Using auxiliary signal to remove the SPR condition from recursive adaptive algorithms

The use of adaptive recursive filters and output error identification techniques has been severely restricted by the need to satisfy the so-called SPR (strictly positive real) condition. A method to remove the SPR condition by using an auxiliary signal is demonstrated. It is based on the HARF (hyperstable adaptive recursive filter). By choosing a proper auxiliary sequence, the adaptive algorithm can asymptotically converge for any possible input sequence. The proposed method exhibits low computational complexity, fast convergence, and good rejection of disturbances