Discrete linear and extended Kalman filters (KFs) of integer and fractional orders are presented for estimating the state and unknown parameters of linear and nonlinear discrete fractional-order systems. A comparison of traditional and fractional KFs is given. The features and advantages of the fractional algorithm are considered, which are illustrated with examples of using discrete linear and extended KFs.

This paper introduces an advanced sensor data integration algorithm aimed at enhancing the navigation accuracy and reliability of autonomous snowmobiles in challenging environments. These environments, characterized by snow-covered terrains and limited GPS signal availability, present unique obstacles to traditional navigation systems. The proposed algorithm integrates data from multiple sensors, including RTK systems, inertial measurement units, GPS, and additional components of intelligent transport systems. By employing a Kalman filter, the algorithm adaptively weights and fuses data from these sources, reducing the impact of sensor noise and redundancy while ensuring robust state estimation and accurate trajectory prediction. The experimental study was conducted at the Large Telescope Azimuthal site, where snowmobiles navigated through complex terrains, demonstrating the algorithm’s ability to maintain stable and accurate positioning. The results highlight significant improvements in trajectory precision compared to conventional methods, particularly in environments with poor signal conditions. This research underscores the importance of multi-sensor data fusion in achieving reliable and efficient autonomous navigation. Future research directions include expanding the sensor suite with modalities such as radar and thermal imaging to enhance robustness under extreme weather conditions. Additionally, efforts will be made to optimize the algorithm for real-time applications, reducing latency and improving computational efficiency. These advancements are critical for developing safer and more reliable autonomous transport systems capable of operating effectively in the most demanding environments.

A comprehensive approach to the analysis of electroencephalographic (EEG) signals obtained from human brain and artificially synthesized using machine learning methods is presented. The main focus is on data preprocessing, including signal normalization and filtering, as well as application of various feature extraction methods, in particular, Fast Fourier Transform and Mel-Frequency Cepstral Coefficients. A comparative analysis of classification accuracy using logistic regression, random forest, gradient boosting, and recurrent neural network LSTM is performed. Special attention is given to the effect of filtering parameters on classification accuracy. The results show that filtering and proper tuning of model parameters significantly improve the accuracy of EEG signal classification, ensuring separation of real and synthetic EEG pools. The results and discussion may serve as a basis for further research in the field of biomedical signal analysis and processing.

The vast majority of scheduling problems are NP-hard. To solve each such problem, we need a separate algorithm: an approximation scheme or an algorithm with polynomial average time. The performance of such algorithms strongly depends on the input data.

The time-window orientation problem under consideration belongs to the class of routing and scheduling problems arising from physical allocation. It considers a set of nodes (clients), each with associated profit and processing time (time window), and a set of edges, each characterized by a particular time. The goal of the problem is to construct an acyclic path starting at a given origin and ending at a given destination that maximizes total profit while meeting the time window constraints on all nodes and not exceeding a given time limit. The problem is classified as NP-hard, so an exact algorithm that executes in a reasonable time is unlikely to exist.