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Currently, one of the most effective algorithms for state estimation of stochastic systems is a Kalman filter. This filter provides an optimal root-mean-square error in state vector estimation only when the parameters of the dynamic system and its observer are precisely known. In real conditions, the observer’s parameters are often inaccurately known; moreover, they change randomly over time. This in turn leads to the divergence of the Kalman estimation process. The problem is currently being solved in a variety of ways. They include the use of interval observers, the use of an extended Kalman filter, the introduction of an additional evaluating observer by nonlinear programming methods, robust scaling of the observer’s transmission coefficient, etc. At the same time, it should be borne in mind that, firstly, all of the above ways are focused on application in specific technical systems and complexes, and secondly, they fundamentally do not allow estimating errors in determining the parameters of the observer themselves in order to compensate them for further improving the accuracy and stability of the filtration process of the state vector. To solve this problem, this paper proposes the use of accurate observations that are irregularly received in a complex measuring system (for example, navigation) for adaptive evaluation of the observer’s true parameters of the stochastic system state vector. The development of the proposed algorithm is based on the analytical dependence of the Kalman estimate variation on the observer’s parameters disturbances obtained using the mathematical apparatus for the study of perturbed multidimensional dynamical systems. The developed algorithm for observer’s parameters adaptive estimation makes it possible to significantly increase the accuracy and stability of the stochastic estimation process as a whole in the time intervals between accurate observations, which is illustrated by the corresponding numerical example.

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The article discusses the possibilities of using wireless technologies of the Internet of Things at agricultural facilities using the example of ZigBee technologies. This topic seems to be relevant, since the smart farm market is growing very quickly. This is due to the fact that the use of automated control systems for humidity, temperature, acidity, electrical conductivity of the soil, etc. allows you to increase productivity, reduce costs. The aim of the research is to assess the potential communication range between ZigBee devices, and to analyze the factors affecting the quality of the radio channel. As the results of the work, it should be noted a mathematical study of radio channels at frequencies of 868 and 2400 MHz, analysis of factors affecting signal propagation. The article also provides practical recommendations for choosing a network topology and ZigBee equipment..

Annotation. Currently, the problem of evaluating stochastic processes observed under noisy conditions on a finite time interval is solved only for datasets in the form of time series using a limited number of statistical variational or spectral analysis methods, as well as various modifications of regression methods. In this case, parametric criteria are used that depend on individual parameters of the distribution density of the observed process, and not on the density itself, which significantly limits the possibilities of increasing the estimation accuracy. To solve the problem of high-precision estimation of stochastic processes on a finite time interval of their observation, an approach is proposed, firstly, providing optimal estimation according to the criterion depending on the posterior distribution density - the most informative characteristic of the observed process, and secondly, taking into account the dynamic structure of the process and the finiteness of the interval observation. A numerical example is considered to illustrate the effectiveness of the developed approach. Relevance. Currently, the problem of evaluating stochastic processes observed under noisy conditions on a finite time interval (terminal filtering problem) is solved only for datasets in the form of time series using a limited number of statistical variational or spectral analysis methods, as well as various modifications of regression methods. In this case, parametric criteria are used that depend on individual parameters of the distribution density of the observed process, and not on the density itself, which significantly limits the possibilities of increasing the estimation accuracy. Target. In this regard, for stochastic processes of a general form - described by nonlinear stochastic differential equations, it is necessary to develop a method of terminal filtering according to a criterion that takes into account the finiteness of the observation time interval and depends on the posterior distribution density - the most informative characteristic of the observed process (and not on its individual parameters). Results. The proposed solution to the problem of high-precision terminal filtering of stochastic processes - their optimal estimation over a finite observation time interval - is based on the use of a terminal criterion that depends directly on the posterior distribution density and takes into account the finiteness of the observation time interval. When describing the observed stochastic processes, their most general representation was used - nonlinear stochastic differential equations, which significantly expands the field of application of the results obtained in comparison, for example, with time series. The general solution to the problem of optimal terminal filtering is obtained using the Pontryagin maximum principle, the solution to the problem of suboptimal filtering, which significantly reduces computational costs, is based on the method of invariant immersion. Practical significance. A numerical example is considered to illustrate the effectiveness of the developed method. The proposed approach can be widely used in various fields of scientific and technical research: radio engineering, Earth sensing, satellite navigation, astronomy, seismology, geodesy, etc.