Condition Number of Data Matrix and Persistent Excitation Conditions in RLS Adaptive Filtering

  • Max Gerken
  • Phillip M. S. Burt
  • Maria D. Miranda
Keywords: Adaptive filtering, RLS algorithms, persistent excitation.

Abstract

Persistent excitation and the condition of the data matrix are considered in the framework of RLS adaptive filtering with exponential weighting. Two persistent excitation conditions that are used in convergence and numerical stability analysis of RLS algorithms are shown to be equivalent. The boundedness of the data matrix condition number is also shown to be equivalent to the considered conditions as long as the input signal energy is lower and upper bounded. Some related inequalities are presented that give insight into the numerical stability behavior of RLS algorithms. The relations of excitation persistency with concepts like predictability, spectral content of the excitation signal, identifiability, exponential convergence and numerical stability of RLS algorithms are briefly addressed in order to give an overview of the subject.
Published
12-02-2018
How to Cite
Gerken, M., Burt, P., & Miranda, M. (2018). Condition Number of Data Matrix and Persistent Excitation Conditions in RLS Adaptive Filtering. Journal of Communication and Information Systems, 15(2). https://doi.org/10.14209/jcis.2000.10
Section
Regular Papers