Comparison of Estimation Accuracy of EKF, UKF and PF Filters

Open access


Several types of nonlinear filters (EKF – extended Kalman filter, UKF – unscented Kalman filter, PF – particle filter) are widely used for location estimation and their algorithms are described in this paper. In the article filtering accuracy for non-linear form of measurement equation is presented. The results of complex simulations that compare the quality of estimation of analyzed non-linear filters for complex non-linearities of state vector are presented. The moves of maneuvering object are described in two-dimensional Cartesian coordinates and the measurements are described in the polar coordinate system. The object dynamics is characterized by acceleration described by the univariate non-stationary growth model (UNGM) function. The filtering accuracy was evaluated not only by the root-mean-square errors (RMSE) but also by statistical testing of innovations through the expected value test, the whiteness test and the WSSR (weighted sum squared residual) test as well. The comparison of filtering quality was done in the MATLAB environment. The presented results provide a basis for designing more accurate algorithms for object location estimation.

[1] Arulampalam S., Gordon N., Ristic B., Beyond the Kalman Filter. Particie Fliters for tracking applications, Artech House, London 2004.

[2] Cappe O., Douc R., Moulines E., Comparison of resampling schemes for particle filtering, 4th International Symposium on Image and Signal Processing and Anlysis, 2005.

[3] Doucet A., de Freitas N., Van der Merwe R., Wan E. A., The unscented particle filter, Cambridge University Engineering Department, Cambridge 2000.

[4] Doucet A., Gordon N. J., Krishnamurthy V., Particle Filters for State Estimation of Jump Markov Linear Systems, ‘IEEE Transactions on Signal Processing’, 2001, Vol. 49, No. 3.

[5] Gordon N. J., Salmond N. J., Smith A. F. M., Novel approach to nonlinear/non- -Gaussian Bayesian state estimation, ‘IEE Proceedings-F’, 1993, Vol. 140, No. 2, pp. 107-113.

[6] Julier S. J., Uhlmann J. K., A new extension of the Kalman filter to nonlinear systems, Proceedings of Aero Sense: The 11-th International Symposium on Aerospace/ Defense Sensing, Simulations and Controls, 1997.

[7] Kaniewski P., Structures, models and algorithms in integrated positioning and navigation systems, WAT, Warszawa 2010.

[8] Konatowski S., The development of nonlinear filtering algorithms, ‘Przegląd Elektrotechniczny’, 2010, Vol. 86, No. 9, pp. 272-277.

[9] Konatowski S., Kaczmarek B., Efficiency of the location estimation in nonlinear filtering algorithms, ‘Przegląd Elektrotechniczny’, 2009, Vol. 85, No. 3, pp. 15-21.

[10] Konatowski S., Pieniężny A., A comparison of estimation accuracy by the use of KF, EKF & UKF filters, CMEM, WIT Press Southampton, Boston 2007, pp. 779-789.

[11] Konatowski S., Sipa T., Position estimation using Unscented Kalman Filter, ‘Annual of Navigation’, 2004, No. 8, pp. 97-110.

[12] Lampinen J., Särkkä S., Tamminen T., Vehtari A., Probabilistic Methods in Multiple Target Tracking, Laboratory of Computational Engineering Helsinki University of Technology, Helsinki 2004.

[13] Sosnowski B., Evaluation of estimation accuracy of nonlinear filters, WAT, Warszawa 2012.

[14] 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, 2001.

Annual of Navigation

The Journal of Polish Navigational Forum

Journal Information


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 228 228 45
PDF Downloads 115 115 36