Nonlinear noise reduction

Different methods for removing noise contaminating time series are presented, which all exploit the underlying (deterministic) dynamics. All approaches are embedded in a probabilistic framework for stochastic systems and signals, where the two main tasks, state and orbit estimation, are distinguished. Estimation of the true current state (without noise) is based on previously sampled elements of the time series, only, and corresponds to filtering. With orbit estimation, the entire measured time series is used to determine a less noisy orbit. In this case not only past values but also future samples are used, which, of course, improves performance.