Some new results of designing an IIR filter with colored noise for signal processing

The design of adaptive finite impulse response filters is a linear optimization problem and the design of adaptive infinite impulse response (IIR) filters in the presence of observation noise is a nonlinear optimization problem. This paper considers the parameter estimation issues of an infinite impulse response (IIR) filter with colored noise which is treated as an autoregressive process. The key is to investigate novel estimation methods of an IIR filter with an autoregressive disturbance noise from the viewpoint of the observation data filtering. Firstly, we simply give the least mean square (LMS) algorithm for an IIR filter with autoregressive noise and derive a multi-innovation LMS (MI-LMS) algorithm for improving the parameter estimation accuracy. Secondly, we present a data filtering based LMS algorithm and a data filtering based MI-LMS algorithm for further improving the parameter estimation accuracy. The theoretical analyses show that the proposed algorithms are convergent and the simulation results indicate that the MI-LMS algorithm and the data filtering based MI-LMS algorithm are superior to the LMS algorithm and the data filtering based LMS algorithm in accuracy, respectively. The proposed methods in this paper have been extended to an IIR filter with autoregressive moving average noise. Finally, two simulation examples test the performances of the proposed algorithms.