On the Step-Size of Leakage QN and Leakage LS Algorithms

Recursive Least Squares (RLS) algorithms are known to have fast convergence in the presence of correlated input signals that have persistent excitation. However, when non-persistently excitating signals or quantization errors are present in the system, the RLS algorithms may diverge. This fact happens due to the loss of positive definiteness of the input signal correlation matrix. There is a class of quasi-Newton algorithms that use a correlation matrix that once initialized positive definite, it remains in this state independently of the input signal. In this paper some algorithms are developed using different approaches to the calculation of the step-size, such that the condition of positive definiteness of the correlation matrix is guaranteed.