SET-MEMBERSHIP FILTERING AND A SET-MEMBERSHIP NORMALIZED LMS ALGORITHM WITH AN ADAPTIVE STEP-SIZE

Set-membership identification (SMI) theory is extended to the more gen eral problem of linear-in-parameters filtering by defining a set-membe rship specification, as opposed to a bounded noise assumption, This se ts the framework for several important filtering problems that are not modeled by a ''true'' unknown system with bounded noise, such as adap tive equalization, to exploit the unique advantages of SMI algorithms. A recursive solution for set membership filtering is derived that res embles a variable step size normalized least mean squares (NLMS) algor ithm, Interesting properties of the algorithm, such as asymptotic cess ation of updates and monotonically nonincreasing parameter error, are established. Simulations show significant performance improvement in v aried environments with a greatly reduced number of updates.