Mean Square Projection Error Gradient-based Variable Forgetting Factor FAPI Algorithm

평균 제곱 투영 오차의 기울기에 기반한 가변 망각 인자 FAPI 알고리즘

  • Seo, YoungKwang (Department of Electrical and Computer Engineering, Pusan National University) ;
  • Shin, Jong-Woo (Department of Electrical and Computer Engineering, Pusan National University) ;
  • Seo, Won-Gi (NEXTWILL Co., Ltd.) ;
  • Kim, Hyoung-Nam (Department of Electrical and Computer Engineering, Pusan National University)
  • 서영광 (부산대학교 전자전기컴퓨터공학과) ;
  • 신종우 (부산대학교 전자전기컴퓨터공학과) ;
  • 서원기 ((주) 넥스윌) ;
  • 김형남 (부산대학교 전자전기컴퓨터공학과)
  • Received : 2013.12.30
  • Accepted : 2014.04.30
  • Published : 2014.05.25


This paper proposes a fast subspace tracking methods, which is called GVFF FAPI, based on FAPI (Fast Approximated Power Iteration) method and GVFF RLS (Gradient-based Variable Forgetting Factor Recursive Lease Squares). Since the conventional FAPI uses a constant forgetting factor for estimating covariance matrix of source signals, it has difficulty in applying to non-stationary environments such as continuously changing DOAs of source signals. To overcome the drawback of conventioanl FAPI method, the GVFF FAPI uses the gradient-based variable forgetting factor derived from an improved means square error (MSE) analysis of RLS. In order to achieve the decreased subspace error in non-stationary environments, the GVFF-FAPI algorithm used an improved forgetting factor updating equation that can produce a fast decreasing forgetting factor when the gradient is positive and a slowly increasing forgetting factor when the gradient is negative. Our numerical simulations show that GVFF-FAPI algorithm offers lower subspace error and RMSE (Root Mean Square Error) of tracked DOAs of source signals than conventional FAPI based MUSIC (MUltiple SIgnal Classification).


Supported by : 한국산업기술진흥원


  1. R.O. Schmidt, "Multiple emitter location and signal parameter estimation," IEEE Trans. AP, vol. 34, no. 3, pp. 276-280, Mar. 1986.
  2. S. Haykin, "Adaptive Filter Theory", Englewood Cliffs. NJ: Prentice Hall, 4th ed, 2002.
  3. B. Yang and J. F. Bohme, "Rotation based RLS algorithms: Unified derivations, numerical properties and parallel implementations," IEEE Trans. Signal Processing, vol. 40, no. 5, pp. 1151-1167, May 1992.
  4. R. Badeau, B. David, and G. Richard, "Approximated power iterations for fast subspace tracking," Signal Processing and Its Applications, 2003. Proceedings. Seventh International Symposium on, vol. 2, pp. 583-586, Jul. 2003.
  5. R. Kumaresan and D.W. Tufts, "Estimating the angles of arrival of multiple plane waves," IEEE Trans. Aerosp. Elect. Systems, vol. AES-19, pp. 134-139, Jan. 1983.
  6. Young-Kug Pyeon, Ki-Sung Kang, Sang-Heung Shim, Sang-Ok, Yoon, and Jun-Seok Lim "VFF-PASTd for Nonstationary DOA Estimation," IEIE, vol 41, no. 2, pp. 115-120, Jul. 2004.
  7. D. T. M. Slock, T. Kailath, "Fast transversal filters with data sequence weighting," IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, no. 3, pp. 346-359, Mar. 1989.
  8. B. Toplis, S. Pasupathy, "Tracking Improvements in fast RLS algorithms using a variable forgetting factor," IEEE trans. Acoust., Speech, Signal Processing, vol. 36, no. 2, pp. 206-227, Feb. 1988.
  9. P. Strobach, "Low-rank adaptive filters," IEEE Trans. Signal Processing, vol. 44. no. 12, pp. 293-2947, Dec. 1996.
  10. R.D. DeGroat, "Subspace Tracking," CRC Press LLC, 1999.
  11. B. Yang, "Projection Approximation Subspace Tracking," IEEE Trans. Signal Processing, vol. 43, no. 1, pp. 95-107, Jan. 1995.
  12. Christos G. Tsinos, Kostas Berberidis, "Blind Opportunistic Interference Alignment in MIMO Cognitive Radio Systems," IEEE Emerging and Selected Topics in Circuits and Systems, vol. 3, no. 4, pp. 626-639, Dec. 2013.
  13. Olutayo O. Oyerinde, Stanley H. Mneney, "Regularized Adaptive Algorithms-Based CIR Predictors for Time-Varying Channels in OFDM Systems," IEEE Signal Processing Letters, vol. 18, no. 9, pp. 505-508, Sep. 2011.
  14. P. Comon, G.H. Golub, "Tracking a few extreme singular values and vectors in signal processing," Proceedings of the IEEE, vol. 78, no. 8, Aug. 1990.
  15. R. Badeau, B. David, and G. Richard, "Fast Approximated Power Iterations Subspace Tracking," IEEE Trans. Signal Processing, vol. 53, no. 9, pp. 2931-2941, Aug. 2005.
  16. P.Strobach, "The fast recursive row-Householder subspace tracking algorithm," Signal Processing, vol. 89, no. 12, pp. 2514-2528, Dec, 2009.
  17. Xenofon G. Doukopoulos, George V. Moustakides, "Fast and Stable Subspace Tracking," IEEE Trans. Signal Processing, vol. 56, no. 4, Apr. 2008.
  18. S. Bartelmaos and K. Abed-Meraim, "Principal and minor subspace tracking: Algorithms & stability analysis," in Proc. ICASSP, Toulouse, France, pp. 560-563, May 2006.
  19. Rong Wang, Minli Yao, Daoming Zhang, Hongxing Zou, "Stable and Orthonormal OJA Algorithm with low complexity," IEEE Signal Processing Letters, vol. 18, no. 4, pp. 211-214, Apr. 2011.
  20. Shu-Hong Leung and C.F. So, "Gradient-Based Variable Forgetting Factor RLS Algorithm in Time-Varying Environments," IEEE Trans. Signal Processing, vol. 53, no. 8, Aug. 2005.
  21. J. Landon, B.D. Jeffs, Karl F. Warnick, "Model-Based Subspace Projection Beamforming for Deep Interference Nulling," IEEE Trans, Signal Processing, vol 60, no 3, pp. 1215-1228, Mar. 2012.
  22. S. Dib, M. Barkat, M. Grimes, "PAST and OPAST algorithms for STAP in monostatic airborne radar," International Symposium on Innovations in Intelligent Systems and Applications, pp. 177-181, Jun. 2011.
  23. Pu Wang, Man-On Pun, Z. Sahinoglu, "Low-complexity stap via subspace tracking in compound-Gaussian environment," IEEE Radar Conference, pp. 356-361, May 2011.
  24. K. Kumatani, J. McDonough, B. Raj, "Maximum kurtosis beamforming with a subspace filter for distant speech recognition," IEEE Workshop on. Automatic Speech Recognition and Understanding, pp. 179-184, Dec. 2011.