Parameter estimation only from the symbolic sequences generated by chaos system

Álvarez et al. introduced in 2003 [Phys. Lett. A 311 (2003) 172] how to estimate parameter from the two-valued symbolic sequences generated by iterations of quadratic map when its initial value is known. We further study these kind of two-valued symbolic sequences along the idea of utilizing Gray codes. Some general conclusions are obtained in this paper. Based on these results, an algorithm is given to estimate parameter only from the two-valued symbolic sequences generated by iterations of quadratic map when its initial value is not known. Finally, a general scheme by utilizing fractal codes is presented to estimate parameter from the symbolic sequences generated by chaotic system.