A stochastic filter for planar rigid-body motions

This paper presents a novel algorithm for the estimation of planar rigid-body motions. It is based on using a probability distribution that is inherently defined on the nonlinear manifold representing these motions and on proposing a deterministic sampling scheme that makes consideration of complicated system models possible. Furthermore, we show that the measurement update for a manifold equivalent to noisy direct measurements can be carried out in closed form. Thus, the resulting method avoids errors made due to local linearization and outperforms methods that wrongly assume Gaussian distributions, which we show by comparing the proposed filter to the UKF.

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

[2]  Andrew T. A. Wood,et al.  Saddlepoint approximations for the normalizing constant of Fisher--Bingham distributions on products of spheres and Stiefel manifolds , 2013 .

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

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

[5]  Robert B. McGhee,et al.  An extended Kalman filter for quaternion-based orientation estimation using MARG sensors , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

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

[7]  Joseph J. LaViola,et al.  On Kalman Filtering With Nonlinear Equality Constraints , 2007, IEEE Transactions on Signal Processing.

[8]  Simon J. Julier,et al.  The spherical simplex unscented transformation , 2003, Proceedings of the 2003 American Control Conference, 2003..

[9]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

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

[11]  Marco F. Huber,et al.  Gaussian Filter based on Deterministic Sampling for High Quality Nonlinear Estimation , 2008 .

[12]  E. Kraft,et al.  A quaternion-based unscented Kalman filter for orientation tracking , 2003, Sixth International Conference of Information Fusion, 2003. Proceedings of the.

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

[14]  Nicholas I. Fisher,et al.  Statistical Analysis of Circular Data , 1993 .

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

[16]  Gerhard Kurz,et al.  Efficient Bingham filtering based on saddlepoint approximations , 2014, 2014 International Conference on Multisensor Fusion and Information Integration for Intelligent Systems (MFI).

[17]  Uwe D. Hanebeck,et al.  S2KF: The Smart Sampling Kalman Filter , 2013, Proceedings of the 16th International Conference on Information Fusion.

[18]  Angelo M. Sabatini,et al.  Quaternion-based extended Kalman filter for determining orientation by inertial and magnetic sensing , 2006, IEEE Transactions on Biomedical Engineering.

[19]  Young Soo Suh.  Orientation Estimation Using a Quaternion-Based Indirect Kalman Filter With Adaptive Estimation of External Acceleration , 2010, IEEE Transactions on Instrumentation and Measurement.

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

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

[22]  Robert B. McGhee,et al.  An improved quaternion-based Kalman filter for real-time tracking of rigid body orientation , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[23]  I. Introductiok.  Estimation for Rotational Processes with One Degree of Freedom-Part I1 : Discrete-Time Processes , 1975 .

[24]  Leslie Pack Kaelbling,et al.  Tracking the spin on a ping pong ball with the quaternion Bingham filter , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[25]  Wendelin Feiten,et al.  6D Pose Uncertainty in Robotic Perception , 2009 .

[26]  Gerhard Kurz,et al.  A new probability distribution for simultaneous representation of uncertain position and orientation , 2014, 17th International Conference on Information Fusion (FUSION).

[27]  Igor Gilitschenski,et al.  Deterministic Sampling for Nonlinear Dynamic State Estimation , 2016 .

[28]  Gerhard Kurz,et al.  Non-identity measurement models for orientation estimation based on directional statistics , 2015, 2015 18th International Conference on Information Fusion (Fusion).

[29]  H.F. Durrant-Whyte,et al.  A new approach for filtering nonlinear systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[30]  Anja Vogler,et al.  An Introduction to Multivariate Statistical Analysis , 2004 .