Unified derivation and initial convergence of three prewindowed fast transversal recursive least squares algorithms

Three prewindowed transversal fast RLS (recursive least-squares) algorithms, the FK (fast Kalman), FAEST (fast a posteriori estimation sequential technique), and FTF (fast transversal filter) algorithms, are derived in a unified approach. It is shown that their mathematical equivalence can be established only by properly choosing their initial conditions. It is confirmed by computer simulations that the choice of initial conditions and the algorithmic forgetting factor could strongly affect the speed of the initial convergence