基于Lyapunov指数的水下目标信号混沌特征提取

以Takens定理为基础，通过对几种不同类别舰船信号采用相空间重构，建立了混沌分析的数学模型，研究了它们的相空间轨迹结构并计算最大Lyapunov指数。结果表明，不同类别的般船信号具有不同的空间轨迹，且对应不同的最大Lyapunov指数。这一结果为水下目标信号的检测与识别提供了新的理论和方法。

A New Method for Feature Extraction of Ship Signals

In feature extraction of ship signals, spectral lines are usually used as the feature to distinguish among different kinds of signals. In this paper, we present a new method for feature extraction and identification of ship signals. Such a method uses the Lyapunov exponent as the feature of ship signals. By means of Takens theorem for state space reconstruction, we studied the portraits of several types of ship signals and established their corresponding mathematical model in the form of Eq.(3). The maximum Lyapunov exponents of ship signals were calculated using this model by Eqs.(12) through (15). In the simulation, we chose four types of different ship signals as the sample data. The results as given in Fig. 3 and Tab. 2 show that there exist different portraits and different maximum Lyapunov exponents for different types of ship signals. Therefore, we concluded that the Lyapunov exponents can be used as a new feature of ship signals for detection and identification of ships.