推广形式的自适应算法:理论分析及应用

提出一种广义的最陡梯度下降自适应算法（ＬＭＫ），它可使误差的任意次范数达最 小，分析了算法的收敛性和收敛结果，给出了步长范围估计及据噪声分布形式合理选择 目标函数的公式．在合成数据上做了试验，理论分析和试验结果表明，当噪声是非高斯 分布时．选择非二次范数作为目标函数可获得较好的效果，用于地震信号的反褶积也得 到比最小平方反褶积更好的结果。

A Family of Generalized Adaptive Steepest Descent Algorithms

A generalized steepest descent algorithm for adaptive filtering was devised, which allows error minimization in arbitrary order moment sense. Convergence property of the algorithm was analysed in detail. Formulas for estimating range of step size and selecting of objective function according to distribution form of noise was deduced. Some experimental results on synthetic data was given. Theoretical analysis and experimental results show that. Non mean square objective function can give better results when noise is of non Ganssian distribution. The algorithm can be used in deconvolution. In seismic Signal processing,it gives much better results than conventional least square deconvolution.