Noise Reduction Techniques for Sensor Data: Comparative Analysis of Kalman, Butterworth, Savitzky-Golay, Median, and Moving Average Filters for UWB-Based Position Estimation

Abstract

Accurate localization of autonomous mobile systems has become a critical requirement in modern engineering applications. However, field environments often lead to erroneous position data due to signal interference or unexpected behaviors of signals in the presence of obstacles. In this study, raw data obtained from an Ultra-Wideband (UWB) positioning system was intentionally degraded by amplification and the addition of artificial noise to simulate realistic signal corruption. Subsequently, five different filters were evaluated to denoise this highly contaminated data. The performance of each filter was tested using custom-developed software by comparing its unoptimized and optimized configurations. As a key outcome, the optimal parameter set of the most effective filter for noise reduction was identified and reported.

Keywords

• Kalman
• Butterworth
• Savitzky-Golay
• Median
• Filters
• MAF

References

1. [1]. Wang, W., Guo, Y., Huang, B., Zhao, G., Liu, B., Wang, L. 2011. Analysis of Filtering Methods for 3D Acceleration Signals in Body Sensor Network. Proceedings of the International Symposium on Bioelectronics and Bioinformations. Suzhou, China, pp. 263–266. https://doi.org/10.1109/ISBB.2011.6107697.
2. [2]. Ullah, I., Shen, Y., Su, X., Esposito, C., Choi, C. 2020. A localization based on unscented Kalman Filter and particle filter localization algorithms. IEEE Access, 8: 2233–2246. https://doi.org/10.1109/ACCESS.2019.2961740.
3. [3]. Xu, Y., Shmaliy, Y.S., Li, Y., Chen, X. 2017. UWB-based indoor human localization with time-delayed data using EFIR filtering. IEEE Access, 5: 16676–16683. https://doi.org/10.1109/ACCESS.2017.2743213.
4. [4]. Hurtado-Perez, A.E., Toledano-Ayala, M., Cruz-Albarran, I.A., Lopez-Zúñiga, A.; Moreno-Perez, J.A., Álvarez-López, A., Rodriguez-Resendiz, J., Perez-Ramirez, C.A. 2025. Use of technologies for the acquisition and processing strategies for motion data analysis. Biomimetics, 10: 339. https://doi.org/10.3390/biomimetics10050339.
5. [5]. Borhan, N.; Saleh, I.; Rahiman, W. 2024. Comparative analysis of filtering techniques for AGV indoor localization with ultra-wideband technology. Pertanika Journal of Science & Technology, 32: 2151–2164, https://doi.org/10.47836/pjst.32.5.13.
6. [6]. Kim, Y., Bang, H. 2019. Introduction to Kalman Filter and Its Applications. In: Govaers, F. (ed.) Introduction and Implementations of the Kalman Filter; IntechOpen, London, UK. ISBN 978-1-83880-536-4.
7. [7]. You, W., Li, F., Liao, L., Huang, M. 2020. Data fusion of UWB and IMU based on unscented Kalman Filter for indoor localization of quadrotor UAV. IEEE Access, 8: 64971–64981. https://doi.org/10.1109/ACCESS.2020.2985053.
8. [8]. Bai, Y., Yan, B., Zhou, C., Su, T., Jin, X. 2023. State of art on state estimation: Kalman Filter driven by machine learning. Annual Reviews in Control, 56: 100909. https://doi.org/10.1016/j.arcontrol.2023.100909.

9. [9]. Garcia, R.V., Pardal, P.C.P.M., Kuga, H.K., Zanardi, M.C. 2019. Nonlinear filtering for sequential spacecraft attitude estimation with real data: Cubature Kalman Filter, Unscented Kalman Filter and Extended Kalman Filter. Advances in Space Research, 63: 1038–1050. https://doi.org/10.1016/j.asr.2018.10.003.
10. [10]. Ma, W., Wang, C., Dang, L., Zhang, X., Chen, B. 2023. Robust dynamic state estimation for DFIG via the generalized maximum correntropy criterion Ensemble Kalman Filter. IEEE Transactions on Instrumentation and Measurement, 72: 1–13. https://doi.org/10.1109/TIM.2023.3328095.
11. [11]. Li, Q., Li, R., Ji, K., Dai, W. 2015. Kalman Filter and its application. Proceedings of the 8th International Conference on Intelligent Networks and Intelligent Systems (ICINIS), Tianjin, China, pp. 74–77. https://doi.org/10.1109/ICINIS.2015.35.
12. [12]. Romanenko, A., Castro, J.A.A.M. 2004. The unscented filter as an alternative to the EKF for nonlinear state estimation: a simulation case study. Computers & Chemical Engineering, 28: 347–355. https://doi.org/10.1016/S0098-1354(03)00193-5.
13. [13]. Piskorowski, J. 2006. Phase-compensated time-varying Butterworth filters. Analog Integrated Circuits and Signal Processing, 47: 233–241. https://doi.org/10.1007/s10470-006-5255-9.
14. [14]. Manal, K., Rose, W. 2007. A general solution for the time delay introduced by a low-pass Butterworth digital filter: an application to musculoskeletal modeling. Journal of Biomechanics, 40: 678–681. https://doi.org/10.1016/j.jbiomech.2006.02.001.
15. [15]. Robertson, D.G.E., Dowling, J.J. 2003. Design and responses of Butterworth and critically damped digital filters. Journal of Electromyography and Kinesiology, 13: 569–573. https://doi.org/10.1016/S1050-6411(03)00080-4.
16. [16]. Bharathi, M., Akshitha, K., Divyashree, M., Nagakrupa, B., Sindhu, J. 2021. OTA based 2nd order Butterworth filter for mobile communication using CMOS technology. Proceedings of the First International Conference on Advanced Scientific Innovation in Science, Engineering and Technology (ICASISET), Chennai, India, pp. 1–7. http://doi.org/10.4108/eai.16-5-2020.2304039.
17. [17]. Schmid, M., Rath, D., Diebold, U. 2022. Why and how Savitzky–Golay filters should be replaced. ACS Measurement Science Au, 2: 185–196. https://doi.org/10.1021/acsmeasuresciau.1c00054.
18. [18]. Sadeghi, M., Behnia, F., Amiri, R. 2020. Window selection of the Savitzky–Golay filters for signal recovery from noisy measurements. IEEE Transactions on Instrumentation and Measurement, 69: 5418–5427. https://doi.org/10.1109/TIM.2020.2966310.
19. [19]. Savitzky, A., Golay, M.J.E. 1964. Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 36: 1627–1639. https://doi.org/10.1021/ac60214a047.
20. [20]. Huang, T., Yang, G., Tang, G. 1979. A fast two-dimensional median filtering algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 27: 13–18. https://doi:10.1109/TASSP. 1979.1163188.
21. [21]. Klenk, J., Becker, C., Lieken, F., Nicolai, S., Maetzler, W., Alt, W., et al. 2011. Comparison of acceleration signals of simulated and real-world backward falls. Medical Engineering & Physics, 33: 368–373. https://doi.org/10.1016/j.medengphy.2010.11.003.
22. [22]. Golestan, S., Ramezani, M., Guerrero, J.M., Freijedo, F.D., Monfared, M. 2014. Moving average filter based phase-locked loops: performance analysis and design guidelines. IEEE Transactions on Power Electronics, 29: 2750–2763. https://doi.org/10.1109/TPEL.2013.2273461.
23. [23]. Wang, J., Liang, J., Gao, F., Zhang, L., Wang, Z. 2015. A method to improve the dynamic performance of moving average filter-based PLL. IEEE Transactions on Power Electronics, 30: 5978–5990. https://doi.org/10.1109/TPEL.2014.2381673.
24. [24]. Freijedo, F.D., Doval-Gandoy, J., López, Ó., Acha, E. 2009. A generic open-loop algorithm for three-phase grid voltage/current synchronization with particular reference to phase, frequency, and amplitude estimation. IEEE Transactions on Power Electronics, 24: 94–107. https://doi.org/10.1109/TPEL.2008.2005580.
25. [25]. Van Herbruggen, B., Luchie, S., Wilssens, R., De Poorter, E. 2024. Single anchor localization by combining UWB angle-of-arrival and two-way-ranging: an experimental evaluation of the DW3000. Proceedings of the International Conference on Localization and GNSS (ICL-GNSS), Antwerp, Belgium, pp. 1–7. https://doi.org/10.1109/ICL-GNSS60721.2024.10578498.
26. [26]. Niculescu, V., Palossi, D., Magno, M., Benini, L. 2023. Energy-efficient, precise UWB-based 3-D localization of sensor nodes with a nano-UAV. IEEE Internet of Things Journal, 10: 5760–5777. https://doi.org/10.1109/JIOT.2022.3166651.
27. [27]. Makerfabs. ESP32 UWB Pro with Display. https://www.makerfabs.com/esp32-uwb-pro-with-display.html (accessed at 23.02.2025).
28. [28]. Silva, B., Pang, Z., Akerberg, J., Neander, J., Hancke, G. 2014. Experimental study of UWB-based high precision localization for industrial applications. Proceedings of the IEEE International Conference on Ultra-WideBand (ICUWB), Paris, France, pp. 280–285. https://doi.org/10.1109/ICUWB.2014.6958993
29. [29]. Gonzalez, R.C., Woods, R.E. 2018. Digital Image Processing; 4th ed., Pearson Education: New York, USA: Pearson Education.
30. [30]. Hagedorn, J., Alicke, F., Verma, A. 2017. How to measure total jitter. Texas Instruments Application Note, SCAA120B.
31. [31]. Alt, H., Godau, M. 1995. Computing the Fréchet distance between two polygonal curves. International Journal of Computational Geometry & Applications, 5: 75–91. https://doi.org/10.1142/S0218195995000064.
32. [32]. Chicco, D., Warrens, M.J., Jurman, G. 2021. The coefficient of determination R-Squared is More informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation. PeerJ Computer Science, 7: e623. https://doi.org/10.7717/peerj-cs.623.