It is well known that a pole-zero structure which corresponds to an infinite impulse response (IIR) filter models a physical system better than an all-zero structure, or a finite impulse response (FIR) filtering structure. However, few adaptive IIR filtering algorithms are in existence today due to the non-linearity of the problem. Many issues such as stability and global convergence are not well-solved. Besides, lack of adequate analytic tools makes the analysis of these algorithms a difficult task. On the other hand, recursive system identification, as a well-established subject, has available many well-behaved algorithms. Although the similarities between these two fields have recently been realized, only direct application of some system identification algorithms to adaptive filtering problems is seen in literature. This research focuses on a new adaptive IIR filtering algorithm and a unified analytical method which shows some global convergence. The new method uses an ordinary differential equation (ODE) approach for constant-gain adaptive IIR filtering algorithms which is parallel to the ODE approach in the field of system identification. Hence further insight into the connection between constant-gain adaptive IIR filtering algortihms and their system identification counterparts can be gained. Using this new approach, many existing adaptive IIR filtering algorithms are being analyzed and compared in a unified way. Furthermore, more system identification algorithms are being tailored for adaptive IIR filtering applications with simplified calculation and constant gains. The observed global convergence phenomenon is also being investigated using the same approach, and should lead to the development of new globally convergent algorithms for certain classes of environment. Adaptive filers are used in a wide spectrum of applications such as noise cancellation, channel equalization, spectral estimation, and antenna array processing. This proposal focuses research on these adaptive filters.
