Applying model parameters as a driving force to a deterministic nonlinear system to detect land cover change

In this paper, we propose a new method for extracting features from time-series satellite data to detect land cover change. We propose to make use of the behavior of a deterministic nonlinear system driven by a time-dependent force. The driving force comprises a set of concatenated model parameters regressed from fitting a model to a Moderate Resolution Imaging Spectroradiometer time series. The goal is to create behavior in the nonlinear deterministic system, which appears predictable for the time series undergoing no change, while erratic for the time series undergoing land cover change. The differential equation used for the deterministic nonlinear system is that of a large-amplitude pendulum, where the displacement angle is observed over time. If there has been no change in the land cover, the mean driving force will approximate zero, and hence the pendulum will behave as if in free motion under the influence of gravity only. If, however, there has been a change in the land cover, this will for a brief initial period introduce a nonzero mean driving force, which does work on the pendulum, changing its energy and future evolution, which we demonstrate is observable. This we show is sufficient to introduce an observable change to the state of the pendulum, thus enabling change detection. We extend this method to a higher dimensional differential equation to improve the false alarm rate in our experiments. Numerical results show a change detection accuracy of nearly 96% when detecting new human settlements, with a corresponding false alarm rate of 0.2% (omission error rate of 4%). This compares very favorably with other published methods, which achieved less than 90% detection but with false alarm rates all above 9% (omission error rate of 66%).