Derivation of a fast algorithm of modified H∞ filters

The fast Kalman filter provides very quick convergence at the computational complexity of the same order that the LMS algorithm requires. Nevertheless, its performance is still unsatisfactory in system identification because the conventional fast Kalman filter fails to track time-varying impulse responses of FIR systems. The failure of tracking is due to the absence of system noise in the state-space model to be used. However, according to the derivation of the fast Kalman filter, it is difficult to theoretically introduce the term of system noise into the algorithm. In the paper, to overcome the difficulties, a new fast filtering algorithm, called a fast H_∞ filter, is derived based on the H_∞ theory