Recursive inverse adaptive algorithm: a second-order version, a fast implementation technique, and further results

Abstract

A variable step-size and first-order recursive estimate of the autocorrelation matrix have been used in the update equation of the recently proposed recursive inverse (RI) algorithm. These lead to an improved performance of the RI algorithm compared with some well-known adaptive algorithms. In this paper, the RI algorithm is first briefly reviewed. An improved version of the RI algorithm, which uses a second-order recursive estimation of the correlations, is introduced. A general fast implementation technique for the RI algorithms is presented. The performances of the fast RI and fast second-order RI algorithms are compared to that of the RLS algorithm in stationary white and correlated noise environments in a noise cancellation setting. The simulation results show that the fast RI algorithms outperform the others compared either in speed of convergence and/or the computational complexity when the MSE is held constant. The performance of the original RI algorithms is compared to that of the RLS algorithm in a system identification setting. Simulations show that the RI algorithms perform similar or better than the other algorithms.