The Greedy Dirichlet Process Filter - An Online Clustering Multi-Target Tracker

Reliable collision avoidance is one of the main requirements for autonomous driving. Hence, it is important to correctly estimate the states of an unknown number of static and dynamic objects in real-time. Here, data association is a major challenge for every multi-target tracker. We propose a novel multi-target tracker called Greedy Dirichlet Process Filter (GDPF) based on the non-parametric Bayesian model called Dirichlet Processes and the fast posterior computation algorithm Sequential Updating and Greedy Search (SUGS). By adding a temporal dependence we get a real-time capable tracking framework without the need of a previous clustering or data association step. Real-world tests show that GDPF outperforms other multi-target tracker in terms of accuracy and stability

Singularity-free methods for aircraft flight path optimization using Euler angles and quaternions

The purpose of this work is to rewrite the equations of motion such that even third-class trajectories can be optimized with the current parameter optimization methods. At first the commonly used coordinate systems and Euler angles are presented in Section II. It will be realized that the definition of the Euler angles introduces additional singularities. A short derivation of the commonly-used equations of motion follows for comparison and better understanding of the later derived sets of equations of motion. Section II closes with a reduction of the optimal control problem to a parameter optimization problem. Some characteristic properties and assumptions of the parameter optimization problem are pointed out along with the necessary equations and conditions needed to solve it. Section III introduces several methods that allow integration of second- and third-class trajectories as long as some restrictions are imposed on the allowable trajectories. The first method is the so-called inertial-acceleration method. It is based on the idea that the velocity yaw angle and the velocity pitch angle can be replaced by the velocity components as measured in an inertial reference frame. The so-called two-system method is derived next. It employes the idea of having two sets of equations of motion derived in different reference frames, and thus, having their singularities at different points. In detailed discussions the problems that appear with both methods are explained, and solutions are presented, the emphasis always being on the use of these equations with optimization methods. Section III also includes a method that allows integration of third-class trajectories as long as they can be flown in the vertical plane. This method results directly from the commonly-used equations of motion after removing a restriction on the flight path angle. Because all methods of Section III have still the bank angle as the control, they are referred to here as Euler-angle methods. Section IV presents the quaternion method. Although this method has been investigated first, it is presented last because it yields the best overall solution and because many details and improvements were not found until the other methods were analyzed. Understanding the Euler-angle methods will also help in understanding the properties of the quaternion method. Because the available literature on quaternions is either complex or erroneous, the quaternion is covered in much detail. The concept of the quaternion is explained, and the rules of quaternion algebra are stated in the first two sections. Next, some necessary relationships are developed. It will then be rather straightforward to derive the actual equations of motion. How to use the quaternion method for parameter optimization methods is emphasized in the following sectionsAerospace Engineerin

The Total Gaussian Class of Quasiprobabilities and its Relation to Squeezed-State Excitations

The class of quasiprobabilities obtainable from the Wigner quasiprobability by convolutions with the general class of Gaussian functions is investigated. It can be described by a three-dimensional, in general, complex vector parameter with the property of additivity when composing convolutions. The diagonal representation of this class of quasiprobabilities is connected with a generalization of the displaced Fock states in direction of squeezing. The subclass with real vector parameter is considered more in detail. It is related to the most important kinds of boson operator ordering. The properties of a specific set of discrete excitations of squeezed coherent states are given