The paper presents a concept of an indoor navigation system, using Ultra Wideband (UWB) radio modules. The system can be used to provide for position awareness inside buildings where no other means of positioning systems are available or the quality of the positioning service is poor. The system is composed of several beacons and mobile modules that are used inside the building. The beacons and mobile stations are equipped with UWB ranging modules and Two-Way Time-of-Flight technique is used for ranging. The structure of the proposed system, its mathematical model, positioning algorithm and chosen simulation results are presented in the paper.

The paper presents a concept of a mobile, short-range system capable of localizing people inside buildings. The system uses ultra-wideband radio modules for accurate ranging. A drone-based localizing unit circulates around the area of interest, calculates its position, gathers ranging measurements to the personal units of system users, calculates their positions and reports them to the monitoring station. As the ultrawideband signals penetrate light covers such as windows, doors and thin walls, the system can locate its users even inside buildings. It can locate several people at a time, making the system adequate for providing positions of members of e.g. firemen, police or military teams operating in partially closed spaces. The structure of the system, its mathematical model, position estimation algorithm and chosen simulation results are presented in the paper.

The paper presents an approach to differential equation solutions for the stiff problem. The method of using the classic transformer model to study nonlinear steady states and to determine the current pulses appearing when the transformer is turned on is given. Moreover, the stiffness of nonlinear ordinary differential state equations has to be considered. This paper compares Runge–Kutta implicit methods for the solution of this stiff problem.

Landmines and explosive remnants of war are a significant threat in tens of countries and other territories, causing the deaths or injuries of thousands of people every year, even long after military conflicts. Effective technical means of remote detecting, localizing, imaging, and identifying mines and other buried explosives are still sought and have a great potential utility. This paper considers a positioning system used as a supporting tool for a handheld ground penetrating radar. Accurate knowledge of the radar antenna position during terrain scanning is necessary to properly localize and visualize the shape of buried objects, which helps in their remote classification and makes demining safer. The positioning system proposed in this paper uses ultrawideband radios to measure the distances between stationary beacons and mobile units. The measurements are processed with an extended Kalman filter based on an innovative dynamics model, derived from the model of a pendulum motion. The results of simulations included in the paper prove that using the proposed pendulum dynamics model ensures a better accuracy than the accuracy obtainable with other typically used dynamics models. It is also demonstrated that our positioning system can estimate the radar antenna position with the accuracy of single centimeters which is required for appropriate imaging of buried objects with the ground penetrating radars.