Design of multi-innovation hierarchical fractional adaptive algorithm for generalized bilinear-in-parameter system using the key term separation principle

This paper mainly studies the issue of fractional parameter identification of generalized bilinear-in-parameter system(GBIP) with colored noise. Hierarchical fractional least mean square algorithm based on the key term separation principle(K-HFLMS) and multi-innovation hierarchical fractional least mean square algorithm based on the key term separation principle (K-MHFLMS) are presented for the effective parameter estimation of GBIP system. The K-MHFLMS expands the scalar innovation into the vector innovation by making full use of the system input and output data information at each recursive step. The detailed performance analyses of the K-MHFLMS strategy are compared with the K-HFLMS algorithm for GBIP identification model based on the Fitness metrics, the mean square error metrics and the average predicted output error. The effectiveness and reliability of K-HFLMS and K-MHFLMS algorithms are further verified through the simulation experimentation under different noise variances, fractional orders and innovation lengths, and the K-MHFLMS yields faster convergence speed than the K-HFLMS by increasing the innovation length.