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Positive Descriptor Time-varying Discrete-time Linear Systems and Their Asymptotic Stability

Kaczorek T.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2015

Vol. 9, no. 1

83--89

The positivity and asymptotic stability of the descriptor time-varying discrete-time linear systems are addressed. The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to the time-varying discrete-time descriptor linear systems. Using the extension necessary and sufficient conditions for the positivity of the systems are established. Sufficient conditions for asymptotic stability of the positive systems are presented. The effectiveness of the tests is demonstrated on the example.

On Modelling of Nonlinear Systems and Phenomena with the Use of Volterra and Wiener Series

Borys A.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2015

Vol. 9, no. 1

91--98

This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener kernels and operators. Also, the problem of a best approximation of large-scale nonlinear systems using Volterra operators in weighted Fock spaces is described. Examples of applications considered are the following: Volterra series use in description of nonlinear distortions in satellite systems and their equalization or compensation, exploiting Wiener kernels to modelling of biological systems, the use of both Volterra and Wiener theories in description of ocean waves and in magnetic resonance spectroscopy. Moreover, connections between Volterra series and neural network models, and also input-output descriptions of quantum systems by Volterra series are discussed. Finally, we consider application of Volterra series to solving some nonlinear problems occurring in hydrology, navigation, and transportation.

Algorithms for Ship Movement Prediction for Location Data Compression

Czapiewska A., Sadowski J.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2015

Vol. 9, no. 1

75--81

Due to safety reasons, the movement of ships on the sea, especially near the coast should be tracked, recorded and stored. However, the amount of vessels which trajectories should be tracked by authorized institutions, often in real time, is usually huge. What is more, many sources of vessels position data (radars, AIS) produces thousands of records describing route of each tracked object, but lots of that records are correlated due to limited dynamic of motion of ships which cannot change their speed and direction very quickly. In this situation it must be considered how many points of recorded trajectories really have to be remembered to recall the path of particular object. In this paper, authors propose three different methods for ship movement prediction, which explicitly decrease the amount of stored data. They also propose procedures which enable to reduce the number of transmitted data from observatory points to database, what may significantly reduce required bandwidth of radio communication in case of mobile observatory points, for example onboard radars.