A Decomposition-Based RLS Algorithm with Variable Forgetting Factors

The performance of the recursive least-squares (RLS) algorithm is mainly controlled by the forgetting factor. Using a constant value of this important parameter leads to a compromise between the main performance criteria, i.e., low misadjustment versus fast tracking. In this paper, we propose a variable forgetting factor (VFF) solution applicable to the recently developed RLS algorithm based on the nearest Kronecker product decomposition (namely RLS-NKP). The RLS-NKP algorithm exploits an efficient decomposition of the impulse response, thus being suitable for the identification of long length systems (like echo paths). The resulting VFF-RLS-NKP algorithm inherits the performance features of its original counterpart, while also achieving improvements due to the VFF approach. Simulations performed in the context of echo cancellation support this behavior.