State Estimation and Forecasting of the Ski-Slope Model Using an Improved Shadowing Filter

Abstract

In this paper, we present the application of the gradient descent of indeterminism (GDI) shadowing filter to a chaotic system, that is the ski-slope model. The paper focuses on the quality of the estimated states and their usability for forecasting. One main problem is that the existing GDI shadowing filter fails to provide stability to the convergence of the root mean square error and the last point error of the ski-slope model. Furthermore, there are unexpected cases in which the better state estimates give worse forecasts than the worse state estimates. We investigate these unexpected cases in particular and show how the presence of the humps contributes to them. However, the results show that the GDI shadowing filter can successfully be applied to the ski-slope model with only slight modification, that is, by introducing the adaptive step-size to ensure the convergence of indeterminism. We investigate its advantages over fixed step-size and how it can improve the performance of our shadowing filter.