Constrained adaptive filtering algorithms: asymptotic convergence properties for dependent data

The convergence properties of constrained adaptive filtering algorithms are established. The constraint is in the form of a bounded set in which the filter's coefficients must lie. A recursive procedure that converges to the deterministic solution of the constrained linear mean-square estimation problem is obtained, using an appropriate contraction mapping. The recursion is used to derive the adaptive algorithm for the filter coefficients. Bounds on the mean-square error of the coefficients. Bounds on the mean-square error of the estimates of the filter coefficients and on the excess error of the input signal estimate are derived for processes that are either strong mixing or asymptotically uncorrelated. The algorithms use a moving window of size n on the data from one adaptation step to the next. However, tighter bounds can be obtained when a skipped sampling mechanism is used