Bias-free adaptive IIR filtering

We present a new family of algorithms that solve the bias problem in the equation-error based adaptive infinite impulse response (IIR) filtering. A novel constraint, called the constant-norm constraint, unifies the quadratic constraint and the monic one. By imposing the monic constraint on the mean square error (MSE) optimization, the merits of both constraints are inherited and the shortcomings are overcome. A new cost function based on the constant-norm constraint and Lagrange multiplier is defined. Minimizing the cost function gives birth to a new family of bias-free adaptive IIR filtering algorithms. For example, three efficient algorithms belonging to the family are proposed. The analysis of the stationary points is presented to show that the proposed methods can indeed produce bias-free parameter estimates in the presence of noise. The simulation results demonstrate that the proposed methods perform better than existing algorithms, while being very simple both in computation and implementation