Fisher information and Cramér-Rao bound analysis with stable gradients for ocean acoustic models

Abstract

The Fisher Information Matrix (FIM) and the Cramér-Rao Bound (CRB) are powerful tools for quantifying uncertainty in multi-parameter models. However, it is difficult to estimate the derivatives needed to calculate the FIM and CRB in ocean acoustic models. In this work, a methodology for estimating derivatives using physics-guided parameter preconditioning and Richardson extrapolation is presented. The method is validated on a case study of transmission loss from a range-independent normal mode model in ocean environments with a single sediment layer over a basalt basement. Five examples of sediment types ranging from mud to gravel are considered across frequencies from 50–400 Hz. Results demonstrate the utility of FIM and CRB analysis in quantifying both model sensitivities and parameter uncertainties, and in revealing parameter coupling in the model. This methodology is a general tool that can inform model selection and experimental design for inverse problem applications. [Work supported by ONR Contract No. N00014-19-C-2001.]