Pose Estimation using Dual Quaternions and Moving Horizon Estimation

Sveier, Aksel; Egeland, Olav

doi:10.1016/j.ifacol.2018.07.275

Cited by 5 publications

(7 citation statements)

References 11 publications

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“…The convergence and promising enhanced performance are obtained; Simulated signal with observation noise used for prediction; Sveier and Egeland 59 Dual quaternion and moving horizon estimation (DQ-MHE) method…”

Section: Motivations and Contributionsmentioning

confidence: 99%

New approach for multidimensional prognostic of stochastic time series based on sparse-based fractional Levy quaternion extended Kalman filter

2022

Structural Health Monitoring

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Multidimensional data are frequently encountered in numerous industrial systems, standard techniques regarding statistical multichannel prognostic methods naturally cannot fully exploit and capture the coupled nature and spatiotemporal relationship of the available information among channels. To alleviate a bottleneck problem, in this paper, a new approach named sparse-based fractional Levy quaternion extended Kalman filter (SFLQEKF) is formulated for the prognostic of stochastic time series. Initially, the stochastic time series is decomposed into the static component and the dynamic component resorting to the piecewise representation through a new improved sparse low-rank matrix (SLRM) approximation algorithm namely singular value penalty resonance sparse signal decomposition (SVP-RSSD). Afterward, both static component and dynamic component are predicted individually through the proposed fractional Levy quaternion extended Kalman filter (FLQEKF) method, the final time series of interest can be obtained by integrating the predicted static- and dynamic components correspondingly, in which a new predictive derivation of the proposed FLQEKF model is formulated for the first time by considering fractional-order characteristic and Levy flight process damping term, hence the issue of oscillating indeterminacy induced from classical extended Kalman filter (EFK) can be addressed. Eventually, the prognostic behavior of the proposed approach is investigated via the stochastic time series conducted from two experimental cases, the predicted results illustrate the availability and applicability of the proposed approach compared with three state-of-the-art benchmarks.

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Section: Motivations and Contributionsmentioning

confidence: 99%

New approach for multidimensional prognostic of stochastic time series based on sparse-based fractional Levy quaternion extended Kalman filter

2022

Structural Health Monitoring

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“…Here, (RT R * ) describes a rotated point after (10), implying that the order of sequence is first rotation, afterwards translation.…”

Section: Rigid Transformation Using Dual Quaternionsmentioning

confidence: 99%

“…Hence, the prediction of rigid body kinematics and dynamics is particularly important for design and control of rigid bodies. Furthermore, various different applications exist in which prediction of object movements or the existence and relations of objects are relevant, like computer vision and blending [8], pose estimation [9], [10] or neuroscience [11].…”

Section: Introductionmentioning

confidence: 99%

Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Pöppelbaum

Schwung

2022

IEEE Access

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We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements. After introducing the underlying dual quaternion math, we derive dual quaternion valued neural network layer which are generally applickable to all sorts of problems which can benefit from a mathematical description in dual quaternion space. To cover the dynamic behavior inherent to rigid body movements, we propose recurrent architectures in the neural network. To further model the rigid bodies interactions efficiently, we incorporate a novel attention mechanism employing dual quaternion algebra. The introduced architecture is trainable by means of gradient based algorithms. We apply our approach to a parcel prediction problem where a rigid body with an initial position, orientation, velocity and angular velocity moves through a fixed simulation environment which exhibits rich interactions between the parcel and the boundaries. There we can show that the dual quaternion valued models outperform their counterparts operation on the real numbers, confirming the successful introduction of an inductive bias through the usage of dual quaternion math. Furthermore, we used an advantageous custom data augmentation technique specifically tailored for the usage with our dual quaternion valued input data. INDEX TERMSdual quaternion attention, dual duaternion neural networks, hypercomplex neural networks, rigid body dynamics

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“…The unit dual quaternion pose measurementq m,k+1 is now available. We use the measurement relation proposed in [17], where the noise η q,k+1 ∼ N (0, R) acting on the unit dual quaternion is modeled as a screw displacement. This is mapped with the Cayley transform to give the pose measurement model…”

Section: ) Dual Quaternion Measurementsmentioning

confidence: 99%

“…We also show how to include specific force measurements from an accelerometer with bias and noise by replacing the linear velocity measurements. In the measurement update, we first consider the case where pose measurements are available in the form of unit dual quaternions and use the measurement relation suggested in [17]. This is used for verification of the filter through simulations, including a comparison with the dual quaternion UKF presented in [8].…”

Section: Introductionmentioning

confidence: 99%

Dual Quaternion Particle Filtering for Pose Estimation

Sveier

Egeland

2021

IEEE Trans. Contr. Syst. Technol.

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This article presents a particle filter for pose estimation using unit dual quaternion kinematics. The eight-parameter unit dual quaternion is used for global representation of the pose, whereas the six parameters of the dual modified Rodrigues parameters (MRPs) are used for local pose representation in the state-space model. The dual MRPs enable estimates of the mean and the covariance to be calculated from the particles without violating the algebraic constraint of the unit dual quaternion. For verification of the filter and comparison with state of the art, we consider pose measurements available in the form of unit dual quaternions. Angular velocity and specific force measurements from a body-mounted inertial measurement unit are also considered in the filtering. We show through simulations that the suggested particle filter has comparable accuracy with a previously proposed unscented Kalman filter based on unit dual quaternions. We also consider a practical application where the pose of an arbitrary rigid object is estimated using a sequence of point clouds from a 3-D camera. A model point cloud of the object is displaced with the unit dual quaternion associated with each particle, and a fitting score is calculated between the displaced model point cloud and the measured point cloud from the 3-D camera. The likelihoods of the fitting scores are calculated from an exponential distribution and are used to update the weights of the particles. The system was verified in an experiment where the motion of a swinging payload hanging from a crane was estimated using a 3-D camera.

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Pose Estimation using Dual Quaternions and Moving Horizon Estimation

Cited by 5 publications

References 11 publications

New approach for multidimensional prognostic of stochastic time series based on sparse-based fractional Levy quaternion extended Kalman filter

New approach for multidimensional prognostic of stochastic time series based on sparse-based fractional Levy quaternion extended Kalman filter

Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Dual Quaternion Particle Filtering for Pose Estimation

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