Observation Of Trajectories Research Articles

The Frenet-Serret description of Born rigidity and its application to the Dirac equation

The role played by non-inertial frames in physics is one of the most interesting subjects that we can study when dealing with a physical theory. It does not matter whether we are studying classical theories such as special relativity or quantum theory, the idea of an accelerated frame is always one of the first ideas to come to our minds. In the case of special relativity, a problem with the concept of rigidity emerged as soon as Max Born gave a reasonable definition of rigid motion: the Herglotz-Noether theorem imposes a strong restriction on the possible rigid motions. In this paper, the equivalence of this theorem with another one that is formulated with the help of Frenet-Serret formalism is proved, showing the connection between the rigid motion and the curvatures of the observer's trajectory in spacetime. In addition, the Dirac equation in the Frenet-Serret frame for an arbitrary observer is obtained and applied to the rotating observers. The solution in the rotating frame is given in terms of that of an inertial one.

Moving observer trajectory control by angular measurements in tracking problem

An optimal path synthesis problem for a moving observer that performs angular observations over a target moving uniformly along a straight line on a plane is solved. It is supposed that elevation and azimuth angles can be observed when the observer moves in space and only the azimuth angle can be observed when the observer moves on a plane. Observer's trajectories are obtained with the help of Pontryagin'smaximum principle as numerical solutions of an optimal control problem. As a performance criterion the trace of covariance matrix of the target motion elements estimate is used. A possibility of solving the problem in real time on board for unmanned aerial vehicle is investigated. A comparison with the scenario of two unmanned aerial vehicles using is given.

Walking pedestrian recognition

In previous years, many methods providing the ability to recognize rigid obstacles-sedans and trucks-have been developed. These methods provide the driver with relevant information. They are able to cope reliably with scenarios on motorways. Nevertheless, not much attention has been given to image processing approaches to increase the safety of pedestrians in urban environments. In the paper, a method for the detection, tracking, and final recognition of pedestrians crossing the moving observer's trajectory is suggested. A combination of data- and model-driven approaches is realized. The initial detection process is based on a fusion of texture analysis, model-based grouping of, most likely, the geometric features of pedestrians, and inverse-perspective mapping (binocular vision). Additionally, motion patterns of limb movements are analyzed to determine initial object-hypotheses. The tracking of the quasirigid part of the body is performed by different algorithms that have been successfully employed for the tracking of sedans, trucks, motorbikes, and pedestrians. The final classification is obtained by a temporal analysis of the walking process.

Mass-analytic quantization, uniform acceleration, and black-hole space-times

The notion of a "natural" vacuum state, defined by the resolvent property of the Feynman propagator, is combined with that of observer-dependent particle modes, based on the distinguished role of the Fermi coordinates associated with the observer's trajectory. If augmented by a minimal support property of the corresponding wave functions, these concepts provide an alternative derivation of the thermal radiation encountered by a uniformly accelerated detector in the Minkowski vacuum. In the case of the Kruskal manifold our approach yields a "vacuum" state that is entirely different from those proposed by Boulware, Hartle and Hawking, and Unruh, respectively, the reason being the global character of our quantization prescription and its sensitivity with respect to the existence of a "white hole" singularity. Indeed, for a gravitational collapse starting from quasistatic initial conditions the Hawking effect is recovered.