Estimation of initial conditions and parameters of a chaotic evolution process from a short time series

Tracing back to the initial state of a time-evolutionary process using a segment of historical time series may lead to many meaningful applications. In this paper, we present an estimation method that can detect the initial conditions, unobserved time-varying states and parameters of a dynamical (chaotic) system using a short scalar time series that may be contaminated by noise. The technique based on the Newton-Raphson method and the least-squares algorithm is tolerant to large mismatch between the initial guess and actual values. The feasibility and robustness of this method are illustrated via the numerical examples based on the Lorenz system and Rossler system corrupted with Gaussian noise.