Communications for Statistical Applications and Methods

  • 제25권1호
  • /
  • Pages.99-107
  • /
  • 2018
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Robustizing Kalman filters with the M-estimating functions

  • Pak, Ro Jin (Department of Applied Statistics, Dankook University)
  • 투고 : 2017.10.27
  • 심사 : 2017.12.02
  • 발행 : 2018.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This article considers a robust Kalman filter from the M-estimation point of view. Pak (Journal of the Korean Statistical Society, 27, 507-514, 1998) proposed a particular M-estimating function which has the data-based shaping constants. The Kalman filter with the proposed M-estimating function is considered. The structure and the estimating algorithm of the Kalman filter accompanying the M-estimating function are mentioned. Kalman filter estimates by the proposed M-estimating function are shown to be well behaved even when data are contaminated.

키워드

참고문헌

  1. Brockwell PJ and Davis RA (1986). Time Series: Theory and Methods, Springer-Verlag, New York
  2. Gandhi MA and Mili L (2010). Robust Kalman filter based on a generalized maximum-likelihoodtype estimator, IEEE Transactions on Signal Processing, 58, 2509-2520. https://doi.org/10.1109/TSP.2009.2039731
  3. Hampel FR, Ronchetti EM, Rousseeuw PJ, and Stahel WA (2011). Robust Statistics: The Approach Based on Influence Functions, John Wiley & Sons, New York.
  4. Huber PJ (1964). Robust estimation of a location parameter, The Annals of Mathematical Statistics, 35, 73-101.
  5. Huber PJ and Ronchetti EM (2009). Robust Statistics (2nd ed), John Wiley, Chichester.
  6. Kalman RE (1960). A new approach to linear filtering and prediction problems, Journal of Basic Engineering, 82, 35-45. https://doi.org/10.1115/1.3662552
  7. Kay SM (1993). Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice Hall, NJ.
  8. Lee SD, Han EH, and Kim DK (2011). Kalman-Filter estimation and prediction for a spatial time series model, Communications for Statistical Applications and Methods, 18, 79-87. https://doi.org/10.5351/CKSS.2011.18.1.079
  9. Lee SD and Kim DK (2010). The comparison of imputation methods in space time series data with missing values, Communications for Statistical Applications and Methods, 17, 263-273.
  10. Pak RJ (1998). M-estimation function induced from minimum l2 distance estimation, Journal of the Korean Statistical Society, 27, 507-514.
  11. Ruckdeschel P (2000). Robust Kalman Filtering (discussion paper), Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  12. Scott DW (2009). Multivariate Density Estimation: Theory, Practice, and Visualization, John Wiley & Sons, New York.
  13. Sheather SJ and Jones MC (1991). A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Society, Series B (Methodological), 53, 683-690.
  14. Silverman BW (1986). Density Estimation for Statistics and Data Analysis, CRC Press, New York.
  15. Thrun S (2002). Particle filters in robotics. In Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence, 511-518.