A Fast Quasi-Newton Adaptive Filtering Algorithm

An important consideration in the design of an adaptive system is the convergence rate of the system. This is closely related to the system's ability to track a time-varying optimum. Basic adaptive filtering algorithms give poor convergence performance when the input to the adaptive system is colored. There are more sophisticated algorithms which converge very rapidly regardless of the input spectrum, but these algorithms typically require O(N2) computation, where N is the order of the adaptive filter. This is a significant disadvantage for real-time applications, especially where economic constraints must be met. Also, many of these algorithms have a reputation for behaving poorly in finite precision implementation. In this paper, an adaptive filtering algorithm is introduced which employs a quasi-Newton approach to give rapid convergence even with colored inputs. The algorithm achieves an overall computational requirement of O(N). And this fast quasi-Newton (FQN) algorithm appears to be quite robust in finite precision implementations.