An optimizing search based algorithm for FIR filtering with noisy input-output data

In this paper the problem of finite impulse response (FIR) filtering with noisy input-output data is investigated. A set of algebraic equations is derived for noisy FIR filtering. An analysis reveals that the derived set of algebraic equations provides a way for separating the estimation of the FIR filter parameters from that of the input noise variance that determines the noise-induced bias in the standard least-squares parameter estimates. This separation enables that the input noise variance is estimated by conducting optimizing search over an objective function. With this done, an estimate of the FIR filter parameters can be easily obtained without involving any iteration procedure. Numerical results are given to demonstrate the effectiveness of the proposed algorithm for noisy FIR filtering.