BAYESIAN METHOD FOR RECURSIVE COMBINATION OF MEASUREMENT AND PRIOR INFORMATION FOR ACCURACY IMPROVEMENT IN VIDEO-BASED MEASUREMENTS
DOI:
https://doi.org/10.68302/std2026.vol2.203Keywords:
Video-based measurements, machine vision, object tracking, Bayesian estimation, recursive methods, measurement noise varianceAbstract
This paper presents a Bayesian method for the recursive combination of prior and measurement information aimed at improving the accuracy of video-based measurements. The proposed approach is based on a probabilistic formulation in which measurements are affected by stochastic noise with time-varying characteristics. The main contribution is the development of an adaptive mechanism for estimating the measurement noise variance, based on normalized innovation and a variable smoothing coefficient. This enables dynamic adjustment of the influence of measurements according to their current reliability, without the need for an explicit dynamic model. The effectiveness of the method is evaluated through simulations at different noise levels, with results demonstrating robust and accurate estimation, effective suppression of noise-induced deviations, and consistent uncertainty quantification. The method is applicable to machine vision and video-based object tracking tasks under varying measurement conditions.
Supporting Agencies
The authors acknowledge the support of the European Regional Development Fund, within the Operational Programme “Research, Innovation and Digitalization Programme for Intelligent Transformation 2021–2027”, through Project No. BG16RFPR002-1.014-0006 for the experimental investigations and measurement equipment, and through Project No. BG16RFPR002-1.014-0005 for the theoretical development and analytical framework of the study.Downloads
References
[1] L. Zhang, X. Jia, Q. Chang, X. Liu, Z. Zhang, Y. Cao, and Y. Yang, “The development of machine vision and its applications in different industries: A review,” Mechanical Engineering Advances, vol. 2, no. 2, p. 1746, 2024.
[2] J. Werheid, H. Behnen, J. H. Woltersmann, S. He, T. Hamann, A. Abdelrazeq, and R. H. Schmitt, “Machine vision in manufacturing SMEs: A review,” Discover Applied Sciences, vol. 7, no. 5, p. 371, 2025.
[3] T. Wang, B. Chen, Z. Zhang, H. Li, and M. Zhang, “Applications of machine vision in agricultural robot navigation: A review,” Computers and Electronics in Agriculture, vol. 198, p. 107085, 2022.
[4] N. Zhang, J. Yang, Z. Li, and Y. Xie, “Deep learning-based image denoising: A comprehensive survey,” in Proc. 5th Int. Conf. Artificial Intelligence and Industrial Technology Applications (AIITA), 2025, pp. 896–910.
[5] G. Iliev and H. Hristov, “Modelling and simulation of dynamic processes in an electropneumatic positioning system with high-speed valves and PWM control,” Journal of Physics: Conference Series, vol. 3127, no. 1, p. 012012, 2025, doi: 10.1088/1742-6596/3127/1/012012.
[6] I. Malakov, V. Zaharinov, S. Nikolov, and R. Dimitrova, “Computer-aided choosing of an optimal structural variant of a robot for extracting castings from die casting machines,” Actuators, vol. 12, p. 363, 2023, doi: 10.3390/act12090363.
[7] P. Mitev and I. Malakov, “Development of a system for automatic feeding and orientation of cylindrical parts,” AIP Conference Proceedings, vol. 3063, no. 1, p. 060017, 2024, doi: 10.1063/5.0195879.
[8] A. A. Volkov, A. V. Kozlov, P. A. Cheremkhin, D. A. Rymov, A. V. Shifrina, R. S. Starikov, and V. G. Rodin, “A review of neural network-based image noise processing methods,” Sensors, vol. 25, no. 19, p. 6088, 2025.
[9] S. Singh, R. Kumari, P. Pallavi, and P. Saurabh, “A systematic review of deep learning methods for low-light image enhancement and object detection,” Discover Applied Sciences, vol. 8, no. 3, 2026.
[10] D. Dichev, D. Diakov, I. Zhelezarov, S. Valkov, M. Ormanova, R. Dicheva, and O. Kupriyanov, “A method for correction of dynamic errors when measuring flat surfaces,” Sensors, vol. 24, no. 16, 2024, doi: 10.3390/s24165154.
[11] J. Li, X. Xu, Z. Jiang, and B. Jiang, “Adaptive Kalman filter for real-time visual object tracking based on autocovariance least square estimation,” Applied Sciences, vol. 14, no. 3, p. 1045, 2024.
[12] D. Dichev, D. Diakov, R. Dicheva, I. Zhelezarov, and O. Kupriyanov, “Analysis of instrumental errors influence on the accuracy of instruments for measuring parameters of moving objects,” in Proc. XXXI Int. Scientific Symp. Metrology and Metrology Assurance (MMA), Sozopol, Bulgaria, 2021, pp. 91–95, doi: 10.1109/MMA52675.2021.9610855.
[13] Z. Huang, Q. Xu, M. Sun, X. Zhu, and S. Fan, “Adaptive Kalman filtering localization calibration method based on dynamic mutation perception and collaborative correction,” Entropy, vol. 27, no. 4, p. 380, 2025.
[14] I. Malakov, Tz. Georgiev, V. Zaharinov, A. Tzokev, and V. Tzenov, “Demand modeling for the optimization of size ranges,” in Proc. 26th DAAAM Int. Symp., Vienna, Austria, 2015, pp. 435–444, doi: 10.2507/26th.daaam.proceedings.058.
[15] P. Mitev, “Development of a training station for the orientation of dice parts with machine vision,” Engineering Proceedings, vol. 70, p. 57, 2024, doi: 10.3390/engproc2024070057.
[16] T. Islam, M. Ferrer, M. de Diego, and A. Gonzalez, “An error innovation-based adaptive Kalman filter for multi-channel active noise control,” Mechanical Systems and Signal Processing, vol. 249, p. 114113, 2026.
[17] G. Iliev and H. Hristov, “Selection and verification of an accurate mathematical model of a proportional directional control valve,” Journal of Physics: Conference Series, vol. 3145, no. 1, p. 012025, 2025, doi: 10.1088/1742-6596/3145/1/012025.
[18] G. Dinev, I. Malakov, and D. Dotsev, “CAD optimal design, documentation and automated assembly of mechanical product,” Advanced Materials Research, vols. 463–464, pp. 1202–1205, 2012, doi: 10.4028/www.scientific.net/AMR.463-464.1202.
[19] X. Liu, H. Xu, D. Zheng, and Y. Quan, “A novel variational Bayesian adaptive Kalman filter with mismatched process noise covariance matrix,” IET Radar, Sonar & Navigation, vol. 17, no. 6, pp. 967–977, 2023.
[20] Q. Ge, X. Hu, Y. Li, H. He, and Z. Song, “A novel adaptive Kalman filter based on credibility measure,” IEEE/CAA Journal of Automatica Sinica, vol. 10, no. 1, pp. 103–120, 2023.
[21] D. Dichev, F. Kogia, H. Nikolova, and D. Diakov, “A mathematical model of the error of measuring instruments for investigating the dynamic characteristics,” Journal of Engineering Science and Technology Review, vol. 11, no. 6, pp. 14–19, 2018, doi: 10.25103/jestr.116.03.
[22] Y. Cheng, S. Zhang, X. Wang, and H. Wang, “Self-tuning process noise in variational Bayesian adaptive Kalman filter for target tracking,” Electronics, vol. 12, no. 18, p. 3887, 2023.
[23] V. Zimparov, V. Petkov, and H. Hristov, “Optimal spacings for channels with Hagen–Poiseuille fluid-flow and mass transfer,” Thermal Science, vol. 25, spec. issue 2, pp. 295–301, 2021, doi: 10.2298/TSCI21S2295Z.
[24] H. Fu and Y. Cheng, “Variational adaptive Kalman filter for unknown measurement loss and inaccurate noise statistics,” Signal Processing, vol. 212, p. 109184, 2023.
[25] P. Mitev, “Development of a system for flexible feeding of parts with robot and machine vision,” Engineering Proceedings, vol. 104, p. 84, 2025, doi: 10.3390/engproc2025104084.
[26] D. Xu, Z. Wu, and Y. Huang, “A new adaptive Kalman filter with inaccurate noise statistics,” Circuits, Systems, and Signal Processing, vol. 38, no. 9, pp. 4380–4404, 2019, doi: 10.1007/s00034-019-01053-w.
[27] N. Madzharov and N. Hinov, “High-performance power converter for charging electric vehicles,” Energies, vol. 14, no. 24, p. 8569, 2021, doi: 10.3390/en14248569.
[28] Y. Bar-Shalom, X. R. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation: Theory, Algorithms, and Software. New York, NY: Wiley, 2001.
[29] X. R. Li and V. P. Jilkov, “Survey of maneuvering target tracking. Part V: Multiple-model methods,” IEEE Trans. Aerosp. Electron. Syst., vol. 41, no. 4, pp. 1255–1321, 2005.
[30] S. Akhlaghi, N. Zhou, and Z. Huang, “Adaptive adjustment of noise covariance in Kalman filter for dynamic state estimation,” in Proc. IEEE Power & Energy Society General Meeting, 2017, pp. 1–5.
[31] S. Särkkä and L. Svensson, Bayesian Filtering and Smoothing, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 2023.
[32] L. Lazov, E. Teirumnieks, N. Angelov, and E. Teirumnieka, “Methodology for automatic determination of contrast of laser marking for different materials,” in ENVIRONMENT. TECHNOLOGY. RESOURCES. Proceedings of the International Scientific and Practical Conference, vol. 3, Jun. 2019, pp. 134–136.
[33] D. Pulov, “ Passive Athermalization of Compact IR Lenses for Accurate Measurements and Visualization of Temperature Fields”, in. Proceedings of the 34th International Scientific Symposium Metrology and Metrology Assurance, MMA 2024. Sozopol, 2024, DOI: 10.1109/MMA62616.2024.10817630.
[34] Z. Chen, “Bayesian filtering: From Kalman filters to particle filters, and beyond,” Statistics, vol. 182, no. 1, pp. 1–69, 2003.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Dimitar Dichev, Iliya Zhelezarov, Tsanko Karadzhov, Kaloyan Libchev
This work is licensed under a Creative Commons Attribution 4.0 International License.
