Bias removal algorithm for 2-D equation error adaptive IIR filters

This paper proposes a bias removal algorithm for equation error-based 2-D adaptive cascade IIR filters with separable denominator function. As well known, equation error-based adaptive IIR filtering algorithms have the advantages of fast convergence and unimodal mean-square-error surface. These advantages, however, come along with the drawback of biased parameter estimates in the presence of measurement noise. The adaptive filter structure in the proposed algorithm is based on the concept of backpropagating the desired signal through a cascade of the denominator vertical and horizontal sections. To handle the bias problem, the proposed algorithm uses a scaled value of the output error of each of the cascaded sections as an estimate for the measurement noise embedded in the signal part of the coefficient-update procedure of that section. Thus, while maintaining the advantages of easy stability monitoring, fast convergence, and low computational load, the effect of the measurement noise is suppressed. Input-Output stability analysis is carried out, and the constraints required to maintain stability are derived. Simulation examples are presented to support the effectiveness and the usability of the proposed bias removal algorithm in 2-D system identification and image enhancement applications.