Abstract
In this paper, in order to reduce the linearization error of Kalman filters family, three new methods are proposed and their effectiveness and feasibility are evaluated by means of Simultaneous Localization and Mapping (SLAM) problem. In derivative based methods of Kalman filters family, linearization error is brought into estimation unavoidably because of using Taylor expansion to linearize nonlinear motion model and observation model. These three methods lessen the linearization error by replacing the Jacobian matrix of observation function with new formulas. Simulation results done with ‘Car Park Dataset’ indicate that all proposed methods have less linearization error than other mentioned methods and the method named Improved Weighted Mean Extended Kalman Filter (IWMEKF) performs much better than other mentioned Kalman filters in this paper on linearization error. In addition, simulation results confirm that our proposed approaches are computationally efficient. From estimation accuracy and computational complexity point of view, IWMEKF is the best solution for solving nonlinear SLAM problem among all Kalman filters mentioned in this paper.
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Lee, D., Kim, D., Lee, S., Myung, H., Choi, H.-T.: Experiments on localization of an AUV using graph-based SLAM, In: 2013 10th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), pp. 526–527 (2013)
Lourenco, P., Guerreiro, B.J., Batista, P., Oliveira, P., Silvestre, C.: Preliminary results on globally asymptotically stable simultaneous localization and mapping in 3-D. In: American Control Conference (ACC), 2013, pp. 3087–3092 (2013)
Pailhas, Y., Capus, C., Brown, K., Petillot, Y.: Design of artificial landmarks for underwater simultaneous localisation and mapping, In: IET Radar, Sonar & Navigation, vol. 7, pp. 10–18 (2013)
Yoon, S., Hyung, S., Lee, M., Roh, K.S., Ahn, S., Gee, A., Bunnun, P., Calway, A., Mayol-Cuevas, W.W.: Real-time 3D simultaneous localization and map-building for a dynamic walking humanoid robot. Adv. Robot. 1–14 (2013)
Roy, D.: Simultaneous Localization and Mapping for an Autonomous Vehicle using Extended Kalman Filter, Indian Institute of Technology (2004)
Thrun, S., Fox, D., Burgard, W.: A probabilistic approach to concurrent mapping and localization for mobile robots. Mach. Learn. 31(1-3), 29–53 (1998)
Abrate, F., Bona, B., Indri, M.: Experimental EKF-based SLAM for mini-rovers with IR sensors only, In: EMCR (2007)
Weingarten, J., Siegwart, R.: EKF-based 3D SLAM for structured environment reconstruction. In: 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005 (IROS 2005), pp. 3834–3839 (2005)
Ceriani, S., Marzorati, D., Matteucci, M., Sorrenti, D.G.: Single and multi camera simultaneous localization and mapping using the extended Kalman Filter. Journal of Mathematical Modelling and Algorithms in Operations Research, pp. 1–35 (2013)
Wang, H., Wang, J., Qu, L., Liu, Z.: Simultaneous localization and mapping based on multilevel-EKF. In: 2011 International Conference on Mechatronics and Automation (ICMA), pp. 2254–2258 (2011)
Shojaie, K., Ahmadi, K., Shahri, A.M.: Effects of iteration in Kalman filters family for improvement of estimation accuracy in simultaneous localization and mapping. In: 2007 IEEE/ASME International Conference on Advanced intelligent Mechatronics, pp. 1–6 (2007)
Zhou, W., Zhao, C., Guo, J.: The study of improving Kalman filters family for nonlinear SLAM. J. Intell. & Robot. Syst. 56, 543–564 (2009)
Chen, Z., Dai, X., Jiang, L., Yang, C., Cai, B.: Adaptive iterated square-root cubature Kalman filter and its application to SLAM of a mobile robot. TELKOMNIKA Indones. J. Electr. Eng. 11, 7213–7221 (2013)
Martinez-Cantin, R., Castellanos, J.A.: Unscented SLAM for large-scale outdoor environments. In: 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2005 (IROS 2005), pp. 3427–3432 (2005)
Montemerlo, M.: A Factored Solution to the Simultaneous Localization and Mapping Problem with unknown Data Association. Ph.D. thesis school of computer science Carnegie Mellon University, Pittsburgh, USA (2003)
Song, Y., Li, Q., Kang, Y.: CFastSLAM: a new Jacobian free solution to SLAM problem. In: 2012 IEEE International Conference on Robotics and Automation (ICRA), pp. 3063–3068 (2012)
http://www.cas.kth.se/SLAM/ (2002)
Corke, P.: Robotics, Vision and Control: Fundamental Algorithms in MATLAB, vol. 73. Springer (2011)
Guivant, J., Nebot, E., Baiker, S.: Autonomous navigation and map building using laser range sensors in outdoor applications. J. Robot. Syst. 17, 565–583 (2000)
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Yadkuri, F.F., Khosrowjerdi, M.J. Methods for Improving the Linearization Problem of Extended Kalman Filter. J Intell Robot Syst 78, 485–497 (2015). https://doi.org/10.1007/s10846-014-0089-7
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DOI: https://doi.org/10.1007/s10846-014-0089-7