Nonlinear Progressive Filtering for SE(2) Estimation

In this paper, we present a novel nonlinear progressive filtering approach for estimating S E (2) states represented by unit dual quaternions. Unlike previously published approaches, the measurement model no longer needs to be assumed as identity. Our solution utilizes deterministic sampling on a Bingham-like probability distribution, which has been adapted to simultaneously model orientation and translation. During the measurement update step, the estimate gets progressively updated. Our approach inherently incorporates the nonlinear structure of S E (2) and enables a flexible measurement update step. We also give an evaluation for planar rigid body motion estimation with a case study that is close to real-world scenarios.

[1]  Kyle J. DeMars,et al.  Uncertainty Propagation of correlated quaternion and Euclidean states using partially-conditioned Gaussian mixtures , 2016, 2016 19th International Conference on Information Fusion (FUSION).

[2]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[3]  Gerhard Kurz,et al.  Unscented Orientation Estimation Based on the Bingham Distribution , 2013, IEEE Transactions on Automatic Control.

[4]  Serge Reboul,et al.  A multi-temporal multi-sensor circular fusion filter , 2014, Inf. Fusion.

[5]  Howie Choset,et al.  Estimating SE(3) elements using a dual quaternion based linear Kalman filter , 2016, Robotics: Science and Systems.

[6]  S. R. Jammalamadaka,et al.  Directional Statistics, I , 2011 .

[7]  Gerhard Kurz,et al.  Recursive Bayesian filtering in circular state spaces , 2015, IEEE Aerospace and Electronic Systems Magazine.

[8]  Sadri Hassani.  Dirac Delta Function , 2000 .

[9]  Anurag Sai Vempati,et al.  Onboard real-time dense reconstruction of large-scale environments for UAV , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[10]  Ben Kenwright,et al.  A Beginners Guide to Dual-Quaternions: What They Are, How They Work, and How to Use Them for 3D Character Hierarchies , 2012, WSCG 2012.

[11]  Christopher Bingham.  An Antipodally Symmetric Distribution on the Sphere , 1974 .

[12]  Gerhard Kurz,et al.  Nonlinear measurement update for estimation of angular systems based on circular distributions , 2014, 2014 American Control Conference.

[13]  Roland Siegwart,et al.  Robust visual inertial odometry using a direct EKF-based approach , 2015, IROS 2015.

[14]  Clifford,et al.  Preliminary Sketch of Biquaternions , 1871 .

[15]  Mongi A. Abidi,et al.  Pose and motion estimation from vision using dual quaternion-based extended kalman filtering , 1997 .

[16]  Nicholas Roy,et al.  Extrinsic Calibration from Per-Sensor Egomotion , 2013 .

[17]  W. Hamilton.  II. On quaternions; or on a new system of imaginaries in algebra , 1844 .

[18]  Serge Reboul,et al.  A recursive fusion filter for angular data , 2009, 2009 IEEE International Conference on Robotics and Biomimetics (ROBIO).

[19]  Jack B. Kuipers,et al.  Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality , 2002 .

[20]  Gerhard Kurz,et al.  A stochastic filter for planar rigid-body motions , 2015, 2015 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI).

[21]  Uwe D. Hanebeck,et al.  Progressive Gaussian filtering using explicit likelihoods , 2014, 17th International Conference on Information Fusion (FUSION).

[22]  Gerhard Kurz,et al.  Bivariate angular estimation under consideration of dependencies using directional statistics , 2014, 53rd IEEE Conference on Decision and Control.

[23]  Wendelin Feiten,et al.  MPG - Fast Forward Reasoning on 6 DOF Pose Uncertainty , 2012, ROBOTIK.

[24]  Udo Frese,et al.  Integrating generic sensor fusion algorithms with sound state representations through encapsulation of manifolds , 2011, Inf. Fusion.

[25]  Gerhard Kurz,et al.  Nonlinear toroidal filtering based on bivariate wrapped normal distributions , 2017, 2017 20th International Conference on Information Fusion (Fusion).