Estimating initial conditions in coupled map lattices from noisy time series using symbolic vector dynamics

In this Letter, we investigate the symbolic vector dynamics method for initial condition estimation in additive white Gaussian noisy environment. We apply this scheme not only to the skewed-tent-CMLs and logistic-CMLs but also to the piecewise-linear-CMLs and Chebyshev-CMLs. We also discuss the symbol vector error probability in additive white Gaussian noisy condition, and evaluate the performance of this scheme at high signal-to-noise ratio (SNR). It is found that the SNR, the total number of CMLs' site and the length of generating partition will affect the symbol vector error probability. Both theoretical and experimental results show that this algorithm enables us to recover initial condition of CMLs exactly in both noisy and noise free cases. Therefore, we provide novel analytical techniques for understanding turbulences in coupled map lattices.