A steady state analysis of competitive prediction using LMMN combination

Abstract

In this thesis, the adaptive linear prediction of autoregressive signals under additive Gaussian noise model is investigated in a competitive algorithm framework. In this framework, there is a comparison class of predictors of different models, model orders or model parameters that work in parallel to estimate the same desired signal. The outputs of the constituent algorithms in this competing class are then combined using another adaptive algorithm to improve the overal performance over the comparison class. As the combination method, the Least Mean Mixed Norm (LMMN) algorithm is proposed without any constraints in converging to the optimal Wiener solution. This method is specificly applied to: a comparison class of two LMMN predictors of the same model order but different model parameters; a comparison class of an RLS and an LMMN predictor of the same model order; and finally a comparison class of M different order LMMN predictors with the same algoritmic parameters. For each of the combination schemes, the LMMN combination method is shown to yield a smaller MSE in the steady state than the best predictor in the comparison class when the step size is choosen appropriately. Furthermore, for the LMMN-LMMN and the RLS-LMMN combinations, i.e., the first two combination classes, it has been observed through simulations that the combination filter converges more rapidly than the most rapidly converging filter in the comparison class when the parameters of the LMMN combination filter are choosen properly.