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Volume 7 Issue 1
Jan.  2020

IEEE/CAA Journal of Automatica Sinica

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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
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  • 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.


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    • 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.


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