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Article

The State Space Subdivision Filter for Estimation on SE(2)

Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany
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Academic Editor: Andrey V. Savkin
Sensors 2021, 21(18), 6314; https://doi.org/10.3390/s21186314
Received: 18 August 2021 / Revised: 16 September 2021 / Accepted: 17 September 2021 / Published: 21 September 2021
(This article belongs to the Section Sensors and Robotics)
The SE(2) domain can be used to describe the position and orientation of objects in planar scenarios and is inherently nonlinear due to the periodicity of the angle. We present a novel filter that involves splitting up the joint density into a (marginalized) density for the periodic part and a conditional density for the linear part. We subdivide the state space along the periodic dimension and describe each part of the state space using the parameters of a Gaussian and a grid value, which is the function value of the marginalized density for the periodic part at the center of the respective area. By using the grid values as weighting factors for the Gaussians along the linear dimensions, we can approximate functions on the SE(2) domain with correlated position and orientation. Based on this representation, we interweave a grid filter with a Kalman filter to obtain a filter that can take different numbers of parameters and is in the same complexity class as a grid filter for circular domains. We thoroughly compared the filters with other state-of-the-art filters in a simulated tracking scenario. With only little run time, our filter outperformed an unscented Kalman filter for manifolds and a progressive filter based on dual quaternions. Our filter also yielded more accurate results than a particle filter using one million particles while being faster by over an order of magnitude.
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Keywords: grid filter; nonlinear filtering; periodic manifold; special Euclidean group grid filter; nonlinear filtering; periodic manifold; special Euclidean group
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MDPI and ACS Style

Pfaff, F.; Li, K.; Hanebeck, U.D. The State Space Subdivision Filter for Estimation on SE(2). Sensors 2021, 21, 6314. https://doi.org/10.3390/s21186314

AMA Style

Pfaff F, Li K, Hanebeck UD. The State Space Subdivision Filter for Estimation on SE(2). Sensors. 2021; 21(18):6314. https://doi.org/10.3390/s21186314

Chicago/Turabian Style

Pfaff, Florian, Kailai Li, and Uwe D. Hanebeck. 2021. "The State Space Subdivision Filter for Estimation on SE(2)" Sensors 21, no. 18: 6314. https://doi.org/10.3390/s21186314

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