基于改进的G-P算法的相空间嵌入维数选择

对混沌时间序列相空间重构中嵌入维数的选择进行了研究，针对饱和关联维数算法（G-P算法）存在的四点不足，提出了一种计算最佳嵌入维数的改进算法。通过对邻域半径区间的自适应选择，采用均匀变化步长的方式；对无标度区间利用基于BDS统计限定范围的快速自动判定法进行识别，实现了系统维数的自动计算；针对原算法存在的重复运算、繁杂计算问题，从算法原理和程序结构上进行了改良，大大加快求解速率。在理论分析的基础上，用新算法进行试验，仿真结果表明设计的算法对嵌入维数的选择更准确更高效。

Determination of embedding dimension for phase space based on improved G-P method

This paper makes a study on the determination of embedding dimension for phase space reconstruction. A new algorithm is proposed based on the improved G-P method modifying the origin G-P method in four aspects. New algo-rithm realizes automatic calculation of dimension through self-adaptive choice of neighborhood radius, evenly changing step size and identification of non-scale range by rapid automatic judgement based on BDS statistic. By deleting duplicat-ed and complex computing, proposed algorithm greatly speeds up solving rate. The MATLAB simulation results show that the algorithm proposed in this paper is more accurate and efficient.