非线性局部Lyapunov指数方法在目标观测中的应用初探

本文初步探讨了非线性局部Lyapunov指数方法(NLLE)在目标观测中的应用。首先, 在NLLE理论基础上研究了非线性动力系统内局部平均误差相对增长(LAGRE)特征, 证明了在误差发展进入随机状态前, LAGRE与初始误差大小无关而是与初始状态有关;在演化进入随机状态后, LAGRE的饱和值由初始误差大小决定这一特征。同时利用三个变量的常微分方程模型Lorenz63验证了这一结论。其次, 从非线性局部误差增长理论出发, 在局部动力演化相似方法(LDA)的基础上提出向前局部动力演化相似方法(FLDA)的概念, 并通过两个混沌个例来说明LDA和FLDA方法能够有效的利用历史资料还原任意初始状态的LAGRE。这些方法的提出为NLLE理论应用于观测资料研究目标观测问题提供了依据。

Preliminary Application of the Nonlinear Local Lyapunov Exponent to Target Observation

This study investigates the preliminary application of the nonlinear local Lyapunov exponent (NLLE) to target observation.Based on NLLE theory, we analyze the essential feature of the local average relative growth of initial error (LAGRE) in nonlinear dynamical systems.Our results prove that the LAGRE is determined by the initial state before it evolves into chaos, whereas afterwards the development of error become unpredictable.The saturation value of LAGRE is determined by the magnitude of the initial error.Lorenz63 model, a set of ordinary differential equations contain three variables, is used to confirm these conclusions.We then develop a forward local dynamic evolution analog method (FLDA) from the local dynamic evolution analog method (LDA).Two chaotic cases are subsequently used as examples to illustrate the feasibility of using LDA and FLDA to calculate the LAGRE of a random initial state from historical records.These methods provide a scientific basis, via NLLE theory, for the study of target observation using observational datasets.