基于非线性约束的局部投影降噪

Local Projection Noise Reduction Based on Nonlinear Constraints

基于相空间重构理论,该文提出了一种改进的混沌时序降噪方法。首先利用递归图对实际观测的时间序列进行混沌特性分析,然后将非线性约束条件引入局部投影方法之中,并在局部邻域内进行奇异谱(SSA)分析,利用代表吸引子的主分量来重构时间序列。该算法克服了传统局部投影方法不能充分刻画系统内在非线性关系的问题,减小了重构误差,提高了系统的信噪比。通过对Lorenz模型和太阳黑子混沌时间序列进行仿真分析,证实了该文算法对实际观测混沌时序降噪的有效性。

An improved method is proposed for noise reduction of chaotic time series based on the reconstruction of phase space theory. Recursive map is firstly used for the chaos characteristics analysis of the time series observed, then the conditions of nonlinear constraints are introduced to the local projection method, and Singular Spectrum Analysis（SSA） is combined in the local neighborhood, which uses the main components representing the attractors to reconstruct the time series. The improved method raised in this paper overcomes the problems that the traditional local projection can not fully character the nonlinear relationship of system, reduces the deviation of the reconstruction, and improves the signal-to-noise ratio of the system. The chaotic time series generated by Lorenz model and sunspot time series are respectively applied to simulation analysis. The numerical experiment results confirm the effect of the method raised in this paper for noise reduction in the time series observed.