Fast two-dimensional adaptive IIR algorithms

Several new two-dimensional adaptive infinite-impulse response (IIR) filtering algorithms are derived and simulated. These new algorithms are based upon the one-dimensional version of the algorithm developed by Fan and Jenkins (1986). This algorithm was shown to experimentally possess the ability to converge to the global minimum of the mean square error (MSE) even in cases where the MSE surface is ill-conditioned. In addition, further enhancements to this new algorithm were made to improve convergence rate performance. An estimate of the Hessian is incorporated into the adaptive filter coefficient update expressions. Least Mean Square (LMS), Recursive Least Square (RLS), Gauss-Newton (GN), and Fast Quasi-Newton (FQN) forms of the two-dimensional Fan-Jenkins algorithm are formulated and compared via simulation for several examples.