The use of large adaptation gains to remove the SPR condition from recursive adaptive algorithms

Adaptive recursive algorithms using output error have some very attractive properties for both adaptive recursive filtering and system identification. However, their use has been severely restricted by the need to satisfy the so-called SPR condition. In this paper we demonstrate on the well known HARF algorithm that the use of large gains can essentially eliminate the need for the SPR condition. This should allow for more widespread use of adaptive recursive filtering and output error system identification.