Conditions of parameter identification from time series

We study the problem of synchronization-based parameters identification of dynamical systems from time series. Through theoretical analysis and numerical examples, we show that some recent research reports on this issue are not perfect or even incorrect. Long-time full rank and finite-time full rank conditions of Gram matrix are pointed out, which are sufficient for parameters identification of dynamical systems. The influence of additive noise on the proposed parameter identifier is also investigated. The mean filter is used to suppress the estimation fluctuation caused by the noise.