Filtering of nonlinear chaotic time-series with noise

It has been observed that when filtering chaotic time series using a linear Infinite Impulse Response filter, the Lyapunov dimension can become dependent on the contraction rates associated with filter dynamics. In this paper we obtain necessary and sufficient conditions which guarantee that the Lyapunov dimension remains unchanged in the presence of external disturbances that act on the filter. These conditions apply to a certain class of noise sequences, and ensure that the Lyapunov dimension of the attractor in the extended state space, consisting of the chaotic system, filter and noise, is the same as the dimension of the attractor in the chaotic system.