Meta-optimization of the Extended Kalman filter's parameters through the use of the Bias-Variance Equilibrium Point criterion

Abstract

The extraction of information on land cover classes using unsupervised methods has always been of relevance to the remote sensing community. In this paper, a novel criterion is proposed, which extracts the inherent information in an unsupervised fashion from a time series. The criterion is used to fit a parametric model to a time series, derive the corresponding covariance matrices of the parameters for the model, and estimate the additive noise on the time series. The proposed criterion uses both spatial and temporal information when estimating the covariance matrices and can be extended to incorporate spectral information. The algorithm used to estimate the parameters for the model is the extended Kalman filter (EKF). An unsupervised search algorithm, specifically designed for this criterion, is proposed in conjunction with the criterion that is used to rapidly and efficiently estimate the variables. The search algorithm attempts to satisfy the criterion by employing density adaptation to the current candidate system. The application in this paper is the use of an EKF to model Moderate Resolution Imaging Spectroradiometer time series with a triply modulated cosine function as the underlying model. The results show that the criterion improved the fit of the triply modulated cosine function by an order of magnitude on the time series over all seven spectral bands when compared with the other methods. The state space variables derived from the EKF are then used for both land cover classification and land cover change detection. The method was evaluated in the Gauteng province of South Africa where it was found to significantly improve on land cover classification and change detection accuracies when compared with other methods.