A new approach for estimating the robustness of parameter estimates to measurement noise

We consider the nonlinear, grey-box system identification problem. We establish an approximation of the covariance of a parameter estimate in this context, with several attractive theoretical properties. Our approximation is analogous to the inverse Fisher Information matrix, which approximates the covariance through the Cramer-Rao Lower bound. Indeed, it agrees asymptotically with the Cramer-Rao based covariance estimate in the limit of increasing data, where the theoretical assumptions necessary for both methods hold. However, our approximation requires fewer assumptions. In particular, it can be applied when the process is undermodelled, and does not require consideration of either the magnitude or form of the undermodelling. Thus our covariance approximation is relevant when it is known that the physical process cannot be perfectly recreated by any allowable parameterisation of the model structure.