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-This paper provides new results and insights for tracking an extended target object modeled with an Elliptic Random Hypersurface Model (RHM). An Elliptic RHM specifies the relative squared Mahalanobis distance of a measurement source to the center of the target object by means of a one-dimensional random scaling factor. It is shown that uniformly distributed measurement sources on an ellipse lead to a uniformly distributed squared scaling factor. Furthermore, a Bayesian inference mechanisms tailored to elliptic shapes is introduced, which is also suitable for scenarios with high measurement noise. Closed-form expressions for the measurement update in case of Gaussian and uniformly distributed squared scaling factors are derived.

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In state estimation theory, two directions are mainly followed in order to model disturbances and errors. Either uncertainties are modeled as stochastic quantities or they are characterized by their membership to a set. Both approaches have distinct advantages and disadvantages making each one inherently better suited to model different sources of estimation uncertainty. This paper is dedicated to the task of combining stochastic and set-membership estimation methods. A Kalman gain is derived that minimizes the mean squared error in the presence of both stochastic and additional unknown but bounded uncertainties, which are represented by Gaussian random variables and ellipsoidal sets, respectively. As a result, a generalization of the well-known Kalman filtering scheme is attained that reduces to the standard Kalman filter in the absence of set-membership uncertainty and that otherwise becomes the intersection of sets in case of vanishing stochastic uncertainty. The proposed concept also allows to prioritize either the minimization of the stochastic uncertainty or the minimization of the set-membership uncertainty.

Optical belt sorters are a versatile, state-of-the art technology to sort bulk materials that are hard to sort based on only nonvisual properties. In this paper, we propose an extension to current optical belt sorters that involves replacing the line camera with an area camera to observe a wider field of view, allowing us to observe each particle over multiple time steps. By performing multitarget tracking, we are able to improve the prediction of each particle’s movement and thus enhance the performance of the utilized separation mechanism. We show that our approach will allow belt sorters to handle new classes of bulk materials while improving cost efficiency. Furthermore, we lay out additional extensions that are made possible by our new paradigm

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Multitarget tracking problems arise in many realworld applications. The performance of the utilized algorithm strongly depends both on how the data association problem is handled and on the suitability of the motion models employed. Especially the motion models can be hard to validate. Previously, we have proposed to use multitarget tracking to improve optical belt sorters. In this paper, we evaluate both the suitability of our model and the tracking and then of our entire system incorporating the image processing component via the use of highly realistic numerical simulations. We first assess the model using noise-free measurements generated by the simulation and then evaluate the entire system by using synthetically generated image data