Generalization of exponentially weighted RLS algorithm based on a state-space model

We develop a generalized RLS (G-RLS) algorithm described by a state-space model through some modification of the procedure for Kalman filter derivation. It is shown that the G-RLS algorithm reduces to the conventional RLS when the state transition matrix is an identity matrix, and that the G-RLS algorithm without exponential weighting and Kalman filtering become identical when the state model is an unforced dynamical model. The G-RLS algorithm does not require model statistics, and can be implemented once the forgetting factor is chosen. The performances of the G-RLS and Kalman filtering are compared through computer simulation. Specifically, they are applied to the derivation of variable loop gains of a digital phase-locked loop (DPLL). The results indicate that the G-RLS algorithm can act like the Kalman filter if its forgetting factor is properly chosen