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.