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An Introduction to the Kalman Filter

by M. Hebert, E. Krotkov, Jaebum Choi, Simon Ulbrich, Bernd Lichte, Markus Maurer, Gangqiang Zhao, Xuhong Xiao, Junsong Yuan, Brian Yamauchi, Crosby Drive, Nicolai Wojke, H Marcel, Greg Welch, Gary Bishop, Jianhua Wang, Pingping Huang, Changfeng Chia-yen Chi-fa Chen, Wei Gu, Jianxin Chu, Autonomous Underwater, Surface Vessels, Unmanned Aircraft Systems, D. Steinhauser, O. Ruepp, D. Burschka, S. Schneider, M. Himmelsbach, T. Luettel, H.-J. Wuensche, R. Sandoval, M. Pusateri, J. Fry, D. Lesutis, J. Siviter, Patrick F Rynne, Karl D Von Ellenrieder, Hyun Chul Roh, Chang Hun Sung, A. Quadros, J. P Underwood, B. Douillard, Thomas J. Pastore, Andrew N. Patrikalakis, Lionel Ott, Fabio Ramos, Chiemela Onunka, Glen Bright, E. Oleynikova, N.B. Lee, A.J. Barry, J. Holler, D. Barrett, Naveed Muhammad, Simon Lacroix, Julien Moras, Veronique Cherfaoui, Phillipe Bonnifait, Frank Moosmann, Christoph Stiller, O. Pink, Jorge L Mart, Anthony Mandow, Antonio J Reina, Javier Ser, Alfonso Garc, Paul Mahacek, Ignacio Mas, Christopher Kitts, R.M. Lucas, A.C. Lee, M.L. Williams, Jc Leedekerken, Mf Fallon, Jj Leonard, Petra Kocmanova, Farid Kendoul, B Kalyan, K W Lee, D Moratuwage, Suk-ho Jang, Dong-jin Yoon, Jae-hwan Kim, Byong-woo Kim, Hordur K. Heidarsson, Gaurav S. Sukhatme, Ryan Halterman, Michael Bruch, Naval Warfare, D. Habermann, A. Hata, D. Wolf, F.S. Osorio, Chunzhao Guo, Seiichi Mita, David McAllester, W Shane Grant, Randolph C Voorhies, Laurent Itti, Andreas Geiger, Omer Car, Bernhard Schuster, P Lenz, R Urtasun, Angel-Ivan Garcia-Moreno, Jose-Joel Gonzalez-Barbosa, H.F. Fauadi, M.H. Nordin, Z.M. Zainon, Takuro Egawa, Ippei Samejima, Yuma Nihei, Satoshi Kagami, Hiroshi Mizoguchi, N. Kuntz, V. Vlaskine, P. Morton, A. Frenkel, A. Brooks, M De Deuge, M De Deuge, S Hugosson, M Hallstrom, T Bailey, M.S. Darms, P.E. Rybski, C. Baker, C. Urmson, G Daniel, Miao Wang, Michael Schn, Tinosch Ganjineh, Ying-chen Lin, Sheng-wen Huang, Baifan Chen, Zixing Cai, Zheng Xiao, Jinxia Yu, Limei Liu, C Blanc, L Trassoudaine, R Moreira, Csaba Benedek, Jens Behley, Volker Steinhage, Armin B Cremers, S P Baker, R W Sadowski, Asma Azim, Olivier Aycard show all authors
In Practice ()

Abstract

In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

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