Publisher : The Korean Institute of Electrical Engineers
DOI : 10.5370/JEET.2014.9.6.2107
Title & Authors
Performance Degradation Due to Particle Impoverishment in Particle Filtering Lim, Jaechan;
Particle filtering (PF) has shown its outperforming results compared to that of classical Kalman filtering (KF), particularly for highly nonlinear problems. However, PF may not be universally superior to the extended KF (EKF) although the case (i.e. an example that the EKF outperforms PF) is seldom reported in the literature. Particularly, PF approaches show degraded performance for problems where the state noise is very small or zero. This is because particles become identical within a few iterations, which is so called particle impoverishment (PI) phenomenon; consequently, no matter how many particles are employed, we do not have particle diversity regardless of if the impoverished particle is close to the true state value or not. In this paper, we investigate this PI phenomenon, and show an example problem where a classical KF approach outperforms PF approaches in terms of mean squared error (MSE) criterion. Furthermore, we compare the processing speed of the EKF and PF approaches, and show the better speed performance of classical EKF approaches. Therefore, PF approaches may not be always better option than the classical EKF for nonlinear problems. Specifically, we show the outperforming result of unscented Kalman filter compared to that of PF approaches (which are shown in Fig. 7(c) for processing speed performance, and Fig. 6 for MSE performance in the paper).
Carrier frequency offset;Extended Kalman filter;Particle filtering;Particle impoverishment;
Joint Estimation of CFO and Channel in OFDM Systems with Blind Noise Statistics, IETE Technical Review, 2016, 1
Rudolph Emil Kalman, "A new approach to linear filtering and prediction problems," Transactions of the ASME-Journal of Basic Engineering, vol. 82, no. Series D, pp. 35-45, March 1960.
M. Arulampalam, Simon Maskell, Neil Gordon, and Tim Clapp, "A tutorial on particle filters for online nonlinear / non-Gaussian Bayesian tracking," IEEE Trans. Signal Processing, vol. 50, no. 2, pp. 174-188, Feb. 2002.
Monson H. Hayes, Statistical digital signal processing and modeling, John wiley & sons, inc., 1996.
Steven M. Kay, Fundamentals of statistical signal processing, vol. 1, Prentice hall signal processing series, 1993, Estimation Theory.
H. Lee, W. Ra, J. Lee, Y. Song, and I. Whang, "Aerodynamic derivatives identification using a nonconservative robust Kalman filter," Journal of Electrical Engineering & Technology, vol. 7, no. 1, pp. 132-140, January 2012.
H. Sim, J. Lee, and K. Lee, "On-line parameter estimation of interior permanent magnet synchronous motor using an extended Kalman filter," Journal of Electrical Engineering & Technology, vol. 9, no. 2, pp. 600-608, March 2014.
C. Musso, N. Oudjane, and F. LeGland, "Improving regularised particle filters," in Sequential Monte Carlo Methods in Practice, A. Doucet, J. F. G. de Freitas, and N. J. Gordon, Eds. Springer-Verlag, New York, 2001.
J. H. Kotecha and P. M. Djuric, "Gaussian particle filtering," IEEE Transactions on Signal Processing, vol. 51, no. 10, pp. 2592-2601, October 2003.
Rudolph van der Merwe, Sigma-point Kalman filters for probabilistic inference in dynamic state-space models, Ph.D. thesis, OGI School of Science & Engineering, Oregon Health & Science University, Portland, Oregon, April 2004.
Jaechan Lim, "A target tracking based on bearing and range measurement with unknown noise statistics," Journal of Electrical Engineering & Technology, vol. 8, no. 6, pp. 1520-1529, November 2013.
J. Lim and D. Hong, "Inter-carrier interference estimation in OFDM systems with unknown noise distributions," IEEE Signal Processing Letters, vol. 16, no. 6, pp. 493-496, June 2009.
J. Lim and D. Hong, "Gaussian particle filtering approach for carrier frequency offset estimation in OFDM systems," IEEE Signal Processing Letters, vol. 20, no. 4, pp. 367-370, April 2013.
M. Chowdhury, Y. Jang, and Z. Haas., "Network evolution and QoS provisioning for integrated femtocell / macrocell networks", International Journal of Wireless & Mobile Networks, Vol. 2, No. 3, Aug. 2010.