2012 Volume E95.A Issue 7 Pages 1175-1179
The hyper H∞ filter derived in our previous work provides excellent convergence, tracking, and robust performances for linear time-varying system identification. Additionally, a fast algorithm of the hyper H∞ filter, called the fast H∞ filter, is successfully developed so that identification of linear system with impulse response of length N is performed at a computational complexity of O(N). The gain matrix of the fast filter is recursively calculated through estimating the forward and backward linear prediction coefficients of an input signal. This suggests that the fast H∞ filter may be applicable to linear prediction of the signal. On the other hand, an alternative fast version of the hyper H∞ filter, called the J-fast H∞ filter, is derived using a J-unitary array form, which is amenable to parallel processing. However, the J-fast H∞ filter explicitly includes no linear prediction of input signals in the algorithm. This work reveals that the forward and backward linear prediction coefficients and error powers of the input signal are indeed included in the recursive variables of the J-fast H∞ filter. These findings are verified by computer simulations.