Affine Combination of General Adaptive Filters

Combination schemes are very effective for adaptive filters; yet, they are still constrained to use a linear model and the mean-square error (MSE) cost. All types of models, both linear and nonlinear, are accommodated in this work by expanding combination schemes to generic cost functions. Specifically, in this kind of combination framework, two candidate filters are firstly designed by optimizing separate general cost functions; then, to optimize overall performance, the combination coefficients that are given to these filters are fine-tuned by minimizing a third general cost function. Separately, we set and optimize each of the three generic cost functions. After that, we design an affine combination scheme by using the stochastic sign-gradient descent to adjust combination coefficients. Also, to enhance its performance, we include a weight-copying trick. Finally, simulation results are provided to validate their effectiveness for both the MSE and the logistic risk cost functions.