Recursive quadratically constrained least squares bias-free IIR system identification via variable loading

Abstract

Infinite Impulse Response (IIR) filters have very attractive properties. They can more accurately mimic the impulse response of a linear system than a Finite Impulse Response (FIR) filter with smaller number of coefficients. The cost function based on the Equation Error (EE) criterion has a global minimum for the IIR adaptive system identification. However, the solution found by minimizing the Mean Square Equation Error (MSEE) is biased and the bias increases with the power of the noise in the observed output signal. In this paper, a recursive algorithm based on the Recursive Least Squares (RLS) implementation of the EE criterion with a quadratic constraint is presented to get a fast algorithm without bias. A recursion method called variable loading is embedded into the RLS update equations with the constraint to adapt the coefficients of the denominator resulting in a simple recursive algorithm. The speed of convergence is increased considerably without bias.