Mechatronics pp 321-329 | Cite as

Extended Kalman Filter and Discrete Difference Filter Comparison

  • M. Laurinec


In this paper we focused our attention on the mathematical background of the Extended Kalman Filter and its comparison to the Discrete Difference filter. Both of the filters are capable to estimate states of nonlinear systems but each one has its advantages and drawbacks we would like to outline. In addition to the mathematical derivation, we will show also the details of software implementation in Matlab.


Kalman Filter Extend Kalman Filter Jacobi Matrice Cholesky Factor Magic Formula 
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  1. 1.
    Laurinec, M., Porteš, P., Blaťák, O.: Discrete-difference filter in vehicle dynamics analysis. In: Recent Advances in Mechatronics, pp. 19–24. Springer, Heidelberg (2009) ISBN 978-3-642-05021-3Google Scholar
  2. 2.
    Kalman, R.E.: A new approach to linear filtering and prediction problems. Transaction of the ASME - Journal of basic engineering, 35–45 (1960)Google Scholar
  3. 3.
    Havlena, V., Štecha, J.: Modern control theory. Scriptum ČVUT (2000), ISBN 80-01-02095-9Google Scholar
  4. 4.
    Julier, S., Uhlmann, K.J.: A general method for approximating nonlinear transformations of probability distributions. Robotics Research Group, University of Oxford (1996)Google Scholar
  5. 5.
    Grewal, M., Andrews, A.: Kalman Filtering: Theory and Practice Using MATLAB, 2nd edn. John Wiley and Sons, Chichester (2001)Google Scholar
  6. 6.
    Nørgaard, M., Poulsen, N.K., Ravn, O.: Advances in Derivative-Free State Estimation for Nonlinear Systems, Revised Edition. IMM-Technical Report-1998-15 (2004)Google Scholar
  7. 7.
    Laurinec, M.: Extended and Derivative Free Kalman Filter. In: Advances in Automotive Engineering, vol. II, pp. 135–279. Tribun EU, Brno (2008), ISBN: 978-80-7399-497-6Google Scholar
  8. 8.
    Vlk, F.: Motor vehicle dynamics. VLK, Brno (2000), ISBN 80-238-5273-6 Google Scholar
  9. 9.
    Scheit, T.S.: A Finite-Difference Method for Linearization in Nonlinear Estimation Algorithms. Automatica 33(11), 2053–2058 (1997), ISSN 0005-1098 MathSciNetCrossRefGoogle Scholar
  10. 10.
    Froberg Carl, E.: Introduction to Numerical Analysis, 433 p. Addison-Wesley, Reading (1970), ASIN B000NKJ5LCGoogle Scholar
  11. 11.
    Moler, C.: Numerical Computing with MATLAB Interpolation (April 23, 2011),
  12. 12.
    CORRYS-DATRON: GPS sensors-MicroSAT (May 10, 2007),
  13. 13.
    ISO/WD 3888-2, Passenger cars Test track for a severe lane-change manoeuvre, Part 2: Obstacle avoidance (1999)Google Scholar
  14. 14.
    Web source (April 23 , 2011),

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • M. Laurinec
    • 1
  1. 1.Faculty of Mechanical Engineering, Institute of Automotive EngineeringBrno University of TechnologyBrnoCzech Republic

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