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Sensors 2018, 18(4), 1236;

A Closed-Form Error Model of Straight Lines for Improved Data Association and Sensor Fusing

Department of Computer Science and Media, Beuth University of Applied Sciences, Luxemburger Str. 10, D-13353 Berlin, Germany
Received: 12 March 2018 / Revised: 12 April 2018 / Accepted: 13 April 2018 / Published: 17 April 2018
(This article belongs to the Collection Multi-Sensor Information Fusion)
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Linear regression is a basic tool in mobile robotics, since it enables accurate estimation of straight lines from range-bearing scans or in digital images, which is a prerequisite for reliable data association and sensor fusing in the context of feature-based SLAM. This paper discusses, extends and compares existing algorithms for line fitting applicable also in the case of strong covariances between the coordinates at each single data point, which must not be neglected if range-bearing sensors are used. Besides, in particular, the determination of the covariance matrix is considered, which is required for stochastic modeling. The main contribution is a new error model of straight lines in closed form for calculating quickly and reliably the covariance matrix dependent on just a few comprehensible and easily-obtainable parameters. The model can be applied widely in any case when a line is fitted from a number of distinct points also without a priori knowledge of the specific measurement noise. By means of extensive simulations, the performance and robustness of the new model in comparison to existing approaches is shown. View Full-Text
Keywords: linear regression; covariance matrix; data association; sensor fusing; SLAM linear regression; covariance matrix; data association; sensor fusing; SLAM

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Sommer, V. A Closed-Form Error Model of Straight Lines for Improved Data Association and Sensor Fusing. Sensors 2018, 18, 1236.

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