Modern methods of measurement, data processing, and their mathematical models in metrological problems

Modern metrology increasingly demands high precision, reliability, and reproducibility, particularly under complex and variable environmental and instrumental conditions. This paper presents a comprehensive analysis of advanced measurement data processing methods tailored to metrological challenges, including humidity, pressure, and aerosol concentration assessments. By integrating classical statistical techniques with contemporary computational approaches, such as regression analysis, Bayesian estimation, spectral filtering, and machine learning algorithms (notably neural networks and ensemble methods), the study demonstrates effective reduction of random and systematic errors, improved data interpretability, and enhanced automation for large-scale datasets. The practical utility of these methods is exemplified through the calibration of a humidity measurement device, with a detailed evaluation of deviations and uncertainties. Results indicate high measurement accuracy, with deviations ranging from 0.12% to 0.51%, although increased uncertainty is observed at higher humidity levels. Mathematical modeling, especially uncertainty estimation in accordance with the ISO Guide to the Expression of Uncertainty in Measurement, provides a robust framework for predicting measurement reliability. The findings emphasize that the combined use of traditional and modern data processing techniques substantially enhances measurement quality and system adaptability in real-world scenarios, offering particular benefits for high-sensitivity applications such as environmental monitoring and industrial process control.