Steady state MSE analysis of convexly constrained mixture methods

We study the steady-state performances of four convexly constrained mixture algorithms that adaptively combine outputs of two adaptive filters running in parallel to model an unknown system. We demonstrate that these algorithms are universal such that they achieve the performance of the best constituent filter in the steady-state if certain algorithmic parameters are chosen properly. We also demonstrate that certain mixtures converge to the optimal convex combination filter such that their steady-state performances can be better than the best constituent filter. Furthermore, we show that the investigated convexly constrained algorithms update certain auxiliary variables through sigmoid nonlinearity, hence, in this sense, related.