An engineer's guide to particle filtering on matrix Lie groups

Marjanovic, Goran; Solo, Victor

doi:10.1109/icassp.2016.7472422

Cited by 10 publications

(5 citation statements)

References 33 publications

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“…We assume the reader is familiar with Unscented Kalman Filters [15], Particle Filters [11], and matrix Lie groups [20], [18]. We will use calligraphic letters to denote a Lie group G, and fraktur letters to denote its corresponding Lie algebra g. Since G is not a vector space, we cannot apply the usual approach of additive noise.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

“…The velocity and pose at the end of the time-step are computed using ( 13) and ( 14), respectively. The values for dP N and dP T are found by solving the so-called contact problem, defined by the setvalued force laws of ( 16), (17), (18), and (19). We use an augmented Lagrangian approach as discussed in [29] to solve this contact problem, due to its simplicity and effectiveness in our specific case of a single rigid body.…”

Section: Numerical Integration Using Time-steppingmentioning

confidence: 99%

“…As the 6D pose of an object in 3D space does not evolve in a vector space, but rather on a Lie group, we propose a version of the UPF for a system whose state lives in a Lie group. Although literature exists for particle filters on Lie groups [9], [18] or Unscented Kalman filters on Lie Groups [19], to the best of the authors knowledge, there does not exist literature on the UPF on Lie Groups. We name this new variant of the filter the Geometric Unscented Particle Filter (GUPF), which can be seen as the first contribution of this paper.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Model-Based 6D Visual Object Tracking with Impact Collision Models

Jongeneel

Bernardino

Wouw

et al. 2022

2022 American Control Conference (ACC)

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3D Object tracking is an essential technique in computer vision and has many fields of application. In this study, the focus lies on tracking objects impacting the environment. We show that state-of-the-art methods lose track of objects in this context and we investigate how to overcome this problem by adding prior information regarding the object and surface where collision is expected to occur. For illustration purposes and application relevance, we focus on the case of a box impacting a surface, which is, e.g., encountered in robot tossing in logistics applications. We model the effects of impacts and friction in a motion model, and consider the state of the box to evolve in a Lie group. We present an object tracking algorithm, based on an Unscented Particle Filter, for systems whose state lives in a Lie group and incorporate this motion model. The observations are taken from a single RGB camera and make use of the known 3D model of the object and color characteristics to predict its appearance in the 2D image. We quantitatively evaluate the effectiveness of our proposed methods by means of simulations on synthetic images.

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Section: Mathematical Preliminariesmentioning

confidence: 99%

Section: Numerical Integration Using Time-steppingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Model-Based 6D Visual Object Tracking with Impact Collision Models

Jongeneel

Bernardino

Wouw

et al. 2022

2022 American Control Conference (ACC)

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“…Apart from the EKF, particle filters for matrix Lie groups has been an active area of research [16], [32], [38]. Typically, particle filters adopt discrete-time description of the dynamics and are based on importance sampling and resampling numerical procedures.…”

Section: B Literature Reviewmentioning

confidence: 99%

Feedback particle filter on matrix lie groups

Zhang

Taghvaei

Mehta

2016

2016 American Control Conference (ACC)

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This paper is concerned with the problem of continuous-time nonlinear filtering for stochastic processes on a connected matrix Lie group. The main contribution of this paper is to derive the feedback particle filter (FPF) algorithm for this problem. In its general form, the FPF is shown to provide a coordinate-free description of the filter that automatically satisfies the geometric constraints of the manifold. The particle dynamics are encapsulated in a Stratonovich stochastic differential equation that retains the feedback structure of the original (Euclidean) FPF. The implementation of the filter requires a solution of a Poisson equation on the Lie group, and two numerical algorithms are described for this purpose. As an example, the FPF is applied to the problem of attitude estimation -a nonlinear filtering problem on the Lie group SO(3). The formulae of the filter are described using both the rotation matrix and the quaternion coordinates. Comparisons are also provided between the FPF and some popular algorithms for attitude estimation, namely the multiplicative EKF, the unscented quaternion estimator, the left invariant EKF, and the invariant ensemble Kalman filter. Numerical simulations are presented to illustrate the comparisons.

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“…To apply filtering on LGs, several dedicated analytical algorithms have been developed in the literature, such as the Lie Group-Extended Kalman Filter (LG-EKF) [15], the Invariant Kalman filter [16,17], the Unscented Kalman filter (LG-UKF) [18], the information Kalman filter (LG-IKF) [19], but also Monte-Carlo filtering, such as particle filters [20]. In the context of SLAM, several works have been made.…”

mentioning

confidence: 99%

Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm

2022

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This paper addresses the problem of monocular Simultaneous Localization And Mapping on Lie groups using fiducial patterns. For that purpose, we propose a reformulation of the classical camera model as a model on matrix Lie groups. Thus, we define an original-state vector containing the camera pose and the set of transformations from the world frame to each pattern, which constitutes the map’s state. Each element of the map’s state, as well as the camera pose, are intrinsically constrained to evolve on the matrix Lie group SE(3). Filtering is then performed by an extended Kalman filter dedicated to matrix Lie groups to solve the visual SLAM process (LG-EKF-VSLAM). This algorithm has been evaluated in different scenarios based on simulated data as well as real data. The results show that the LG-EKF-VSLAM can improve the absolute position and orientation accuracy, compared to a classical EKF visual SLAM (EKF-VSLAM).

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An engineer's guide to particle filtering on matrix Lie groups

Cited by 10 publications

References 33 publications

Model-Based 6D Visual Object Tracking with Impact Collision Models

Model-Based 6D Visual Object Tracking with Impact Collision Models

Feedback particle filter on matrix lie groups

Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm

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