The study and analysis of the problem of simulation modeling of multipath radio channels based on the use of systems of differential equations is carried out. Mathematical models of continuous communication channels, presented in the form of stochastic differential equations, as well as approaches to their practical application in creating physical channel simulators and developing algorithms for optimal signal reception, are considered. Particular attention is paid to non-Gaussian models described by nonlinear stochastic differential equations. Methods of analysis of such models, their construction on the basis of initial data on probabilistic characteristics of signals and interference, as well as identification procedures performed on the results of measurements on real communication lines are considered in detail. In addition to theoretical aspects, engineering issues related to the implementation of channel simulators functioning according to the specified principles are also covered.
In most relevant publications, the correlation of slopes of statistically uneven surfaces is usually not taken into account, which can lead to significant errors. This paper shows how the local nature of Fresnel reflection coefficients, the correlation of surface slopes and the dependence of slopes on surface height influence the calculation of fields when a signal is reflected from statistically uneven surfaces. The probability distribution density of a subsystem of a normally distributed system is determined. The average density (variance) was determined for vertical and horizontal polarization, as well as for cross-polarization fields. A special case of surfaces with a large modulus of dielectric constant is studied. The specific scattering cross-section for a narrow antenna pattern has been determined. It is shown that for surfaces with low dielectric constant, the viewing angle should be taken into account. Taking into account the influence of the correlation of surface slopes results in a significant change in the calculated values of density and specific scattering cross-section. The specific scattering cross-section was calculated based on experimental data and the obtained expressions, which showed the need to take into account the correlation of slopes of statistically uneven surfaces.
В теории марковской фильтрации до настоящего времени весьма актуальной является задача решения уравнений фильтрации при полимодальной форме апостериорной плотности распределения вероятности. Основная трудность разработки алгоритма фильтрации состоит в надежной идентификации аномальных режимов функционирования, характеризуемых появлением так называемых ложных захватов. В ряде работ был предложен алгоритм пошаговой оценки процесса, полученный на основе полигауссовской аппроксимации решения, однако сделан вывод о невозможности учета срывов слежения путем моделирования совокупности дифференциальных уравнений, задающих параметры аппроксимации. Недостаточность системы уравнений устраняется путем решения уравнения для весовых коэффициентов на последовательных временных интервалах с соответствующим переопределением начальных условий в начале каждого из интервалов. В данной работе для случая одномерных наблюдений и фильтруемого процесса уточнены дифференциальные уравнения, определяющие динамику весовых коэффициентов в полигауссовской аппроксимации по форме решения уравнения Стратоновича. Показано, что моделирование уточненной системы уравнений, без разбиения времени наблюдения на интервалы и введения в начале интервалов внешних начальных условий на весовые коэффициенты, позволяет осуществлять фильтрацию процесса с учетом аномальных режимов функционирования. In the theory of Markov filtering, the problem of solving the filtering equations in the case of a polymodal form of the posterior probability density distribution is still relevant. The main difficulty in developing a filtering algorithm is the reliable identification of abnormal operating modes characterized by the occurrence of so-called false captures. Several studies have proposed a step-by-step process estimation algorithm based on a poly-Gaussian approximation of the solution, but it has been concluded that it is not possible to account for tracking failures by modeling a set of differential equations that define the approximation parameters. The inadequacy of the system of equations is eliminated by solving the equation for the weight coefficients on successive time intervals, with corresponding redefinition of the initial conditions at the beginning of each interval. In this work, for the case of one-dimensional observations and a filtered process, the differential equations that determine the dynamics of the weight coefficients in the poly-Gaussian approximation based on the solution of the Stratonovich equation are refined. It is shown that modeling the refined system of equations, without dividing the observation time into intervals and introducing external initial conditions on the weight coefficients at the beginning of the intervals, allows for the filtering of the process, taking into account abnormal operating modes.
The article analyzes retrospectively and systematizes the stages of animation evolution in digital user interfaces. Unlike works focusing exclusively on web design, this study examines the evolution of animation in the broader context of human-computer interaction (HCI), including desktop GUIs, web interfaces, and mobile platforms. The relevance of the study is due to the transformation of the role of animation from a purely aesthetic element to a key tool for functional communication, attention management, and user experience formation. The aim of the work is to identify patterns and paradigmatic shifts in the use of animation in interface design based on analysis of scientific works and professional practice. The methodology includes historical-genetic analysis, comparative analysis of approaches in different periods of HCI development, and generalization of data from dissertation research and modern scientific publications. Four key stages of evolution are identified: emergence of micro-animation and GUI metaphors (1980s – mid-1990s), the era of "dynamic web" and Flash (late 1990s – late 2000s), functionalization and standardization (2010s), and the modern stage of communicative and predictive animation (2020s). Based on the analysis, promising vectors of development are formulated, including the integration of animation with predictive interfaces and further democratization of creation tools through no-code platforms.
