners, but any pixels with sufficient gradient magnitude. Neglecting rolling-shutter effects in the visual part severely degrades accuracy and robustness of the system. In this paper, we incorporate a rolling-shutter model into the photometric bundle adjustment that estimates a set of recent keyframe poses and the inverse depth of a sparse set of points.IMU information is accumulated between several frames using measurement preintegration, and is inserted into the optimization as an additional constraint between selected keyframes. For every keyframe we estimate not only the pose but also velocity and biases to correct the IMU measurements. Unlike systems with global-shutter cameras, we use both IMU measurements and rolling-shutter effects of the camera to estimate velocity and biases for every state.Last, we evaluate our system on a new dataset that contains global-shutter and rolling-shutter images, IMU data and ground-truth poses for ten different sequences, which we make publicly available. Evaluation shows that the proposed method outperforms a system where rolling shutter is not modelled and achieves similar accuracy to the global-shutter method on global-shutter data.

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“…But these support variables are essential for the formulation of the optimization problem, and need to be considered when constructing factor nodes of the target variables. Then, these factor nodes can be called smart factors [7]. The idea of smart factor applies to all types of navigation sensors.…”

Section: Equivalent Ins Factor Graphmentioning

confidence: 99%

An Improved INS Factor Graph Formulation and Its Application in Integrated Navigation System

Gao¹,

Tang²,

Zhang³

2017

MATEC Web Conf.

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Abstract.A new method of establishing INS factor graph is proposed to deal with the serious waste of INS measurements in current integrated navigation factor graph algorithm. The INS observations pre-integrated to construct a smart factor during a time period, are used to solution simultaneously, to get the navigation states estimation. Then the estimated values can be used to construct an INS factor, adding into the INS factor graph. As a result, the new model is larger than the original, but the incremental inference technology makes sure the real-time ability of the factor graph algorithm. To analysis the performance of the proposed algorithm, INS and GNSS data are simulated, and the navigation position error of either the INS factors are added or not are compared. The results show that, the precision and stability of the factor graph algorithm are greatly improved by adding the INS factors. The proposed algorithm makes full use of the INS accuracy, and reflects the advantage of INS high stability.

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Eliminating conditionally independent sets in factor graphs: A unifying perspective based on smart factors

Cited by 77 publications

References 27 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

Rolling-Shutter Modelling for Direct Visual-Inertial Odometry

An Improved INS Factor Graph Formulation and Its Application in Integrated Navigation System

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