Abstract:

It is difficult for model-unknown non-hyperbolic non-linear sequence to realize denoising or shadowing of non-linear time sequences. Aiming at the problem, based on the minimal description length criteria, this paper points out that the marginal error algorithm is not optimal to the discrete system, sometimes even inadaptable from the viewpoint of over-fitting and under-fitting. A modified algorithm named total error algorithm is proposed and analyzed. And a highly-stable-but-fast hybrid algorithm is developed which compensates both the slower convergence of gradient decent algorithm and the worse stability of Newton-Raphson algorithm. The machine precision is obtained for the noisy time sequences of model- unknown non-linear discrete system. Experimental results prove that the method is efficient to solve the denoising or shadowing problem of non-linear time sequences.

Key words: non-hyperbolic non-linear sequence, Minimal Description Length(MDL), Newton-Raphson algorithm, gradient descent method, noise reduction algorithm

摘要：

针对模型未知的非双曲型非线性序列难以实现去噪和轨迹重影的问题，基于模型选取的最小描述长度准则，从过拟合和欠拟合的角度分析边缘误差算法对离散系统的非最优性和不适应性，利用改进的全局误差算法对系统进行建模，结合梯度下降方法的稳定性和Newton-Raphson算法的快速收敛性提出一种融合算法，用于在机器精度内实现非双曲型非线性离散系统时间序列的去噪和轨迹重影。通过辅以极少点数的无污染序列和仅从单变量受扰观测序列2项实验验证该算法的有效性。

关键词: 非双曲型非线性序列, 最小描述长度, Newton-Raphson算法, 梯度下降方法, 去噪算法

CLC Number: 

• N94