MATHEMATICAL MODELING AND STABILITY ANALYSIS OF VISUAL LOCALIZATION ALGORITHMS UNDER BRIGHTNESS AND NOISE VARIATIONS

Visual localization algorithms are an integral part of modern robotics and navigation systems, providing object position determination based on visual features or images. However, their effectiveness is largely dependent on external factors, such as image brightness and noise level, which directly affect landmark recognition and coordinate accuracy. Subject of research: analysis of the impact of image brightness and noise on the accuracy and stability of adaptive localization algorithms. The purpose of the work is to quantify the impact of image parameters on the robustness of various localization methods and to identify algorithms most suitable for real-time operation under unstable visual conditions. Research methods: A two-factor experimental design with brightness and noise level variables was applied, within which a series of localization experiments were conducted. Mathematical modeling was performed to obtain analytical dependences of the minimum, average, and maximum localization errors for four algorithms – Proximity, Centroid, Weighted Centroid, and Lateration. Based on the obtained models, a stability coefficient was introduced as an indicator of the algorithm's robustness. Results: the constructed regression models demonstrated high adequacy and allowed us to visualize the influence of brightness and noise on localization accuracy. It was found that the Weighted Centroid and Lateration methods provide the highest stability of operation, maintaining low error variation when changing image parameters, while the Proximity and Centroid algorithms showed greater sensitivity to noise and lighting fluctuations.