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As an alternative to Kalman filters and particle filters, recently the progressive Gaussian filter (PGF) was proposed for estimating the state of discrete-time stochastic nonlinear dynamic systems. Like Kalman filters, the estimate of the PGF is a Gaussian distribution, but like particle filters, its measurement update works directly with the likelihood function in order to avoid the inherent linearization...
In this paper, we propose an algorithm for tracking mobile devices (such as smartphones, tablets, or smartglasses) in a known environment for augmented reality applications. For this purpose, we interpret the environment as an extended object with a known shape, and design likelihoods for different types of image features, using association models from extended object tracking. Based on these likelihoods,...
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...
For decentralized fusion problems, ellipsoidal intersection has been proposed as an efficient fusion rule that provides less conservative results as compared to the well-know covariance intersection method. Ellipsoidal intersection relies on the computation of a common estimate that is shared by the estimates to be fused. In this paper, an algebraic reformulation of ellipsoidal intersection is discussed...
Multitarget tracking problems arise in many real-world 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...
Various applications necessitate the estimation of quantities defined on intervals or the unit circle, which can also be parameterized as an interval. These applications include estimation of joint angles that are either limited to a certain range or that are 360-degree-periodic. For this purpose, we consider two approaches based on discretizing the state space that use fundamentally different density...
Fingerprinting localization is to estimate a mobile terminal's location using its online received signal strength (RSS) measurement and offline RSS database originated from multiple access points (APs). Kernel-based fingerprinting localization is such a competitive algorithm. However, all training data need to be considered in its offline model learning stage. This render high risks for overfitting...
The recently proposed Kernel-SME filter for multi-object tracking is a further development of the Symmetric Measurement Equation (SME) idea introduced by Kamen in the 1990s. The Kernel-SME constructs a symmetric, i.e., permutation invariant, measurement equation by transforming the measurements to a kernel mixture function. This transformation is scalable to a large number of objects and allows for...
While nonlinear filtering for circular quantities is closely related to nonlinear filtering on linear domains, the underlying manifold enables the development of novel filters that take advantage of the boundedness of the domain. Previously, we introduced Fourier filters that approximate the density or its square root using Fourier series. For these filters, we proposed filter steps for arbitrary...
In this work, a new method for approximating circular probability distributions by a mixture of weighted discrete samples is proposed. Particularly, the wrapped normal distribution, the von Mises distribution, and the Bingham distribution are considered. The approximation approach is based on formulating a quantizer and a global optimality measure, which can be optimized directly. Furthermore, a relationship...
Chance-constrained control is a difficult problem even if the considered system dynamics are linear. The difficulty stems from the facts that the chance constraints are difficult to evaluate and that the control law is nonlinear due to the constraints. In this paper, we present a novel approach to chance-constrained control, where we solve the unconstrained control problem first and then use a progressive...
We look at the task of estimating the parameters of a geometric constraint from noisy points in 2D. The classical approach of minimizing the Euclidean distance error between points and constraint generally yields biased estimates for nonlinear constraints and higher noise levels. To deal with this issue, the expected distribution of the distance error can be explicitly incorporated in the estimator...
This paper introduces an enhanced method for progressive Bayesian estimation based on a set of deterministic samples. The information of a given measurement is gradually introduced in order to avoid particle degeneration, which is usually encountered in standard particle filters. The main contribution of this paper is to derive a new method for exploiting smoothness assumptions about the unknown underlying...
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,...
When approximating one probability density with another density, it is desirable to minimize the information loss of the approximation as quantified by, e.g., the Kullback-Leibler divergence (KLD). It has been known for some time that in the case of the Gaussian distribution, matching the first two moments of the original density yields the optimal approximation in terms of minimizing the KLD. In...
State estimation concepts like the Kalman filter heavily rely on potentially noisy sensor data. In general, the estimation quality depends on the amount of sensor data that can be exploited. However, missing observations do not necessarily impair the estimation quality but may also convey exploitable information on the system state. This type of information—noted as negative information—often requires...
In this paper, we present a novel approach to optimally fuse estimates in distributed state estimation for linear and nonlinear systems. An optimal fusion requires the knowledge of the correct correlations between locally obtained estimates. The naive and intractable way of calculating the correct correlations would be to exchange information about every processed measurement between all nodes. Instead,...
In this paper, we propose a novel approach to track elongated, curved extended targets by representing their shapes with splines. Elongated shapes are forms whose length is much larger than their width, and can be found in many places, such as in connected vehicles like trains, in group targets like a caravan moving along a curved street, or even when estimating the pose of a person. A particular...
We consider stochastic nonlinear time-variant systems with imperfect state information in the context of model predictive control. The optimal control performance can only be achieved by closed-loop feedback policies, which in fact anticipate future behavior. However, the computation of these policies is in general not tractable due to the presence of the dual effect, i.e., the control actions not...
In this paper, we address control of Markov Jump Linear Systems without mode observation via dynamic output feedback. Because the optimal nonlinear control law for this problem is intractable, we assume a linear controller. Under this assumption, the control law computation can be expressed in terms of an optimization problem that involves Bilinear Matrix Inequalities. Alternatively, it is possible...
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