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For manifolds with topologies that strongly differ from the standard topology of Rn, using common filters created for linear domains can yield misleading results. While there is a lot of ongoing research on estimation on the unit circle, higher-dimensional problems particularly pose a challenge. One important generalization of the unit circle is the unit hypersphere. In this paper, we propose a recursive...
Estimation of periodic quantities such as angles or phase values is a common problem. However, standard approaches, for example the Kalman filter and extensions thereof, have difficulties when estimating periodic quantities. To address this problem, circular filtering algorithms have been proposed but they are limited to just a single angle. In order to deal with multiple, possibly correlated angles,...
In this paper, we propose a novel approach to track extended objects by incorporating negative information. While traditional techniques to track extended targets use only positive measurements, assumed to stem from the target, the proposed estimator is also capable of incorporating negative measurements, which tell us where the target cannot be. To achieve this, we introduce a simple, robust, and...
We propose a novel progressive Gaussian filter for nonlinear stochastic systems. A Gaussian approximation of the posterior is computed without an explicit assumption of a linear relation between the system state and the measurement. This allows for better quality of the estimation compared to Kalman filters for nonlinear problems like the EKF or UKF. In this work, we use the progressive filter framework,...
We consider the task of recursively estimating the pose and shape parameters of 3D objects based on noisy point cloud measurements from their surface. We focus on objects whose surface can be constructed by transforming a plane curve, such as a cylinder that is constructed by extruding a circle. However, designing estimators for such objects is challenging, as the straightforward distance-minimizing...
Recursive filtering with multimodal likelihoods and transition densities on periodic manifolds is, despite the compact domain, still an open problem. We propose a novel filter for the circular case that performs well compared to other state-of-the-art filters adopted from linear domains. The filter uses a limited number of Fourier coefficients of the square root of the density. This representation...
In this work, the problem of pole identification of discrete-time single-input single-output (SISO) linear time-invariant (LTI) systems directly from input-output data is considered. The solution to this nonlinear estimation problem is derived in form of the general Bayesian estimation framework, as well as a practical approximate solution by application of statistical linearization. The derived direct...
In this paper, a novel Bayesian estimator for the minimum bounding axis-aligned rectangle of a point set based on noisy measurements is derived. Each given measurement stems from an unknown point and is corrupted with additive Gaussian noise. Extreme value theory is applied in order to derive a linear measurement equation for the problem. The new estimator is applied to the problem of group target...
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...
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