Comparing Kalman Filter and Diffuse Kalman Filter on a GPS Signal with Noise
Volume 9, Issue 1, Page No 124-132, 2024
Author’s Name: Maximo Giovani Tandazo Espinozaa)
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Universidad Politécnica Salesiana, Computer Science, Guayaquil, Ecuador
a)whom correspondence should be addressed. E-mail: mtandazo@ups.edu.ec
Adv. Sci. Technol. Eng. Syst. J. 9(1), 124-132 (2024); 
DOI: 10.25046/aj090112
Keywords: Kalman Filter, Fuzzy Logic, Noise, Measurement, Filtered
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The navigation control of an autonomous vehicle can be determined by the coordinates of a GPS (Global Positioning System) positioning system, angular velocity, and acceleration with an INS (Inertial Navigation System). However, the errors associated with these devices do not allow it to be the only measurement system used in an autonomous vehicle. The need arises to implement tools that determine the system’s state reliably at any instant and perform the necessary control actions to fulfill the trajectory optimally, considering the system’s internal model. Therefore, applying a Diffuse Kalman filter is vital, allowing information integration from GPS and other devices. This work was divided into three essential parts such as the Kalman filter, the fuzzy control, and the simulation of a GPS sensor signal, taking into account that, in this last part, a comparison is made with the behavior of a Diffuse Kalman filter. In general, due to the comparisons of the position estimations in GPS measurements, it is evident that the DKF achieves more efficient reliability values since the position estimation error is reduced.
Received: 21 November 2023, Revised: 21 January 2024, Accepted: 21 January 2024, Published Online: 21 February 2024
- R. E. Kalman, “A New Approach to Linear Filtering and Prediction Problems.” ASME. J. Basic Eng., 82(1): 35–45, 1960, doi:10.1115/1.3662552.
- E. A. Wan, R. van der Merwe, “The unscented Kalman filter for nonlinear estimation,” Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373), 153–158, 2000.
- D.-J. Jwo, S.-Y. Lai, “Navigation Integration Using the Fuzzy Strong Tracking Unscented Kalman Filter,” The Journal of Navigation, 62(2), 303–322, 2009, copyright – Copyright © The Royal Institute of Navigation 2009; U´ ltima actualizaci´on – 2023-11-28.
- C. K. Chui, G. Chen, “Kalman Filtering with Real-Time Applications,” Springer Berlin, Heidelberg, XV, 191, 2009, doi:10.1007/978-3-662-02508-6.
- J. T. Jalles, “Structural Time Series Models and the Kalman Filter: A Concise Review,” SSRN, 541, 153–158, 2009, doi:10.2139/ssrn.1496864.
- G. Bishop, G. Welch, et al., “An introduction to the kalman filter,” Proc of SIGGRAPH, Course, 8(27599-23175), 41, 2001.
- R. J. Meinhold, N. . D. Singpurwalla, “Understanding the kalman filter,” Am. Stat., vol. 37(No. 2), 123–127, 1983.
- H. W. Sorenson, “Least-squares estimation: from Gauss to Kalman,” IEEE Spectrum, 7(7), 63–68, 1970, doi:10.1109/MSPEC.1970.5213471.
- B. Yildirim, Sigmarho Kalman Filter Implementation and Analysis, Ph.D. thesis, California State University, 2020, copyright – Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works; U´ ltima actualizacio´n – 2023-06-21.
- A. Khalid, R. K. Syed Abdul, N. U. Ain, M. Awais, A. S. Majid, J. E. M. Carre˜no, J. C. Vasquez, J. M. Guerrero, B. Khan, “Comparison of Kalman
Filters for State Estimation Based on Computational Complexity of Li-Ion Cells,” Energies, 16(6), 2710, 2023. - M. Grewal, A. Andrews, “Kalman filtering: theory and practice using MATLAB,” New York: John Wiley and Sons, 14, 2001, doi:10.1002/9780470377819.
- R. L. Thomas Doan, C. Sims, “Forecasting and conditional projection using realistic prior distributions,” Econometric Reviews, 3(1), 1–100, 1984, doi:10.1080/07474938408800053.
- J. A. Goguen, “L. A. Zadeh. Fuzzy sets. Information and control, vol. 8 (1965), pp. 338–353. – L. A. Zadeh. Similarity relations and fuzzy orderings. Information sciences, vol. 3 (1971), pp. 177–200.” The Journal of Symbolic Logic, 38(4), 656–657, 1973, doi:10.2307/2272014.
- T. J. Ross, “Fuzzy Logic with Engineering Applications,” Wiley, 3, 1–100, 2010, doi:10.1002/9781119994374.
- I. P. B. Leon, “Logica difusa para principiantes. Teoria y practica,” Publicaciones UCAB, 3, 2007.
- J. Yen, R. Langari, “Fuzzy logic: Intelligence, control, and information,” Prentice Hall, Upper Saddle River NJ, 1999.
- C. Ni, X. Ma, “An integrated long-short term memory algorithm for predicting polar westerlies wave height,” Ocean Engineering, 215, 107715, 2020, doi:https://doi.org/10.1016/j.oceaneng.2020.107715.
- C. Lu, “Concrete materials compressive strength using soft computing techniques,” Multiscale and Multidisciplinary Modeling, Experiments and Design, 2023, doi:10.1007/s41939-023-00276-4.
- R. Srivastava, M. P. S. Bhatia, “Quantifying modified opinion strength: A fuzzy inference system for Sentiment Analysis,” in 2013 International Conference on Advances in Computing, Communications and Informatics (ICACCI), 1512–1519, 2013, doi:10.1109/ICACCI.2013.6637404.
- M. G. Voskoglou, “Fuzzy Logic as a Tool for Assessing Students’ Knowledge and Skills,” Education Sciences, 3(2), 208–221, 2013, doi:10.3390/educsci3020208.
- R. Woo, E.-J. Yang, D.-W. Seo, “A Fuzzy-Innovation-Based Adaptive Kalman Filter for Enhanced Vehicle Positioning in Dense Urban Environments,” Sensors, 19(5), 2019, doi:10.3390/s19051142.
- B. Parrell, V. Ramanarayanan, S. Nagarajan, J. Houde, “The FACTS model of speech motor control: fusing state estimation and task-based control,” bioRxiv, 2019, doi:10.1101/543728.