A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 7 Issue 1
Jan.  2020

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 15.3, Top 1 (SCI Q1)
    CiteScore: 23.5, Top 2% (Q1)
    Google Scholar h5-index: 77, TOP 5
Turn off MathJax
Article Contents
Abhinoy Kumar Singh, "Fractionally Delayed Kalman Filter," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 169-177, Jan. 2020. doi: 10.1109/JAS.2019.1911840
Citation: Abhinoy Kumar Singh, "Fractionally Delayed Kalman Filter," IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 169-177, Jan. 2020. doi: 10.1109/JAS.2019.1911840

Fractionally Delayed Kalman Filter

doi: 10.1109/JAS.2019.1911840
Funds:  This work was supported by the Department of Science and Technology, Government of India under the Inspire Faculty Award
More Information
  • The conventional Kalman filter is based on the assumption of non-delayed measurements. Several modifications appear to address this problem, but they are constrained by two crucial assumptions: 1) the delay is an integer multiple of the sampling interval, and 2) a stochastic model representing the relationship between delayed measurements and a sequence of possible non-delayed measurements is known. Practical problems often fail to satisfy these assumptions, leading to poor estimation accuracy and frequent track-failure. This paper introduces a new variant of the Kalman filter, which is free from the stochastic model requirement and addresses the problem of fractional delay. The proposed algorithm fixes the maximum delay (problem specific), which can be tuned by the practitioners for varying delay possibilities. A sequence of hypothetically defined intermediate instants characterizes fractional delays while maximum likelihood based delay identification could preclude the stochastic model requirement. Fractional delay realization could help in improving estimation accuracy. Moreover, precluding the need of a stochastic model could enhance the practical applicability. A comparative analysis with ordinary Kalman filter shows the high estimation accuracy of the proposed method in the presence of delay.


  • loading
  • [1]
    R. E. Kalman, " A new approach to linear filtering and prediction problems,” Jr. Basic Eng., vol. 82, no. 1, pp. 35–45, 1960. doi: 10.1115/1.3662552
    B. D. O. Anderson and J. B. Moore, Optimal Filtering. New York: Dover, 2005.
    Y. Bar-Shalom, X. R. Li, and T. Kirubarajan, Estimation With Application to Tracking and Navigation. New York: John Wiley and Sons, 2001.
    D. L. Mills, " Internet Time Synchronization: the network time protocol,” IEEE Trans. Comm., vol. 39, no. 10, pp. 1482–1493, Oct. 1991. doi: 10.1109/26.103043
    U. K. Singh, R. Mitra, V. Bhatia, and A. K. Mishra, " Kernel LMS based estimation techniques for radar systems, ” IEEE Trans. Aero. Elect. Syst., in press, DOI: 10.1109/TAES.2019.2891148.
    A. K. Singh, P. Date, and S. Bhaumik, " A modified Bayesian filter for randomly delayed measurements,” IEEE Trans. Auto. Cont., vol. 62, no. 1, pp. 419–424, Jan. 2017. doi: 10.1109/TAC.2016.2531418
    A. H. Carazo and J. L. Perez, " Extended and unscented filtering algorithms using one-step randomly delayed observations,” Appl. Maths. Comp., vol. 190, no. 2, pp. 1375–1393, July. 2007. doi: 10.1016/j.amc.2007.02.016
    Y. Bar-Shalom, " Update with out-of-sequence measurements in tracking: exact solution,” IEEE Trans. Aero. Elect. Sys., vol. 38, no. 3, pp. 769–777, Jul. 2002. doi: 10.1109/TAES.2002.1039398
    S. Challa, R. J. Evans, and X. Wang, " A Bayesian solution and its approximations to out-of-sequence measurement problems,” Infor. Fusion, vol. 4, no. 3, pp. 185–199, Sep. 2003. doi: 10.1016/S1566-2535(03)00037-X
    S. C. A. Thomopoulos, " Decentralized filtering with random sampling and delay,” Infor. Scien., vol. 81, no. 1–2, pp. 117–131, Nov. 1994. doi: 10.1016/0020-0255(94)90093-0
    S. T. Pan and F. H. Hsiao, " Robust Kalman filter synthesis for uncertain multiple time-delay stochastic systems,” J. Dyn. Sys. Meas. Control, vol. 118, no. 4, pp. 803–808, Dec. 1996. doi: 10.1115/1.2802363
    T. D. Larsen, N. A. Andersen, O. Ravn, et al., " Incorporation of time delayed measurements in a discrete-time Kalman filter, ” in Proc. IEEE Conf. Decis. Control, Tampa, 1998, pp. 16–18.
    J. Nilsson, B. Bernhardsson, and B. Wittenmark, " Stochastic analysis and control of real-time systems with random time delays,” Automatica, vol. 34, no. 1, pp. 57–64, Jan. 2002.
    I. V. Kolmanovskya and T. L. Maizenbergb, " Optimal control of continuous-time linear systems with a time-varying, random delay,” Automatica, vol. 44, no. 2, pp. 119–126, Oct. 2001.
    K. W. Lo, B. G. Ferguson, Y. J. Gao, and A. Maguer, " Aircraft flight parameter estimation using acoustic multipath delays,” IEEE Trans. Aero. Elect. Syst., vol. 39, no. 1, pp. 259–268, Jan. 2003. doi: 10.1109/TAES.2003.1188908
    X. Song, Z. Duan and J. H. Park, " Linear optimal estimation for discretetime systems with measurement-delay and packet dropping,” Appl. Math. Comp., vol. 284, pp. 115–124, July. 2016. doi: 10.1016/j.amc.2016.02.046
    Z. Tang, J. H. Park, and T. H. Lee, " Dynamic output-feedback-based H design for networked control systems with multipath packet dropouts,” Appl. Math. Comp., vol. Feb, pp. 121–133, Mar. 2016.
    A. Ray, L. W. Liou, and J. H. Shen, " State estimation using randomly delayed measurements,” J. Dyn. Sys. Meas. Control, vol. 115, no. 1, pp. 19–26, Mar. 1993. doi: 10.1115/1.2897399
    E. Yaz and A. Ray, " Grammian assignment for stochastic-parameter systems and their stabilization under randomly varying delays, ” in Proc. IEEE Conf. Decis. Control, USA, 1994, pp. 2176–2181.
    E. Yaz and A. Ray, " Linear unbiased state estimation under randomly varying bounded sensor delay,” Appl. Math. Lett., vol. 11, no. 4, pp. 27–32, 1998. doi: 10.1016/S0893-9659(98)00051-2
    X. Lu, H. Zhang, W. Wang, et al, " Kalman filtering for multiple timedelay systems,” Automatica, vol. 41, no. 8, pp. 1455–1461, Aug. 2005. doi: 10.1016/j.automatica.2005.03.018
    X. Lu, L. Xie, H. Zhang, and W. Wang, " Robust Kalman filtering for discrete-time systems with measurement delay,” IEEE Trans. Circ. Sys. II:Exp. Brief, vol. 54, no. 6, pp. 522–526, June. 2007.
    M. Moayedi, Y. K. Foo and Y. C. Soh, " Adaptive Kalman filtering in networked systems with random sensor delays, multiple packet dropouts and missing measurements,” IEEE Trans. Sign. Process., vol. 58, no. 3, pp. 1577–1588, Dec. 2009.
    X. Lu, L. Xie, H. Zhang, and W. Wang, " Robust Kalman filtering for uncertain state delay systems with random observation delays and missing measurements,” IET Control Theo. Appl., vol. 5, no. 17, pp. 1945–1954, Oct. 2011. doi: 10.1049/iet-cta.2010.0685
    S. Sun, " Optimal linear filters for discrete-time systems with randomly delayed and lost measurements with/without time stamps,” IEEE Trans. Auto. Control, vol. 58, no. 6, pp. 1551–1556, Nov. 2012.
    X. Lu, L. Wang, and H. Wang, " Kalman filtering for delayed singular systems with multiplicative noise,” IEEE/CAA J. Autom. Sinica, vol. 3, no. 1, pp. 51–58, Jan. 2016. doi: 10.1109/JAS.2016.7373762
    W. Zimmerman, " On the optimum colored noise Kalman filter,” IEEE Trans. Autom. Cont., vol. 14, no. 2, pp. 194–196, Apr. 1969. doi: 10.1109/TAC.1969.1099149
    W. R. Wu and A. Kundu, " Recursive filtering with non-Gaussian noises,” IEEE Trans. Sign. Proc., vol. 44, no. 6, pp. 1454–1468, Jun. 1996. doi: 10.1109/78.506611
    A. E. Cetin and A. M. Tekalp, " Robust reduced update Kalman filtering,” IEEE Trans. Circ. Syst., vol. 37, no. 1, pp. 155–156, Jan. 1990. doi: 10.1109/31.45708
    D. Liang, " On continuous-time estimation for linear delayed-systems with correlated state and observation noises,” IEEE Trans. Autom. Cont., vol. 22, no. 3, pp. 472–474, Jun. 1977. doi: 10.1109/TAC.1977.1101517
    A. H. Jazwinski, Stochastic Processes and Filtering Theory, New York, 1970.
    S. Sarkka, " On unscented Kalman filtering for state estimation of continuous-time nonlinear systems,” IEEE Trans. Autom. Cont., vol. 59, no. 9, pp. 1631–1641, Sep. 2007.
    X. Wang, Y. Liang, Q. Pan, et al, " Gaussian filter for nonlinear systems with one-step randomly delayed measurements,” Automatica, vol. 49, no. 4, pp. 976–986, April. 2013. doi: 10.1016/j.automatica.2013.01.012


    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(5)  / Tables(2)

    Article Metrics

    Article views (1419) PDF downloads(108) Cited by()


    • A new Kalman filtering algorithm is developed for randomly delayed measurements.
    • Likelihood-based delay identification is introduced to identify the delay.
    • The proposed algorithm accounts for fractional delay possibility.
    • The proposed algorithm precludes a prior knowledge of delay probabilities.


    DownLoad:  Full-Size Img  PowerPoint