This study introduces a variable diagonal-matrix-step-size affine projection algorithm (APA), which shows robustness against to impulsive noises. Unlike the normal scalar step-size method, the independent step size for each input vector is used as the entry of the diagonal matrix, and the optimal step size at each time step is ascertained by conducting mean-square-deviation (MSD) analysis. In addition, a recursive equation of weight update has been derived without approximating posteriori error as priori error. Using the Lagrange multiplier method, we formulate a scalar step size affine projection algorithm that shows resilience to impulsive noises. This algorithm emerges as a solution to a constrained optimization problem. To further enhance convergence performance, a diagonal-matrix-step size is introduced and its MSD is analyzed. The step size at each time step is optimized by interpreting the MSD mathematically, resulting in the variable diagonal-matrix-step size APA (VDMSS-APA). Various simulations exhibit low steady-state error and fast convergence rate of the proposed algorithm.

中文翻译：

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对脉冲噪声具有鲁棒性的可变对角矩阵步长 APA

本研究引入了一种可变对角矩阵步长仿射投影算法（APA），该算法显示出对脉冲噪声的鲁棒性。与普通标量步长方法不同，每个输入向量的独立步长被用作对角矩阵的条目，并且通过进行均方偏差（MSD）分析来确定每个时间步的最佳步长。此外，还推导了权重更新的递归方程，无需将后验误差近似为先验误差。使用拉格朗日乘子方法，我们制定了标量步长仿射投影算法，该算法显示出对脉冲噪声的弹性。该算法是作为约束优化问题的解决方案而出现的。为了进一步提高收敛性能，引入了对角矩阵步长并分析了其MSD。通过对 MSD 进行数学解释来优化每个时间步的步长，从而产生可变对角矩阵步长 APA (VDMSS-APA)。各种模拟显示所提出的算法具有低稳态误差和快速收敛速度。