Biorthogonal Wavelet Based Identification of Fast Linear Time-Varying Systems—Part II: Algorithms and Performance Analysis¹²

The present work proposes a new class of algorithms for identification of fast linear time-varying systems on short time intervals, based on the biorthogonal function decomposition. When certain features of the system dynamics are known a priori, the algorithms admit their embedding into the identification procedure through the choice of the matching bases, yielding the rapidly convergent identification laws. The speed-up is attained via utilizing both time and frequency localized bases, permitting identification of fewer coefficients without noticeable loss of accuracy. Simulation shows that the resulting high speed identification algorithms can reject small persistent random disturbances as well as capture the fast changes in system dynamics. The algorithm development is based on the results of Part I where it is shown that the sets of all bounded-input-bounded-output (BIBO) stable or $l2$-stable linear discrete-time-varying (LTV) systems are Banach spaces, and modeling and identification of these systems are reducible to linear approximation problems in a Banach space setting.