Variable Forgetting Factor RLS Adaptive Algorithms Based on Line Search Methods

Recursive least-squares (RLS) adaptive algorithms are capable of outperforming least-mean-square (LMS) methods for the identification of long-length impulse responses due to their ability to mitigate the high correlation properties of input signals, such as speech. Despite the encouraging results obtained in terms of tracking speed and accuracy, with respect to LMS methods, most RLS algorithms manifest numerical stability issues. Moreover, when an unknown system changes, the identification process needs to adapt to the new impulse response as soon as possible. The algorithm can require a significant amount of time to generate new accurate results in acoustic echo cancellation (AEC) scenarios. Due to the slow propagation speed of sound, acoustic echo paths are usually modeled using thousands of numerical coefficients, and adaptation energy remains relatively limited. A compromise is usually made between tracking capabilities and steady-state accuracy when choosing the forgetting factor (the most important parameter of the RLS algorithm). This paper analyzes a variable forgetting factor (VFF) RLS type of adaptive filter combined with the conjugate gradient (CG) line search method, which is designed to avoid the classical matrix inversion approach. This VFF-RLS-CG adaptive method is not susceptible to numerical stability issues and is designed to adapt its statistical estimates by determining whether a tracking situation occurs or whether the unknown system is not significantly different. Correspondingly, when necessary, the forgetting factor is decreased for faster adaptation to changes in the working environment. When the filter is estimated to work at steady-state, the above-mentioned parameter’s value is increased in order to boost the accuracy of the adaptive filter. The theoretical model is validated using simulations in AEC scenarios with tracking occurrences and relevant steady-state intervals.