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Volume 9 Issue 3
Mar.  2022

IEEE/CAA Journal of Automatica Sinica

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L. J. Dang, B. D. Chen, Y. L. Huang, Y. G. Zhang, and H. Q. Zhao, “Cubature Kalman filter under minimum error entropy with fiducial points for INS/GPS integration,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 450–465, Mar. 2022. doi: 10.1109/JAS.2021.1004350
Citation: L. J. Dang, B. D. Chen, Y. L. Huang, Y. G. Zhang, and H. Q. Zhao, “Cubature Kalman filter under minimum error entropy with fiducial points for INS/GPS integration,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 450–465, Mar. 2022. doi: 10.1109/JAS.2021.1004350

Cubature Kalman Filter Under Minimum Error Entropy With Fiducial Points for INS/GPS Integration

doi: 10.1109/JAS.2021.1004350
Funds:  This work was supported by the Fundamental Research Funds for the Central Universities (xzy022020045) and the National Natural Science Foundation of China (61976175)
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  • Traditional cubature Kalman filter (CKF) is a preferable tool for the inertial navigation system (INS)/global positioning system (GPS) integration under Gaussian noises. The CKF, however, may provide a significantly biased estimate when the INS/GPS system suffers from complex non-Gaussian disturbances. To address this issue, a robust nonlinear Kalman filter referred to as cubature Kalman filter under minimum error entropy with fiducial points (MEEF-CKF) is proposed. The MEEF-CKF behaves a strong robustness against complex non-Gaussian noises by operating several major steps, i.e., regression model construction, robust state estimation and free parameters optimization. More concretely, a regression model is constructed with the consideration of residual error caused by linearizing a nonlinear function at the first step. The MEEF-CKF is then developed by solving an optimization problem based on minimum error entropy with fiducial points (MEEF) under the framework of the regression model. In the MEEF-CKF, a novel optimization approach is provided for the purpose of determining free parameters adaptively. In addition, the computational complexity and convergence analyses of the MEEF-CKF are conducted for demonstrating the calculational burden and convergence characteristic. The enhanced robustness of the MEEF-CKF is demonstrated by Monte Carlo simulations on the application of a target tracking with INS/GPS integration under complex non-Gaussian noises.


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    • The MEEF-CKF is developed by applying the minimum error entropy with fiducial points (MEEF) to CKF, where the MEEF can automatically locate the peak of the error probability density function (PDF) at zero and is beneficial for robustness enhancement
    • A novel optimization approach is presented for determining the free parameters of MEEF-CKF adaptively
    • The complexity of MEEF-CKF is analyzed in detail, which indicates an acceptable burden in comparison with traditional Kalman filters. In addition, a sufficient condition is provided for ensuring the convergence of the fixed-point iteration in MEEF-CKF
    • The novel MEEF-CKF is applied for target tracking with the INS/GPS integration under different non-Gaussian noises. Simulation results have demonstrated the robustness of MEEF-CKF and the effectiveness of parameter optimization


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