Marcus Baum

Random Hypersurface Models for extended object tracking

Target tracking algorithms usually assume that the received measurements stem from a point source. However, in many scenarios this assumption is not feasible so that measurements may stem from different locations, named measurement sources, on the target surface. Then, it is necessary to incorporate the target extent into the estimation procedure in order to obtain robust and precise estimation results. This paper introduces the novel concept of Random Hypersurface Models for extended targets. A Random Hypersurface Model assumes that each measurement source is an element of a randomly generated hypersurface. The applicability of this approach is demonstrated by means of an elliptic target shape. In this case, a Random Hypersurface Model specifies the random (relative) Mahalanobis distance of a measurement source to the center of the target object. As a consequence, good estimation results can be obtained even if the true target shape significantly differs from the modeled shape. Additionally, Random Hypersurface Models are computationally tractable with standard nonlinear stochastic state estimators.

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.

Extended Object Tracking with Random Hypersurface Models

The random hypersurface model (RHM) is introduced for estimating a shape approximation of an extended object in addition to its kinematic state. An RHM represents the spatial extent by means of randomly scaled versions of the shape boundary. In doing so, the shape parameters and the measurements are related via a measurement equation that serves as the basis for a Gaussian state estimator. Specific estimators are derived for elliptic and star-convex shapes.

A novel Bayesian method for fitting a circle to noisy points

This paper introduces a novel recursive Bayesian estimator for the center and radius of a circle based on noisy points. Each given point is assumed to be a noisy measurement of an unknown true point on the circle that is corrupted with known isotropic Gaussian noise. In contrast to existing approaches, the novel method does not make assumptions about the true points on the circle, where the measurements stem from. Closed-form expressions for the measurement update step are derived. Simulations show that the novel method outperforms standard Bayesian approaches for circle fitting.

On Wasserstein Barycenters and MMOSPA Estimation

The two title concepts have been evolving rather rapidly, but independent of each other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image processing as it can describe a measure of similarity between images. Its minimization might, for example, suggest the best match in image alignment. On the other hand, MMOSPA estimation has been applied largely to multi-target tracking. The Optimal Sub-Pattern Assignment (OSPA) measures the distance between two sets and the Mean OSPA (MOSPA) can be minimized to give the Minimum MOPSA (MMOSPA), which improves MMSE estimation of the target locations when the labeling of the targets in the set is not important. Approximate and exact algorithms have evolved for both Wasserstein barycenters and MMOSPA estimation. Here, we draw connections between the two perspectives and elaborate how they can benefit from each other.

A visual interactive debugger based on symbolic execution

We present the concepts, usage, and prototypic implementation of a new kind of visual debugging tool based on symbolic execution of Java source code called visual symbolic state debugger. It allows to start debugging of source code at any code location without the need to write a fixture as well as to visualize all possible symbolic execution paths and all symbolic states up to a finite depth. A code-based test generation facility is integrated.

Data association in a world model for autonomous systems

This contribution introduces a three pillar information storage and management system for modeling the environment of autonomous systems. The main characteristics is the separation of prior knowledge, environment model and sensor information. In the center of the system is the environment model, which provides the autonomous system with information about the current state of the environment. It consists of instances with attributes and relations as virtual substitutes of entities (persons and objects) of the real world. Important features are the representation of uncertain information by means of Degree-of-Belief (DoB) distributions, the information exchange between the three pillars as well as creation, deletion and update of instances, attributes and relations in the environment model. In this work, a Bayesian method for fusing new observations to the environment model is introduced. For this purpose, a Bayesian data association method is derived. The main question answered here is the observation-to-instance mapping and the decision mechanisms for creating a new instance or updating already existing instances in the environment model.

Fitting conics to noisy data using stochastic linearization

Fitting conic sections, e.g., ellipses or circles, to noisy data points is a fundamental sensor data processing problem, which frequently arises in robotics. In this paper, we introduce a new procedure for deriving a recursive Gaussian state estimator for fitting conics to data corrupted by additive Gaussian noise. For this purpose, the original exact implicit measurement equation is reformulated with the help of suitable approximations as an explicit measurement equation corrupted by multiplicative noise. Based on stochastic linearization, an efficient Gaussian state estimator is derived for the explicit measurement equation. The performance of the new approach is evaluated by means of a typical ellipse fitting scenario.

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.

Extended Object Tracking Based on Set-Theoretic and Stochastic Fusion

A novel approach for extended object tracking is presented. In contrast to existing approaches, no statistical assumptions about the location of the measurement sources on the extended target object are made. As a consequence, a combined set-theoretic and stochastic estimator is obtained that is robust to systematic errors in the target model. The benefits of the new approach is demonstrated by means of simulations.