Algorithm Understanding of the J-Fast H-infinity Filter Based on Linear Prediction of Input Signal
The hyper H-infinity 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-infinity filter, called the fast H-infinity 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-infinity filter may be applicable to linear prediction of the signal. On the other hand, an alternative fast version of the hyper H-infinity filter, called the J-fast filter, is derived using a J-unitary array form, which is amenable to parallel processing. However, the J-fast H-infinity 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-infinity filter. These findings are verified by computer simulations.
h-infinity filter system identification fast algorithm backward linear prediction forward linear prediction