Day-boundary discontinuity (DBD) is an effect present in precise GNSS satellite orbit and clock products originating from the method used for orbit and clock determination. The non-Gaussian measurement noise and data processing in 24 h batches are responsible for DBDs. In the case of the clock product, DBD is a time jump in the boundary epochs of two adjacent batches of processed data and its magnitude might reach a couple of ns. This article presents the four GNSS (Global Navigation Satellite System) systems DBD analysis in terms of change over an 8 year period. For each of 118 satellites available in this period, the yearly value of DBD was subject to analysis including standard deviation and frequency of outliers. Results show that the smallest DBDs appear in the GPS system, the biggest – for the BeiDou space segment. Moreover, the phenomenon of changes in DBDs over time is clearly seen at the beginning of the analysed period when the magnitude and number of the DBDs were larger than for current, newest clock products

A companion robot is capable of performing a variety of activities and thus supporting the elderly and people with disabilities. It should be able to overcome obstacles on its own, respond to what is happening around it in real time, and communicate with its surroundings. It is particularly important to pay attention to these issues, as a companion robot is likely to become a participant in traffic. The research aims to develop a mathematical model that considers the use of two navigation solutions in the companion robot. Thanks to this, it will be possible to use the obtained mathematical relationships to compare various types of navigation and make a rational choice, enabling the implementation of the assumed activities in a specific external environment. What is new in this paper is the analysis of several navigation methods and the presentation of research conducted in real time using an actual robot.