A numerically stable fast transversal filter with leakage correction

A derivation of fundamental fast transversal filter equations comes to a 7M fast RLS algorithm for system identification. Yet, this algorithm is not stable due to numerical errors resulting from implementation on a hardware with finite precision arithmetic. The known stabilization methods with feedback of numerical errors require a judicious choice of the feedback gains and depend on the properties of the exciting sequence, as simulations have shown. A new method to stabilize the algorithm is introduced that does not depend on the characteristics of the excitation signal. By inserting leakage factors in the filter equations, a steady contraction of error components is reached.<>