Noisy FIR Identification as a Quadratic Eigenvalue Problem

This correspondence describes a method for identifying FIR models in the presence of input and output noise. The proposed algorithm takes advantage of both the bias compensation principle and the instrumental variable method. It is based on a nonlinear system of equations whose unknowns are the FIR coefficients and the input noise variance. This system allows mapping the noisy FIR identification problem into a quadratic eigenvalue problem. The identification problem is thus solved without requiring the use of iterative least-squares algorithms. The performance of the proposed approach has been tested and compared with that of other identification methods by means of Monte Carlo simulations.