由单变量受扰观测序列估计混沌系统敏感参数

针对高维非双曲线型混沌系统敏感参数难以估计的问题,在充分挖掘非线性系统及其观测序列本身特性的基础上,提出了一种由单状态变量受扰观测序列估计其系统敏感参数的新方法,有效的解决了由正的李雅谱诺夫指数所引起的误差扩散问题。该方法不同于常规的重影轨迹估计算法,故不受非线性系统非双曲线特性的限制,不必考虑系统对单步误差的要求。也不同于常规的序列去噪算法,因为去噪并不能得到系统的一条真实轨迹,因而无法精确估计系统的敏感参数。作为该方法的潜在重要应用,它为压缩非双曲线型混沌系统的受扰观测序列提供了一种新途径。

Estimation of Sensitive Parameters of Chaotic System from Noisy Scalar Series

By exploiting the inherent properties of chaotic system and making use of the underlying information contained in the noisy observational series, a new method for estimating the sensitive parameters only from the noisy observational series of a state variable was developed. The problem of error propagation caused by the positive Lyapunov exponent was settled effectively. This method stems from the thought of the constrained two-point boundary value problem, so it is different from principle the traditional trajectory shadowing methods which must take Mto account the one-step error and the hyperbolic property of the system. It is also different from common noise reduction techniques which can not obtain a true orbit to shadow the noisy observation series. The evolvement process and performance of this method were analyzed. As a byproduct, the method also provided a practical signal compression/code technique for a class of high dimensional nonlinear systems which are not hyperbolic.