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Approximation algorithm supported on minimizing the Kullback-Leibler information divergence in some class of dynamical systems

Owedyk J., Mathia Z., Zarzycki H.

Biuletyn Naukowy Wrocławskiej Wyższej Szkoły Informatyki Stosowanej. Informatyka

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2015

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vol. 5

12--18

EN

In this work an algorithm is presented for creating approximate solutions in some class of dynamical systems describing the time evolution probability densities. The approximate solutions are obtained by minimizing Kullback- Leibler divergence under some constrains. It is shown that the derivatives of the Kullback-Leibler divergence for exact solutions and for approximate solutions are described by the same formula. In consequence if in a dynamical system the Kullback-Leibler divergence decreases in time for exact solutions, it also decreases for approximate solutions.

PL

W pracy przedstawiono algorytm, który umożliwia skonstruowanie przybliżonych rozwiązań dla pewnej klasy systemów dynamiczych opisujących ewolucję w czasie gęstości prawdopodobieństwa. Przybliżone rozwiązania otrzymujemy minimalizując informację Kullbacka-Leiblera przy dodatkowych warunkach. Wykazano, że pochodna informacji Kullbacka-Leiblera dla dokładnych i przybliżonych rozwiązań jest opisana przez tą samą formułę. W konsekwencji gdy w dynamicznym systemie maleje informacja Kullbacka-Leiblera dla dokładnych rozwiązań to także maleje dla przybliżonych rozwiązań.

2

ATR tract II: "The real-time GPS for public security"

Kwiecień J., Bujnowski S., Mathia Z., Malinowski M.

Reports on Geodesy

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2004

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nr 1/68

21--26

EN

ATR Track II is more sophisticated hardware and software technology then previous model (presented on 3-5 July 2000 in Olsztyn during second Workshop of Satellite Navigation), made for Windows 2000/XP , which works as a Command Center in a system with mobile units equipped with GPS and wireless data communication. In the project the GIS MultiViewer application was developed, that visualizes real time GPS navigation data over the public security system. In addition to position messages, vehicle alarm status and text messages can be sent between the vehicles and the Command Center in order to control and supervise the operation. Moreover, areas on the map can be defined as alarm zones and if a vehicle enters such an area, an alarm will be generated and followed on the map and all positions are recorded. In this condition, the red alarm label appears, an alarm signal is generated the vehicle is zoomed.

3

ATR TRACK: realtime tracking system

Kwiecień J., Bujnowski S., Bujarkiewicz A., Mathia Z.

Reports on Geodesy

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2000

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z. 9/55

53-55

EN

This paper describes the prototype of an automobile fleet navigation system. An architecture that provides the basic components of real-time tracking system is presented. The system have been designed and prepared to locate 60 vehicles within 60 seconds. The wireless communication and adequately Command Center make possible to monitor a vehicle fleet on the city map in real-time or later reviewing depending on demended option. Results of field tests using system are also presented.