A guide to using shadowing filters for forecasting and state estimation

Most traditional, and many modern, methods of state estimation have a number a failings when applied to high-dimensional and nonlinear systems. A promising new alternative that avoids many of these failings is a shadowing filter. An additional advantage of shadowing filters is that when combined with indistinguishable states they provide a consistent generalisation to the imperfect model scenario. This paper is a practical guide to implementing shadowing filters in nonlinear systems. It provides a detailed account of various tests and procedures to ensure successful implementation of a shadowing filter using gradient descent of indeterminism.