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Traditional recursive least square (RLS) adaptive filtering is widely used toestimate the impulse responses (IR) of an unknown system. Nevertheless, the RLSestimator shows poor performance when tracking rapidly time-varying systems. Inthis paper, we propose a multi-layered RLS (m-RLS) estimator to address thisconcern. The m-RLS estimator is composed of multiple RLS estimators, each ofwhich is employed to estimate and eliminate the misadjustment of the previouslayer. It is shown that the mean square error (MSE) of the m-RLS estimate canbe minimized by selecting the optimum number of layers. We provide a method todetermine the optimum number of layers. A low-complexity implementation ofm-RLS is discussed and it is indicated that the complexity order of theproposed estimator can be reduced to O(M), where M is the IR length. Inaddition, by performing simulations, we show that m-RLS outperforms the classicRLS and the RLS methods with a variable forgetting factor.

Multi-Layered Recursive Least Squares for Time-Varying System Identification