RECONSTRUCTION OF CHAOTIC SIGNALS USING SYMBOLIC DATA

We discuss the reconstruction of dynamical systems from noisy time-ser ies. In particular, we consider the use of the symbol statistics (coar se-grained signal data) as the target for reconstruction. The statisti cs of symbol sequences is relatively insensitive to moderate amounts o f measurement noise (sigma(noise)/sigma(signal) almost-equal-to 10-20% ), while larger amounts produce a substantial bias. We show that it is possible to produce robust reconstructions even when sigma(noise)/sig ma(signal) almost-equal-to O(1). Our study shows that even at such hig h noise levels the procedure is convergent. i.e. the accuracy of param eter estimates is limited only by the amount of data and computer time available.