Comparative examinations of the nonlinear Kalman filters applied to positioning systems

• Autorzy: Konatowski S.
• Języki publikacji: EN

Abstrakty

EN

In positioning systems Kalman filters are used for estimation and also for integration of data from navigation systems and sensors. The Kalman filter (KF) is an optimal linear estimator when the process noise and the measurement noise can be modeled by white Gaussian noise. In situations when the problems are nonlinear or the noise that distorts the signals is non-Gaussian, the Kalman filters provide a solution that may be far from optimal. Nonlinear problems can be solved with the extended Kalman filter (EKF). This filter is based upon the principle of linearizing the state transition matrix and the observation matrix with Taylor series expansions. Unscented Kalman filter with comparison to EKF does not linearize the model but operates on the statistical parameters of the measurement and state vectors that are subsequently nonlinearly transformed. The unscented Kalman filter is based on the unscented transformation (UT). This paper presents a comparison of the estimation quality for two nonlinear measurement models of the following Kalman filters: covariance filter (KF), extended filter (EKF) and unscented filter (UKF). There are descriptions of models and analysis of obtained results in this article. The comparison of filtration quality was done in MATLAB environment.

Słowa kluczowe

EN

Kalman filter; positioning systems

PL

filtr Kalmana; systemy określania pozycji

• Wydawca: Polskie Forum Nawigacyjne
• Czasopismo: Annual of Navigation
• Rocznik: 2006
• Tom: No. 11
• Strony: 47--62
• Opis fizyczny: Bibliogr. 9 poz., rys., tab.

Twórcy

autor

Konatowski S.

• Military University of Technology, Warsaw

Bibliografia

• [1] Brown R. G., Hwang P. Y. C., Introduction to Random Signals and Applied Kalman Filtering with MATLAB Exercises and Solutions, John Wiley & Sons, Canada, 1997.
• [2] Gordon N. J., Ristic B., Arulampalam S., Beyond the Kalman Filter – Particle Filters for Tracking Applications, Artech House, London 2004.
• [3] Grewal M. S., Andrews A. P, Kalman filtering Theory and Practice Using MATLAB, John Wiley & Sons, Canada, 2001.
• [4] Julier S. J., Uhlmann J. K., Durrant-Whyte H. F., A New Method for the Nonlinear Transformation of Means and Covariances in Filters and Estimators, IEEE Transactions on Automatic Control, March 2000, vol. 45, no. 3, pp. 477 – 482.
• [5] Konatowski S., Sipa T., Position estimation using Unscented Kalman Filter, Annual of Navigation, 2004, no. 8, pp. 97 – 110.
• [6] van der Merwe R., Wan E. A., The Square-root Unscented Kalman Filter for State and Parameter-estimation, Proceedings of International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, May 2001, vol. 6, pp. 3461 – 3464.
• [7] van der Merwe R., Wan E. A., The Unscented Kalman Filter. Department of Electrical and Computer Engineering, Oregon Graduate Institute of Science and Technology, Beaverton, Oregon 2001.
• [8] Wan E. A., van der Merwe R., The Unscented Kalman Filter to appear in Kalman Filtering and Neural Networks, Chap. 7, ed by Simon Haykin, John Wiley & Sons, USA, 2001.
• [9] Wan E. A., van der Merwe R., The Unscented Kalman Filter for Nonlinear Estimation. Proc., IEEE Symp. Adaptive Systems for Signal Proc., Communication and Control (AS-SPCC), Lake Louise, Alberta, Canada, October 2000, pp. 153 – 158.