Gradient-based variable forgetting factor RLS algorithm in time-varying environments

Shu-Hung LEUNG, Chi Fuk Henry SO

Research output: Contribution to journalArticlespeer-review

168 Citations (Scopus)


In this paper, a new control mechanism for the variable forgetting factor (VFF) of the recursive least square (RLS) adaptive algorithm is presented. The control algorithm is basically a gradient-based method of which the gradient is derived from an improved mean square error analysis of RLS. The new mean square error analysis exploits the correlation of the inverse of the correlation matrix with itself that yields improved theoretical results, especially in the transient and steady-state mean square error. It is shown that the theoretical analysis is close to simulation results for different forgetting factors and different model orders. The analysis yields a dynamic equation of mean square error that can be used to derive a dynamic equation of the gradient of mean square error to control the forgetting factor. The dynamic equation can produce a positive gradient when the error is large and a negative gradient when the error is in the steady state. Compared with other variable forgetting factor algorithms, the new control algorithm gives fast tracking and small mean square model error for different signal-to-noise ratios (SNRs). Copyright © 2005 IEEE.

Original languageEnglish
Pages (from-to)3141-3150
JournalIEEE Transactions on Signal Processing
Issue number8
Publication statusPublished - Aug 2005


Leung, S.-H., & So, C. F. (2005). Gradient-based variable forgetting factor RLS algorithm in time-varying environments. IEEE Transactions on Signal Processing, 53(8), 3141-3150. doi: 10.1109/TSP.2005.851110


  • Mean square error analysis
  • RLS
  • Time-varying
  • Variable forgetting factor


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