The Conditioning of Dynamical Inverse Problems

The use of time-series data to infer unknown states and parameters of a dynamical model has wide applications across many fields. Success in this endeavor depends on various properties of both the system being studied and the algorithm used. We introduce a technique for estimating the rate of success, based on an approximate lower bound for the basin of attraction of the Gauss-Newton method, and examine its scaling behavior as a function of these properties. The results are directly related to the notion of conditioning, which has not been fully explored in the context of dynamical inverse problems.