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.
Highlights
Resumo - 0 conceito de excita9ao persistente e o condicionamento da matriz de dados sao considerados no ambito dos algoritmos adaptativos RLS com pondera9ao exponencial
E mostrado tambem que a existencia de urn limite superior para a dispersao dos. valores singulares da matriz de dados e equivalente a estas condi9oes de persistencia de excita9ao, desde que a energia do sinal de entrada seja limitada inferiormente e superiormente
Identification of an unknown system is a central issue in various applications of the communications area such as channel echo cancelation in communication
Summary
Resumo - 0 conceito de excita9ao persistente e o condicionamento da matriz de dados sao considerados no ambito dos algoritmos adaptativos RLS com pondera9ao exponencial. It has been found that keeping the input signal persistently exciting is of paramount importance in practical implementations of RLS algorithms, especially when exponential weighting is used.
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