中文摘要：

针对混沌信号在噪声信号中的提取问题,本文将其建立于线性混合模型进行分析.在该模型下,提出一种结合高维核函数的性能函数,该函数的计算复杂度较低.在使用人工蜂群算法来处理该多峰函数优化问题时,文中采用马尔可夫模型分析了人工蜂群算法的有效性.仿真实验表明本文方法能在较低复杂度下提取出相关系数很高的估计信号.

英文摘要：

This paper is to deal with the blind extraction problem of chaotic signals by using a linear mixing model. In this model, a novel method to describe the distance function in a high dimensional space is proposed which relates the kernel function to objective function. When adopting the artificial bee colony algorithm（ABCA） as an alternative method to solve a multi-modal optimization problem, its analysis under a Markov chain model is also presented. The simulation results show that the objective function of this article has low complexity, and the artificial bee colony algorithm converges to a local minimum quickly. To be specific, the target function is constructed by combining the advantages of the proliferation exponent and the distance kernel function. The proliferation exponent can reflect the chaotic properties of a signal to a large extent, and the distance kernel can help to describe the statistical properties in a higher dimension. Due to the fact that only one frame of time-delay embedded signal is adopted, the computational complexity of our target function is low. The artificial bee colony algorithm is shown to be advantageous over other swarm algorithms. Although adopting ABCA for our evaluation function seems easy, we analyze why this algorithm can work, in contrast to the fact that most literature only runs some simulations to confirm its usefulness. Our analysis is only for a special case when the number of employed bees is set to be 2 and the process of onlooker bees and scouts are temporarily omitted. With smaller complexity than the methods based on proliferation exponents and kurtosises,simulations show that our method can have excellent performance when evaluated by correlation coefficients.