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In this paper, we present a method for designing orthogonal, Legendre type filters. Realization of these filters is very simple and they are very fast, robust and precise. They can be used for generating the sequence of Legendre orthogonal functions. We have also developed a new method for positioning an antenna system, based on these filters, where the filter is applied in detection of electromagnetic field gradient. Control algorithm is based on improved method of gradients. Proposed control algorithm has been verified on practically realized, experimental antenna system and compared with some others tracking control algorithms. Performed experiments have verified efficiency, speed and accuracy of the proposed control method

In this article, we present a new method for the synthesis of almost and quasiorthogonal polynomials of arbitrary order. Filters designed on the bases of these functions are generators of generalised quasi-orthogonal signals for which we derived and presented necessary mathematical background. Based on theoretical results, we designed and practically implemented generalised first-order (k = 1) quasi-orthogonal filter and proved its quasi-orthogonality via performed experiments. Designed filters can be applied in many scientific areas. In this article, generated functions were successfully implemented in Nonlinear Auto Regressive eXogenous (NARX) neural network as activation functions. One practical application of the designed orthogonal neural network is demonstrated through the example of control of the complex technical non-linear system -laboratory magnetic levitation system. Obtained results were compared with neural networks with standard activation functions and orthogonal functions of trigonometric shape. The proposed network demonstrated superiority over existing solutions in the sense of system performances.

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In this article we define a new class of orthogonal filters with complex poles and zeroes inside their transfer function. This further improvement of classical orthogonal filters allows the possibility to model a wider range of real systems, i.e., the systems whose mathematical models have complex zeroes besides real ones. These filters can be applied in the following areas: circuit theory, telecommunications, signal processing, bond graphs, theory approximations, and control system theory First, we describe the rational functions with complex poles and zeroes, and prove their orthogonality. Based on these functions we designed the block diagram of orthogonal Legendre type filter with complex poles and zeroes. After that an appropriate analogue scheme of this filter for practical realization is derived. To validate theoretical results we performed an experiment with a cascade-connected system designed and practically realized in our laboratories. The experiments proved the quality of the designed orthogonal model in terms of accuracy and simplicity.