Unbiased model combinations for adaptive filtering

Suleyman S. Kozat, Andrew C. Singer, Alper Tunga Erdogan, Ali H. Sayed

Research output: Contribution to journalArticlepeer-review


In this paper, we consider model combination methods for adaptive filtering that perform unbiased estimation. In this widely studied framework, two adaptive filters are run in parallel, each producing unbiased estimates of an underlying linear model. The outputs of these two filters are combined using another adaptive algorithm to yield the final output of the system. Overall, we require that the final algorithm produce an unbiased estimate of the underlying model. We later specialize this framework where we combine one filter using the least-mean squares (LMS) update and the other filter using the least-mean fourth (LMF) update to decrease cross correlation in between the outputs and improve the overall performance. We study the steady-state performance of previously introduced methods as well as novel combination algorithms for stationary and nonstationary data. These algorithms use stochastic gradient updates instead of the variable transformations used in previous approaches. We explicitly provide steady-state analysis for both stationary and nonstationary environments. We also demonstrate close agreement with the introduced results and the simulations, and show for this specific combination, more than 2 dB gains in terms of excess mean square error with respect to the best constituent filter in the simulations.

Original languageEnglish (US)
Article number5443449
Pages (from-to)4421-4427
Number of pages7
JournalIEEE Transactions on Signal Processing
Issue number8
StatePublished - Aug 2010


  • Adaptive filtering
  • gradient projection
  • least-mean fourth
  • least-mean square
  • mixture methods

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


Dive into the research topics of 'Unbiased model combinations for adaptive filtering'. Together they form a unique fingerprint.

Cite this