Improved Robust Total Least Squares Adaptive Filter Algorithms Using Hyperbolic Secant Function

Abstract

In the errors-in-variables (EIV) model, the total least squares (TLS) algorithm has shown good convergence performance. In this model, the input and output signals are simultaneously infected with noise. However, when the output signal is contaminated with impulse noise, the convergence performance of TLS will decrease or even diverge. In order to settle this problem, we propose a hyperbolic secant total least squares (HSTLS) algorithm through adopting the hyperbolic secant function as the cost function. The HSTLS algorithm shows better performance in non-Gaussian noise environment. At the same time, in order to deal with the contradiction between the algorithm’s convergence speed and steady-state deviation with the fixed step size, this brief also provides a new variable step size strategy. The improved variable step size HSTLS (VHSTLS) algorithm shows better performance in simulation. Furthermore, to reduce steady-state deviation of the HSTLS algorithm in sparse systems, a series of improved HSTLS algorithms based on the sparse criterion have also been proposed, and they also have excellent convergence performance.