Filtering entropy

We consider a discrete time deterministic chaotic dynamical system: xn+1=T(xn), where T is a nonlinear map of the unit interval into itself. The effect of noise contamination is modeled by xn+1=T(xn)+ξn, where ξn is an independent random variable with small noise level. We present a new theoretical result for estimating the metric entropy of T from the observed data of the noisy system. We introduce a skew product representation for the noisy system and then show that this skew product satisfies a formula similar to Adler’s natural entropy formula.