Efficient adaptive algorithms for ARX identification

Two efficient adaptive algorithmic families are developed for multichannel combiners characterized by unequal memory lengths for each input channel. The prewindowed, the covariance, and the sliding window case are addressed. The difference between the proposed methods lies in the way the Kalman gain vector is order-updated in each case. The first algorithm operates on both inputs simultaneously and thus utilizes block multichannel structured order recursions. The resulting scheme is called the diagonal-update algorithm. The second approach updates the Kalman gain in a two-step procedure by first reducing the size of one input and then the other input. The resulting method is called stairwise-update algorithm. Both algorithms are applicable to adaptive ARX (autoregressive exogenous) system identification, to adaptive control, and to the design of decision-feedback equalizers. Simulations are included