RECONSTRUCTION OF CHAOTIC SIGNALS USING SYMBOLIC DATA

We discuss the reconstruction of dynamical systems from noisy time-series. In particular, we consider the use of the symbol statistics (coarse-grained signal data) as the target for reconstruction. The statistics of symbol sequences is relatively insensitive to moderate amounts of 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)/sigma(signal) almost-equal-to O(1). Our study shows that even at such high noise levels the procedure is convergent. i.e. the accuracy of parameter estimates is limited only by the amount of data and computer time available.