Proportionate Total Adaptive Filtering Algorithms for Sparse System Identification

In the application of system identification, not only the output but also the input of the system may be corrupted by noise, which is often characterized by the errors-in-variables (EIV) model. To identify such systems, a gradient-descent total least-squares (GD-TLS) and a maximum total correntropy (MTC) algorithms were proposed. In some scenarios, the weight vector of the unknown system may be sparse, e.g., the echo path in acoustic echo cancelation (AEC). Employing TLS or MTC to estimate such systems may result in slow convergence rate, since they assign the same gain to the update of each weight and therefore cannot make use of the sparsity feature of the system to accelerate convergence. To address the above problem, this article proposes a uniform optimization model for deriving proportionate total adaptive filtering algorithms, and then two proportionate total adaptive filtering algorithms are developed, namely, the proportionate total normalized least mean square (PTNLMS) algorithm for Gaussian noise disturbance and the proportionate MTC (PMTC) algorithm for impulsive noise interference, which are both derived by utilizing the method of Lagrange multipliers. Moreover, this article also makes a steady-state performance analysis of the two proposed algorithms. Simulations are performed to demonstrate the superior performance of the two proposed algorithms and to test the accuracy of the theory on the steady-state performance analysis.