Enhanced Recursive Adaptive Inversion Algorithm

The recursive inverse (RI) adaptive filtering technique has demonstrated superior performance characteristics compared to various established adaptive filtering methods. A primary challenge facing the RI technique is its dependence on time-varying step-size parameters, which limits its effectiveness in situations involving substantial eigenvalue spread within the covariance matrix. This work presents an enhanced variant of the RI technique. Our proposed methodology employs a nonlinear step-size mechanism designed to mitigate the influence of covariance matrix eigenvalue spread on RI technique performance. Although this nonlinear step-size approach introduces additional computational burden compared to the standard RI technique, the overall complexity remains on par with that of the RLS method. Through implementation of this nonlinear step-size strategy, our proposed technique achieves superior performance in scenarios characterized by large eigenvalue spread within the covariance matrix, effectively resolving the primary constraint of the traditional RI approach. Experimental validation demonstrates that our proposed technique outperforms the traditional RI method and achieves performance levels equivalent to or exceeding those of the RLS technique.