Set-Membership Filtering: A Viable Tool for Non-Linear Adaptive Signal Processing

| This paper formulates, and provides a solution to, a ltering problem based on certain de-terministic constraint imposed on the error sequence. The formulation is called Set-Membership Filtering (SMF) and is a generalization of Set-Membership Identiication (SMI) for system identiication. A Set-Membership Decision Feedback Equalizer (SM-DFE) is proposed as an example of its application to non-linear systems. This paper also establishes connections of SM-DFE with the Minimum Mean Square Error DFE (MMSE-DFE). Recursive solutions to the general SMF problem are also presented.