Global convergence of adaptive IIR filter with recursive least squares algorithm

The application of a recursive least squares algorithm to adaptive infinite impulse response (IIR) filters is investigated. A global convergence of an adaptive IIR filter is developed. It is shown that the null solutions of the parameter error vector, filtered error and output error in the filter are asymptotically stable for a stable reference signal. The analysis proceeds with simple algebra, does not rely on the commonly used hyperstability, strictly passive machinery and lower bounded input. The simulation results are also included to demonstrate the behaviour of the filter