Integrating generic sensor fusion algorithms with sound state representations through encapsulation of manifolds

By Christoph Hertzberg, René Wagner, Udo Frese, Lutz Schröder. Information Fusion, 2011

325 citations recorded by the source corpus.

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 @[email protected][email protected] 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.

Subfields: Aerospace Engineering, Artificial Intelligence, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/f785548c1e136bd88e7774122e2c92c52176e0d2

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Citations in the corpus

Pixel-Level Extrinsic Self Calibration of High Resolution LiDAR and Camera in Targetless Environments (2021, methodology): “parameterize LT in the tangent space of C L T̄ using the operation encapsulated in SE(3) [19, 20]:”
FAST-LIO: A Fast, Robust LiDAR-Inertial Odometry Package by Tightly-Coupled Iterated Kalman Filter (2020, methodology): “Moreover, we characterize the estimation covariance in the tangent space of the state estimate as in [24], [25].”
State estimation for legged robots on unstable and slippery terrain (2013, methodology): “In short we use the exponential mapping, q = exp(θ), between a 3D rotation vector, θ ∈ R3, and the corresponding quaternion q ∈ SO(3).”
OpenVINS: A Research Platform for Visual-Inertial Estimation (2020, background): “For vector variables, the “boxplus” and “boxminus” operations, which map elements to and from a given manifold [27], equate to simple addition and subtraction of their vectors.”
State Estimation for Robotics (2017, methodology): “Our approach to handling sigmapoints is quite similar to that taken by Hertzberg et al. (2013) and also Brookshire and Teller (2012).”
Associating Uncertainty With Three-Dimensional Poses for Use in Estimation Problems (2014, background): “[15] as well as Brookshire and Teller [30].”
Control of a Quadrotor With Reinforcement Learning (2017, methodology): “We use a boxplus operator [16] to improve the accuracy of the integration since the motion of the quadrotor is very dynamic and the simulation might become inaccurate.”
Robust visual inertial odometry using a direct EKF-based approach (2015, methodology): “, using the -operator where appropriate, the above time continuous equation can be transformed into a set of discrete prediction equations which are used during the prediction of the filter state [10].”