Two-dimensional variable step-size sequential adaptive gradient algorithms with applications

The optimality criterion governing the choice of the convergence factor for the 2-D sequential adaptive gradient algorithms is developed. Two 2-D variable step-size sequential algorithms satisfying the proposed optimality constraint are derived and investigated. These are the 2-D individual adaptation (TDIA) algorithm and the 2-D homogeneous adaptation (TDHA) algorithm. The TDIA algorithm uses 2-D optimal convergence factors tailored for each 2-D adaptive filter coefficient at each iteration. The TDHA algorithm uses the same convergence factor for all the filter coefficients, but the convergence factor is optimally updated at each iteration. Neither algorithm requires any a priori knowledge about the statistics of the system signals. In addition, the convergence factors are easily obtained from readily available signals without any differentiation or matrix inversions. The convergence characteristics and adaptation accuracy are greatly improved at the expense of a modest increase in computational complexity