A new hyperstable adaptive recursive filters algorithm with variable convergence factor

A new algorithm is suggested to eliminate the critical stability and poor performance in nonstationary environments problems of the adaptive IIR algorithms. The proposed algorithm is called the automatic hyperstable adaptive recursive filters (AHARF) algorithm working over two phases. In the first phase the error signal is not filtered until it reaches a certain threshold and then the algorithm automatically changes to start the error filtering second phase using the estimated system poles vector. This algorithm provides a very fast convergence rate compared with many existing algorithms, is well suited to highly nonstationary environments, and automatically selects the smoothing vector to fulfill the strictly positive real (SPR) condition. A new variable step-size related to the error signal and the auto-correlation matrix is also proposed and adopted in the AHARF algorithm, which allows a high convergence rate for all highly nonstationary signals.