International Journal of Nonlinear Analysis and Applications
A new modification of Kalman filter algorithm
Document Type : Research Paper
Authors
1 Department of Mathematics, Faculty of Computer Science and Mathematics, University of Kufa, Iraq
2 Ministry of Education, Najaf, Iraq
Abstract
This study is concerned with estimating random data and in the presence of noise, as we used the Kalman filter estimation method through the backpropagation algorithm to estimate these data. This is because modern estimation methods have become more important as they were in the past years due to the expansion of the field of science and technology and the increasing data Therefore, the interest became in estimation methods that solve the noise problems that occur in the data. The Kalman filter has become one of the most popular and most reliable estimators in case of data noise. This study tests the use of the Kalman filter and Back Propagation algorithm to estimate the data containing noise and compare the results with the proposed method on the same data. The data is generated randomly in the simulation study. The results showed that Kalman is more efficient in filtering noise from the data and giving a lower mean square error compared to the backpropagation algorithm, but the results of the proposed method outperformed the results of the Kalman filter and the backpropagation with the least possible error.
Keywords
[3] M. D. Bedworth and J. S. Bridle, Experiments With the Back Propagation Algorithm a Systematic Look at a Small Problem, Royal Singals And Radar Establishment (RSRE), 1987.
[4] N. Bisoyi, H. Gupta, N. P. Padhy and G. J. Chakrapani, Prediction of daily sediment discharge using a back propagation neural network training algorithm: A case study of the Narmada River, India, Int. J. Sediment Res. 34(2) (2018) 125–135.
[5] L. Das, N. Kumar, R. S. Lather and P. Bhatia, Emerging Trends in Mechanical Engineering: Select Proceedings of ICETMIE, Springer, 2021.
[6] F. Govaers, Introduction and Implementations of the Kalman Filter, InTechOpen, 2019.
[7] S. Haykin, Kalman Filtering and Neural Networks, Wiley-Interscience, 2001.
[8] Y. Huang, Y. Zhang, Z. Wu, N. Li and J. Chambers, A novel robust student’s t-based Kalman filter, IEEE Trans. Aerospace Elect. Syst. 53(3) (2017) 1545–1554.
[9] J. Humpherys, P. Redd and J. West, A fresh look at the kalman filter, Siam Review, 54(4) (2012) 801-–823.
[10] D. Jin and S. Lin, Advances in Computer Science and Information Engineering, Springer-Verlag, Berlin Heidelberg, 2012.
[11] R. Kalman, A new approach to linear filtering and prediction problems, J. Basic Eng. 82(1) (1960) 35–45.
[12] R. Kleinbauer, Kalman Filtering Implementation with Matlab, Universit¨at Stuttgart, 2004.
[13] M. Kianpour, E. Mohammadinasab and T. M. Isfahani, Comparison between genetic algorithm-multiple linear regression and back-propagation-artificial neural network methods for predicting the LD50 of organo (phosphate and thiophosphate) compounds, Journal of the Chinese Chemical Soc. 67(8) (2020) 1356–1366.
[14] B. Lagos-Alvarez, L. Padilla, J. Mateu and G. Ferreira, ´ A Kalman filter method for estimation and prediction of space–time data with an autoregressive structure, J. Stat. Plann. Inf. 203 (2019) 117–130.
[15] Q. Li, R. Li, K. Ji and W. Dai, Kalman filter and its application, Int. Conf. Intel. Networks Intel. Syst. (2015), doi: 10.1109/ICINIS.2015.35.
[16] T. P. Lillicrap, A. Santoro, L. Marris, C. J. Akerman and G. Hinton, Backpropagation and the brain, Nature Reviews Neurosci.21 (2020) 335—346.
[17] H. Ma, L. Yan, Y. Xia and M. Fu, Kalman Filtering and Information Fusion, Springer Singapore, 2020.
[18] N. M. Nawi, N. M. Zaidi, N. A. Hamid, M. Z. Rehman, A. A. Ramli and S. Kasim, Optimal parameter selection using three-term back propagation algorithm for data classification, Int. J. Adv. Sci. Engin. Inf. Tech. 7(4-2) (2017) 1528–1534.
[19] B. Nalepa and A. Gwiazda, Kalman filter estimation of angular acceleration, IOP Conf. Series: Mat. Sci. Engin.
2020.
[20] K. L. Priddy and P. E. Keller, Artificial Neural Networks: An Introduction, Spie, 2005.
[21] S. Setti and A. Wanto, Analysis of backpropagation algorithm in predicting the most number of internet users in the world, J. Online Inf. 3(2) (2018) 110–115.
[22] M. Sornam and M. P. Devi, A survey on back propagation neural network, Int. J. Commun. Network. Syst. 5(1) (2016) 70–74.
[23] G. Tricoles, E. Rope and O. Yue, Enhancement of short-range microwave images produced by backward propagation, Soc. Photo-Optical Instrum. Engin. 1977 (1977), https://doi.org/10.1117/12.955670.
[24] B. Ul Islam, A. Mukhtar, S. Saqib, A. Mahmood, S. Rafiq, A. Hameed, M. Saad Khan, K. Hamid, S. Ullah, A. Al-Sehemi and M. Ibrahim, Thermal conductivity of multiwalled carbon nanotubes-kapok seed oil-based nanofluid, Chemical Engin. Tech. 48(8) (2020) 1638–1647.
[25] G. Welch and G. Bishop, An Introduction to the Kalman Filter, University of North Carolina at Chapel Hill, TR, 2006.
[26] X. Zhang, X. Chen and J. Li, Improving dam seepage Prediction using back-propagation neural network and genetic algorithm, Math. Prob. Engin. 2020 (2020) Article ID 1404295.
[27] S. Zhao and B. Huang, Trial-and-error or avoiding a guess? initialization of the Kalman filter, Autom. 121 (2020) 109184.
)
Volume 12, Issue 2
November 2021Pages 1199-1212
- Receive Date: 10 April 2021
- Revise Date: 09 May 2021
- Accept Date: 27 May 2021