Extended Kalman filter application to the nonlinear two-link pendulum model

Authors: Lysukho G.V., Maslennikov A.L.
Published in issue: #8(37)/2019
DOI: 10.18698/2541-8009-2019-8-513
Category: Informatics, Computer Engineering and Control | Chapter: System Analysis, Control, and Information Processing, Statistics
Keywords: extended Kalman filter, Hybrid Kalman filter, nonlinear system, two-link pendulum, numerical differentiation, QR-decomposition, state estimation, estimation theory
Published: 20.08.2019

Various types of Kalman filter are typically used to estimate state vector of dynamical systems. Particularly for nonlinear systems the Extended or Sigma-point Kalman filter are widely, but both of them have practical limitations. Those limitations could lead to instability of the algorithm and to increasing of estimation error. In this paper, we present the practical realization of the first-order Extended Kalman filter that is addressing those limitations with purpose to estimate the state of the continuous-time nonlinear two-link pendulum model with discrete-time measurements. In this realization symmetry of a priory covariance matrix is guaranteed and computational efficiency is increased by utilizing numerical computation of Jacobi matrix and QR-decomposition in computing Kalman gain.

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