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 extract the inherent information in an unsupervised fashion from a time series. The criterion is used to fit a parametric model to a time series and 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. 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 Extended Kalman filter 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 to the other methods. The state space variables derived from the Extended Kalman filter 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 to other methods.

Applying Model Parameters as a Driving Force to a Deterministic Nonlinear System to Detect Land Cover Change

“…It either has the ability to assist in improving the true positive rate [17] or it can lower the false positive rate [25]. Our experiments found that the false positive rate was further reduced as shown in Table II when a SVM was used on the 14-dimensional pendulum.…”

“…As confirmed by (25), the total energy of the pendulum system in the absence of a driving force is constant and equal to the potential energy at the maximum amplitude, namely E = mgL(1 − cos θ) if the potential energy is referenced to the static equilibrium position θ = 0. As shown in Figure 7(a), if the pendulum's amplitude is close to 180…”

“…The regressed model parameters are then used as input to the machine learning method. The model can be fitted on the extracted sub-sequences with either a least squares [25] or a Fourier transform [18]. A windowless approach is also possible based on an extended Kalman filter using internal covariance matrices [19].…”

“…A windowless approach is also possible based on an extended Kalman filter using internal covariance matrices [19]. The extended Kalman filter described in [25] was used to fit a triply modulated cosine model [26]. There is no restriction on the model used, except that it should be appropriate for the study area and model parameters must be regressed with a suitable algorithm.…”

From Land to Sea, a Review of Hypertemporal Remote Sensing Advances to Support Ocean Surface Science

“…Secondly, with sufficient characterisation of surface waters at various scales, it could become feasible to deploy more supervised approaches for which example deployments are evidenced in the terrestrial realm. Possible methodologies could include the use of artificial neural networks [83][84][85] and decision tree classifiers [26] on hypertemporal datasets, or more likely, hypertemporal dataset derivatives. Furthermore, categorisation of the ocean's surface into regions exhibiting different temporal profiles could provide opportunities for these profiles to be examined and explored.…”