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In this paper, we consider the problem of jointly tracking the pose and shape of objects based on noisy data from cameras and depth sensors. Our proposed approach formalizes object silhouettes from image data as measurements within a Bayesian estimation framework. Projecting object silhouettes from images back into space yields a visual hull that constrains the object. In this work, we focus on the...
We propose an algorithm to combine both depth and position measurements when estimating a continuous surface. Position measurements originate from a fixed point on the surface, whereas depth measurements are determined by the intersection of the surface with a line originating from the depth sensor. Through fusion of both types of measurements, it is possible to benefit from the advantages of different...
A new Gaussian filter for estimating the state of nonlinear systems is derived that relies on two main ingredients: i) the progressive inclusion of the measurement information and ii) a tight coupling between a Gaussian density and its deterministic Dirac mixture approximation. No second Gaussian assumption for the joint density of state and measurement is required, so that the performance is much...
This paper proposes Gaussian filters for polynomial systems with efficient solutions for both the prediction and the filter step. For the prediction step, computationally efficient closed-form solutions are derived for calculating the exact moments. In order to achieve a higher estimation quality, the filter step is solved without the usual additional assumption that state and measurement are jointly...
Directional estimation is a common problem in many tracking applications. Traditional filters such as the Kalman filter perform poorly in a directional setting because they fail to take the periodic nature of the problem into account. We present a recursive filter for directional data based on the Bingham distribution in two dimensions. The proposed filter can be applied to circular filtering problems...
In this paper, linear distributed estimation is revisited on the basis of the hypothesizing distributed Kalman filter and equations for a flexible application of the algorithm are derived. We propose a new approximation for the mean-squared-error matrix and present techniques for automatically improving the hypothesis about the global measurement model. Utilizing these extensions, the precision of...
For systems suffering from different types of uncertainties, finding criteria for validating measurements can be challenging. In this paper, we regard both stochastic Gaussian noise with full or imprecise knowledge about correlations and unknown but bounded errors. The validation problems arising in the individual and combined cases are illustrated to convey different perspectives on the proposed...
This paper presents a novel approach to track a non-convex shape approximation of an extended target based on noisy point measurements. For this purpose, a novel type of Random Hypersurface Model (RHM), called Level-Set RHM is introduced that models the interior of a shape with level-sets of an implicit function. Based on the Level-Set RHM, a nonlinear measurement equation can be derived that allows...
To reduce the amount of data transfer in networked systems, measurements are usually taken only when an event occurs rather than periodically in time. However, this complicates estimation problems considerably as it is not guaranteed that new sensor measurements will be sampled. In order to cope with such event sampled measurements, an existing state estimator is modified so that any divergent behavior...
The federated Kalman filter embodies an efficient and easy-to-implement solution for linear distributed estimation problems. Data from independent sensors can be processed locally and in parallel on different nodes without running the risk of erroneously ignoring possible dependencies. The underlying idea is to counteract the common process noise issue by inflating the joint process noise matrix....
Estimation of circular quantities is a widespread problem that occurs in many tracking and control applications. Commonly used approaches such as the Kalman filter, the extended Kalman filter (EKF), and the unscented Kalman filter (UKF) do not take periodicity explicitly into account, which can result in low estimation accuracy. We present a filtering algorithm for angular quantities in nonlinear...
We propose an efficient method for approximating arbitrary Gaussian densities by a mixture of Dirac components. This approach is based on the modification of the classical Cramér-von Mises distance, which is adapted to the multivariate scenario by using Localized Cumulative Distributions (LCDs) as a replacement for the cumulative distribution function. LCDs consider the local probabilistic influence...
An accurate Linear Regression Kalman Filter (LRKF) for nonlinear systems called Smart Sampling Kalman Filter (S2KF) is introduced. It is based on a new low-discrepancy Dirac Mixture approximation of Gaussian densities. The approximation comprises an arbitrary number of optimally and deterministically placed samples in the entire state space, so that the filter resolution can be adapted to either achieve...
Increasing demand for Nonlinear Model Predictive Control with the ability to handle highly noise-corrupted systems has recently given rise to stochastic control approaches. Besides providing high-quality results within a noisy environment, these approaches have one problem in common, namely a high computational demand and, as a consequence, generally a short prediction horizon. In this paper, we propose...
In this paper, we address the problem of controlling a system over an unreliable UDP-like network that is affected by time-varying delays and randomly occurring packet losses. A major challenge of this setup is that the controller just has uncertain information about the control inputs actually applied by the actuator. The key idea of this work is to model the uncertain control inputs by random variables,...
Almost all multi-target tracking systems have to generate point estimates for the targets, e.g., for displaying the tracks. The novel idea in this paper is to consider point estimates for multi-target states that are optimal according to a kernel distance measure. Because the kernel distance is a metric on point sets and ignores the target labels, shortcomings of Minimum Mean Squared Error (MMSE)...
A new method for globally optimal estimation in decentralized sensor-networks is applied to the decentralized control problem. The resulting approach is proven to be optimal when the nodes have access to all information in the network. More precisely, we utilize an algorithm for optimal distributed estimation in order to obtain local estimates whose combination yields the globally optimal estimate...
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...
This paper describes a method to intelligently schedule a network of multiple RGBD sensors in a Bayesian object tracking scenario, with special focus on Microsoft KinectTM devices. These setups have issues such as the large amount of raw data generated by the sensors and interference caused by overlapping fields of view. The proposed algorithm addresses these issues by selecting and exclusively activating...
This paper is about an experimental set-up for tracking a ground moving mobile object from a bird's eye view. In this experiment, an RGB and depth camera is used for detecting moving points. The detected points serve as input for a probabilistic extended object tracking algorithm that simultaneously estimates the kinematic parameters and the shape parameters of the object. By this means, it is easy...
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