Abstract: Cao method proposed in Ref.5 is only applied to determine embedding dimension.The improved Cao method presented extends the Cao method’s application field.This new method can be used to estimate not only embedding dimension but also embedding delay vector.Using the new method，it is possible to settle the phase space reconstruction problem by a multiple delay embedding.The numerical simulation results show preliminarily that the improved method is suitable and valid in phase space reconstruction of time series.Especially in dealing with the time series consisting of multiple strong periodicities with greatly differing timescales，the new method has obvious advantage over other uniform delay embedding methods.

Key words: chaos, phase space reconstruction, embedding delay vector, embedding dimension

摘要： 对文献[5]提出的Cao方法进行了改进，提出一种新的多嵌入延迟相空间重构方法，不仅能够判断最小嵌入维数，还能够确定最佳时间延迟矢量。Cao方法的应用领域得以扩展，使得相空间重构问题可以在一个判断标准下完成。数值仿真结果表明，该改进方法在处理包含多个强烈周期成分的信号时比目前常用的单一嵌入延迟方法有明显优势。

关键词: 混沌, 相空间重构, 嵌入延迟矢量, 嵌入维数