Estimation with Applications to Tracking and Navigation
Estimation with Applications to Tracking and Navigation
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Using Quaternions for Parametrizing 3-D Rotations in Unconstrained Nonlinear Optimization
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Real-Time Simultaneous Localisation and Mapping with a Single Camera
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Global Positioning Systems, Inertial Navigation, and Integration
Global Positioning Systems, Inertial Navigation, and Integration
Apprenticeship learning and reinforcement learning with application to robotic control
Apprenticeship learning and reinforcement learning with application to robotic control
Nonlinear constraint network optimization for efficient map learning
IEEE Transactions on Intelligent Transportation Systems
Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices
Journal of Computational and Applied Mathematics
iSAM: Incremental Smoothing and Mapping
IEEE Transactions on Robotics
Automatica (Journal of IFAC)
Tutorial on quick and easy model fitting using the SLoM framework
SC'12 Proceedings of the 2012 international conference on Spatial Cognition VIII
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Common estimation algorithms, such as least squares estimation or the Kalman filter, operate on a state in a state space S that is represented as a real-valued vector. However, for many quantities, most notably orientations in 3D, S is not a vector space, but a so-called manifold, i.e. it behaves like a vector space locally but has a more complex global topological structure. For integrating these quantities, several ad hoc approaches have been proposed. Here, we present a principled solution to this problem where the structure of the manifold S is encapsulated by two operators, state displacement :SxR^n-S and its inverse :SxS-R^n. These operators provide a local vector-space view @d@?x@d around a given state x. Generic estimation algorithms can then work on the manifold S mainly by replacing +/- with / where appropriate. We analyze these operators axiomatically, and demonstrate their use in least-squares estimation and the Unscented Kalman Filter. Moreover, we exploit the idea of encapsulation from a software engineering perspective in the Manifold Toolkit, where the / operators mediate between a ''flat-vector'' view for the generic algorithm and a ''named-members'' view for the problem specific functions.