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In this paper, we consider mixture approaches that adaptively combine outputs of several parallel running adaptive algorithms. These parallel units can be considered as diversity branches that can be exploited to improve the overall performance. We study various mixture structures where the final output is constructed as the weighted linear combination of the outputs of several constituent filters. Although the mixture structure is linear, the combination weights can be updated in a highly nonlinear manner to minimize the final estimation error such as in Singer and Feder 1999; Arenas-Garcia, Figueiras-Vidal, and Sayed 2006; Lopes, Satorius, and Sayed 2006; Bershad, Bermudez, and Tourneret 2008; and Silva and Nascimento 2008. We distinguish mixture approaches that are convex combinations (where the linear mixture weights are constrained to be nonnegative and sum up to one) [Singer and Feder 1999; Arenas-Garcia, Figueiras-Vidal, and Sayed 2006], affine combinations (where the linear mixture weights are constrained to sum up to one) [Bershad, Bermudez, and Tourneret 2008] and, finally, unconstrained linear combinations of constituent filters [Kozat and Singer 2000]. We investigate mixture structures with respect to their final mean-square error (MSE) and tracking performance in the steady state for stationary and certain nonstationary data, respectively. We demonstrate that these mixture approaches can greatly improve over the performance of the constituent filters. Our analysis is also generic such that it can be applied to inhomogeneous mixtures of constituent adaptive branches with possibly different structures, adaptation methods or having different filter lengths. [ABSTRACT FROM AUTHOR]

In this paper, we consider model combination methods for adaptive filtering that perform unbiased estimation. In this widely studied framework, two adaptive filters are run in parallel, each producing unbiased estimates of an underlying linear model. The outputs of these two filters are combined using another adaptive algorithm to yield the final output of the system. Overall, we require that the final algorithm produce an unbiased estimate of the underlying model. We later specialize this framework where we combine one filter using the least-mean squares (LMS) update and the other filter using the least-mean fourth (LMF) update to decrease cross correlation in between the outputs and improve the overall performance. We study the steady-state performance of previously introduced methods as well as novel combination algorithms for stationary and nonstationary data. These algorithms use stochastic gradient updates instead of the variable transformations used in previous approaches. We explicitly provide steady-state analysis for both stationary and nonstationary environments. We also demonstrate close agreement with the introduced results and the simulations, and show for this specific combination, more than 2 dB gains in terms of excess mean square error with respect to the best constituent filter in the simulations. [ABSTRACT FROM AUTHOR]