Generation of multidimensional variable step size sequential adaptive gradient algorithms with identification and noise cancellation applications

The development of two-dimensional, gradient-based sequential algorithms with applications in 2-D system identification and noise cancellation is addressed. Existing gradient sequential algorithms use a convergence factor which is used to adjust the two-dimensional adaptive filter coefficients at each iteration. The performance of the algorithm depends entirely on the accuracy of the estimated convergence factor. The objective of the present work is to derive the optimality criterion governing the choice of the convergence factor in the case of 2-D gradient-based sequential algorithms. The 2-D variable step-size sequential algorithms meeting the above constraint are proposed and investigated: the 2-D individual adaptive (TDIA) and the 2-D homogeneous adaptive (TDHA) algorithms. The TDIA algorithm uses optimal convergence factors tailored for each 2-D adaptive filter coefficient at each iteration. The TDHA algorithm uses the same convergence factor for all coefficients but is optimally updated at each iteration