Symbolic vector dynamics for processing chaotic signals II: Noise reduction

The estimation precision of symbolic vector dynamic method is determined by the symbol error of symbolic sequence. If we get the original symbolic sequences from the noisy signal, then we can recover the original sequence without any error. The aim of this paper is to further develop symbolic vector dynamical estimation method which has been proposed [K. Wang, Phys. Lett. A 367 (2007) 316-321]. We will prove that any ML methods using MMSE criterion can not correct the symbolic error, because they mistakenly take the error generated by symbolic error as the noise. We can use SVD to develop a novel estimation method, which will correct symbolic error in high SNR.