TLS parameter estimation for filtering chaotic time series

We present a new algorithm for simultaneous filtering and parameter estimation of chaotic time series corrupted by additive measurement noise. This method is based on iteratively minimizing the total least squares (TLS) error in the phase-space using steepest descent. In contrast to prior work, we assume that the dynamic equations modeling the nonlinear time series are known, but the corresponding parameters are not. Specifically, the data is assumed to be generated from time series satisfying a set of coupled logistics equations corrupted by additive white Gaussian noise. This work is motivated in part by language modeling, where the dynamics of a conversation are argued to satisfy the coupled logistics equations and the time series data represents noisy measurements taken from protocols. Accurate estimation of the process parameters is critical, e.g., in diagnosing and treating different types of language disorders and also may prove valuable for testing and improving language understanding systems