Benjamin Noack

Extended object and group tracking with Elliptic Random Hypersurface Models

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.

The Hypothesizing Distributed Kalman Filter

This paper deals with distributed information processing in sensor networks. We propose the Hypothesizing Distributed Kalman Filter that incorporates an assumption of the global measurement model into the distributed estimation process. The procedure is based on the Distributed Kalman Filter and inherits its optimality when the assumption about the global measurement uncertainty is met. Recursive formulas for local processing as well as for fusion are derived. We show that the proposed algorithm yields the same results, no matter whether the measurements are processed locally or globally, even when the process noise is not negligible. For further processing of the estimates, a consistent bound for the error covariance matrix is derived. All derivations and explanations are illustrated by means of a new classification scheme for estimation processes.

Optimal Kalman gains for combined stochastic and set-membership state estimation

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.

An experimental evaluation of position estimation methods for person localization in wireless sensor networks

In this paper, the localization of persons by means of aWireless Sensor Network (WSN) is considered. Persons carry on-body sensor nodes and move within a WSN. The location of each person is calculated on this node and communicated through the network to a central data sink for visualization. Applications of such a system could be found in mass casualty events, firefighter scenarios, hospitals or retirement homes for example. For the location estimation on the sensor node, three derivatives of the Kalman filter and a closed-form solution (CFS) are applied, compared, and evaluated in a real-world scenario. A prototype 65-node ZigBeeWSN is implemented and data are collected in in- and outdoor environments with differently positioned on-body nodes. The described estimators are then evaluated off-line on the experimentally collected data. The goal of this paper is to present a comprehensive real-world evaluation of methods for person localization in a WSN based on received signal strength (RSS) range measurements. It is concluded that person localization in in- and outdoor environments is possible under the considered conditions with the considered filters. The compared methods allow for sufficiently accurate localization results and are robust against inaccurate range measurements.

Minimum Covariance Bounds for the Fusion under Unknown Correlations

One of the key challenges in distributed linear estimation is the systematic fusion of estimates. While the fusion gains that minimize the mean squared error of the fused estimate for known correlations have been established, no analogous statement could be obtained so far for unknown correlations. In this contribution, we derive the gains that minimize the bound on the true covariance of the fused estimate and prove that Covariance Intersection (CI) is the optimal bounding algorithm for two estimates under completely unknown correlations. When combining three or more variables, the CI equations are not necessarily optimal, as shown by a counterexample.

Decentralized data fusion with inverse covariance intersection

In distributed and decentralized state estimation systems, fusion methods are employed to systematically combine multiple estimates of the state into a single, more accurate estimate. An often encountered problem in the fusion process relates to unknown common information that is shared by the estimates to be fused and is responsible for correlations. If the correlation structure is unknown to the fusion method, conservative strategies are typically pursued. As such, the parameterization introduced by the ellipsoidal intersection method has been a novel approach to describe unknown correlations, though suitable values for these parameters with proven consistency have not been identified yet. In this article, an extension of ellipsoidal intersection is proposed that guarantees consistent fusion results in the presence of unknown common information. The bound used by the novel approach corresponds to computing an outer ellipsoidal bound on the intersection of inverse covariance ellipsoids. As a major advantage of this inverse covariance intersection method, fusion results prove to be more accurate than those provided by the well-known covariance intersection method.

Mixture Random Hypersurface Models for tracking multiple extended objects

This paper presents a novel method for tracking multiple extended objects. The shape of a single extended object is modeled with a recently developed approach called Random Hypersurface Model (RHM) that assumes a varying number of measurement sources to lie on scaled versions of the shape boundaries. This approach is extended by introducing a so-called Mixture Random Hypersurface Model (Mixture RHM), which allows for modeling multiple extended targets. Based on this model, a Gaussian-assumed Bayesian tracking method that provides the means to track and estimate shapes of multiple extended targets is derived. Simulations demonstrate the performance of the new approach.

Nonlinear information filtering for distributed multisensor data fusion

The information filter has evolved into a key tool for distributed and decentralized multisensor estimation and control. Essentially, it is an algebraical reformulation of the Kalman filter and provides estimates on the information about an uncertain state rather than on a state itself. Whereas many practicable Kalman filtering techniques for nonlinear system and sensor models have been developed, approaches towards nonlinear information filtering are still scarce and limited. In order to deal with nonlinear systems and sensors, this paper derives an approximation technique for arbitrary probability densities that provides the same distributable fusion structure as the linear information filter. The presented approach not only constitutes a nonlinear version of the information filter, but it also points the direction to a Hilbert space structure on probability densities, whose vector space operations correspond to the fusion and weighting of information.

TrackSort: Predictive tracking for sorting uncooperative bulk materials

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 particles 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.

Bounding linearization errors with sets of densities in approximate Kalman filtering

Applying the Kalman filtering scheme to linearized system dynamics and observation models does in general not yield optimal state estimates. More precisely, inconsistent state estimates and covariance matrices are caused by neglected linearization errors. This paper introduces a concept for systematically predicting and updating bounds for the linearization errors within the Kalman filtering framework. To achieve this, an uncertain quantity is not characterized by a single probability density anymore, but rather by a set of densities and accordingly, the linear estimation framework is generalized in order to process sets of probability densities. By means of this generalization, the Kalman filter may then not only be applied to stochastic quantities, but also to unknown but bounded quantities. In order to improve the reliability of Kalman filtering results, the last-mentioned quantities are utilized to bound the typically neglected nonlinear parts of a linearized mapping.