IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v536y2019ics0378437119314876.html
   My bibliography  Save this article

A noise-immune Kalman filter for short-term traffic flow forecasting

Author

Listed:
  • Cai, Lingru
  • Zhang, Zhanchang
  • Yang, Junjie
  • Yu, Yidan
  • Zhou, Teng
  • Qin, Jing

Abstract

This paper formulates the traffic flow forecasting task by introducing a maximum correntropy deduced Kalman filter. The traditional Kalman filter is based on minimum mean square error, which performs well under Gaussian noises. However, the real traffic flow data are fulfilled with non-Gaussian noises. The traditional Kalman filter may rot under this situation. The Kalman filter deduced by maximum correntropy criteria is insensitive to non-Gaussian noises, meanwhile retains the optimal state mean and covariance propagation of the traditional Kalman filter. To achieve this, a fix-point algorithm is embedded to update the posterior estimations of maximum correntropy deduced Kalman filter. Extensive experiments on four benchmark datasets demonstrate the outperformance of this model for traffic flow forecasting.

Suggested Citation

  • Cai, Lingru & Zhang, Zhanchang & Yang, Junjie & Yu, Yidan & Zhou, Teng & Qin, Jing, 2019. "A noise-immune Kalman filter for short-term traffic flow forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    • Handle: RePEc:eee:phsmap:v:536:y:2019:i:c:s0378437119314876
    DOI: 10.1016/j.physa.2019.122601
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119314876
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.122601?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cheng, Anyu & Jiang, Xiao & Li, Yongfu & Zhang, Chao & Zhu, Hao, 2017. "Multiple sources and multiple measures based traffic flow prediction using the chaos theory and support vector regression method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 422-434.
    2. Cai, Weihong & Yu, Ding & Wu, Ziyu & Du, Xin & Zhou, Teng, 2019. "A hybrid ensemble learning framework for basketball outcomes prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 528(C).
    3. Ma, Tao & Zhou, Zhou & Abdulhai, Baher, 2015. "Nonlinear multivariate time–space threshold vector error correction model for short term traffic state prediction," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 27-47.
    4. E, Jianwei & Ye, Jimin & Jin, Haihong, 2019. "A novel hybrid model on the prediction of time series and its application for the gold price analysis and forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    5. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    6. Xiao, Jianli & Wei, Chao & Liu, Yuncai, 2018. "Speed estimation of traffic flow using multiple kernel support vector regression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 989-997.
    7. Wang, Yibing & Papageorgiou, Markos, 2005. "Real-time freeway traffic state estimation based on extended Kalman filter: a general approach," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 141-167, February.
    8. Yang, Dazhi & Sharma, Vishal & Ye, Zhen & Lim, Lihong Idris & Zhao, Lu & Aryaputera, Aloysius W., 2015. "Forecasting of global horizontal irradiance by exponential smoothing, using decompositions," Energy, Elsevier, vol. 81(C), pages 111-119.
    9. Okutani, Iwao & Stephanedes, Yorgos J., 1984. "Dynamic prediction of traffic volume through Kalman filtering theory," Transportation Research Part B: Methodological, Elsevier, vol. 18(1), pages 1-11, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ze Dong & Yipeng Zhou & Xiongguan Bao, 2024. "A Short-Term Vessel Traffic Flow Prediction Based on a DBO-LSTM Model," Sustainability, MDPI, vol. 16(13), pages 1-21, June.
    2. Chen, Xinqiang & Chen, Huixing & Yang, Yongsheng & Wu, Huafeng & Zhang, Wenhui & Zhao, Jiansen & Xiong, Yong, 2021. "Traffic flow prediction by an ensemble framework with data denoising and deep learning model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    3. Zhanzhong Wang & Ruijuan Chu & Minghang Zhang & Xiaochao Wang & Siliang Luan, 2020. "An Improved Hybrid Highway Traffic Flow Prediction Model Based on Machine Learning," Sustainability, MDPI, vol. 12(20), pages 1-22, October.
    4. Liu, Yang & Song, Yaolun & Zhang, Yan & Liao, Zhifang, 2022. "WT-2DCNN: A convolutional neural network traffic flow prediction model based on wavelet reconstruction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    5. Fang, Weiwei & Zhuo, Wenhao & Yan, Jingwen & Song, Youyi & Jiang, Dazhi & Zhou, Teng, 2022. "Attention meets long short-term memory: A deep learning network for traffic flow forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    6. Ma, Changxi & Zhang, Bowen & Li, Shukai & Lu, Youpeng, 2024. "Urban rail transit passenger flow prediction with ResCNN-GRU based on self-attention mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).
    7. Tian, Jing & Song, Xianmin & Tao, Pengfei & Liang, Jiahui, 2022. "Pattern-adaptive generative adversarial network with sparse data for traffic state estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    8. Yulong Pei & Songmin Ran & Wanjiao Wang & Chuntong Dong, 2023. "Bus-Passenger-Flow Prediction Model Based on WPD, Attention Mechanism, and Bi-LSTM," Sustainability, MDPI, vol. 15(20), pages 1-20, October.
    9. Chih-Yao Chang & Kuo-Ping Lin, 2020. "Developing Support Vector Machine with New Fuzzy Selection for the Infringement of a Patent Rights Problem," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    10. Huang, Haichao & Chen, Jingya & Sun, Rui & Wang, Shuang, 2022. "Short-term traffic prediction based on time series decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    11. Wenguang Chai & Yuexin Zheng & Lin Tian & Jing Qin & Teng Zhou, 2023. "GA-KELM: Genetic-Algorithm-Improved Kernel Extreme Learning Machine for Traffic Flow Forecasting," Mathematics, MDPI, vol. 11(16), pages 1-15, August.
    12. Shihao Zhao & Shuli Xing & Guojun Mao, 2022. "An Attention and Wavelet Based Spatial-Temporal Graph Neural Network for Traffic Flow and Speed Prediction," Mathematics, MDPI, vol. 10(19), pages 1-15, September.
    13. Fei Wang & Yinxi Liang & Zhizhe Lin & Jinglin Zhou & Teng Zhou, 2024. "SSA-ELM: A Hybrid Learning Model for Short-Term Traffic Flow Forecasting," Mathematics, MDPI, vol. 12(12), pages 1-17, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fang, Weiwei & Zhuo, Wenhao & Yan, Jingwen & Song, Youyi & Jiang, Dazhi & Zhou, Teng, 2022. "Attention meets long short-term memory: A deep learning network for traffic flow forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    2. Ma, Tao & Zhou, Zhou & Abdulhai, Baher, 2016. "Time Series Based Hourly Traffic Flow Prediction on the GTA Freeways Using TSTVEC Model," 57th Transportation Research Forum (51st CTRF) Joint Conference, Toronto, Ontario, May 1-4, 2016 319287, Transportation Research Forum.
    3. Ma, Tao & Zhou, Zhou & Antoniou, Constantinos, 2018. "Dynamic factor model for network traffic state forecast," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 281-317.
    4. Zhang, Jie & Song, Chunyue & Cao, Shan & Zhang, Chun, 2023. "FDST-GCN: A Fundamental Diagram based Spatiotemporal Graph Convolutional Network for expressway traffic forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    5. Han, Yu & Zhang, Mingyu & Guo, Yanyong & Zhang, Le, 2022. "A streaming-data-driven method for freeway traffic state estimation using probe vehicle trajectory data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    6. Wei Zhou & Wei Wang & Xuedong Hua & Yi Zhang, 2020. "Real-Time Traffic Flow Forecasting via a Novel Method Combining Periodic-Trend Decomposition," Sustainability, MDPI, vol. 12(15), pages 1-23, July.
    7. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    8. François R. Velde, 2009. "Chronicle of a Deflation Unforetold," Journal of Political Economy, University of Chicago Press, vol. 117(4), pages 591-634, August.
    9. Florin, Ryan & Olariu, Stephan, 2020. "Towards real-time density estimation using vehicle-to-vehicle communications," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 435-456.
    10. Xing, Tao & Zhou, Xuesong & Taylor, Jeffrey, 2013. "Designing heterogeneous sensor networks for estimating and predicting path travel time dynamics: An information-theoretic modeling approach," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 66-90.
    11. Wen Xu, 2016. "Estimation of Dynamic Panel Data Models with Stochastic Volatility Using Particle Filters," Econometrics, MDPI, vol. 4(4), pages 1-13, October.
    12. Huiming Duan & Xinping Xiao & Lingling Pei, 2017. "Forecasting the Short-Term Traffic Flow in the Intelligent Transportation System Based on an Inertia Nonhomogenous Discrete Gray Model," Complexity, Hindawi, vol. 2017, pages 1-16, July.
    13. Alejandro Rodriguez & Esther Ruiz, 2009. "Bootstrap prediction intervals in state–space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 167-178, March.
    14. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    15. Jean-Luc Gaffard, 2014. "Crise de la théorie et crise de la politique économique. Des modèles d'équilibre général stochastique aux modèles de dynamique hors de l'équilibre," Revue économique, Presses de Sciences-Po, vol. 65(1), pages 71-96.
    16. Salman Huseynov, 2021. "Long and short memory in dynamic term structure models," CREATES Research Papers 2021-15, Department of Economics and Business Economics, Aarhus University.
    17. Tsionas, Mike G., 2021. "Bayesian forecasting with the structural damped trend model," International Journal of Production Economics, Elsevier, vol. 234(C).
    18. Tommaso Proietti, 2002. "Some Reflections on Trend-Cycle Decompositions with Correlated Components," Econometrics 0209002, University Library of Munich, Germany.
    19. Tobias Hartl & Roland Jucknewitz, 2022. "Approximate state space modelling of unobserved fractional components," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 75-98, January.
    20. Broto Carmen & Ruiz Esther, 2009. "Testing for Conditional Heteroscedasticity in the Components of Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-30, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:536:y:2019:i:c:s0378437119314876. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.