Condition Number of Data Matrix and Persistent Excitation Conditions in RLS Adaptive Filtering
Main Article Content
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.
Article Details
How to Cite
Gerken, M., Burt, P. M. S., & Miranda, M. D. (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
Issue
Section
Regular Papers
Authors who publish in this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors can enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
___________