Volume 30 Issue 3
May  2021
Turn off MathJax
Article Contents
SUN Xiaohui, WEN Chenglin, WEN Tao, “High-Order Extended Kalman Filter Design for a Class of Complex Dynamic Systems with Polynomial Nonlinearities,” Chinese Journal of Electronics, vol. 30, no. 3, pp. 508-515, 2021, doi: 10.1049/cje.2021.04.004
Citation: SUN Xiaohui, WEN Chenglin, WEN Tao, “High-Order Extended Kalman Filter Design for a Class of Complex Dynamic Systems with Polynomial Nonlinearities,” Chinese Journal of Electronics, vol. 30, no. 3, pp. 508-515, 2021, doi: 10.1049/cje.2021.04.004

High-Order Extended Kalman Filter Design for a Class of Complex Dynamic Systems with Polynomial Nonlinearities

doi: 10.1049/cje.2021.04.004
Funds:

This work is supported by the National Natural Science Foundation of China (No.61751304, No.61806064, No.61933013, No.U1664264) and Science and Technology Project of China Electric Power Research Institute (No.SGHB0000KXJS1800375).

  • Received Date: 2020-06-29
  • A novel High-order extended Kalman Filter (HEKF) is designed for a class of complex dynamic systems with polynomial nonlinearities. The state and measurement models are represented by multi-dimensional high-order polynomials, respectively. All high-order polynomials in the state model are defined as implicit variables. By combining original variables with implicit variables, the state model is equivalently formulated to be a pseudo-linear form. By modeling dynamic relationship between implicit variables and combining original variables with all implicit variables, a new linear augmented state model is established correspondingly. The measurement model can be equivalently formulated as a linear form. On the basis of the new linear state and linear measurement models, the HEKF is designed and derived in detail. Simulation results demonstrate the effectiveness of the proposed estimator.
  • loading
  • Z.H. Li, L. Ning and S.N. Xu, “Nonlinear non-Gaussian system filtering based on Gaussian sum and divided difference filter”, Control and Decision, Vol.27, No.1, pp.129–134, 2012. (in Chinese)
    Q.B. Ge, T.L. Xu, X.L. Feng, et al., “Universal delayed kalman filter with measurement weighted summation for the linear time invariant system”, Chinese Journal of Electronics, Vol.20, No.1, pp.67–72, 2011.
    C.B. Wen, Z.D. Wang, Q.Y. Liu, et al., “Recursive distributed filtering for a class of state-saturated systems with fading measurements and quantization effects”, IEEE Transactions on Systems, Man and Cybernetics: Systems, Vol.48, No.6, pp.930–941, 2018.
    T. Wen, C. Constantinou, L. Chen, et al., “A practical access point deployment optimization strategy in communication-based train control systems”, IEEE Transactions on Intelligent Transportation Systems, Vol.20, No.8, pp.3156–3167, 2019.
    C.L. Wen, Q.B. Ge, X.S. Cheng, et al., “Filters design based on multiple characteristic functions for the grinding process cylindrical workpieces”, IEEE Transactions on Industrial Electronics, Vol.64, No.6, pp.4671–4679, 2017
    C.L. Wen, X.S. Cheng, D.X Xu, et al., “Filter design based on characteristic functions for one class of multidimensional nonlinear non-Gaussian systems”, Automatica, Vol.82, pp.171–180, 2017.
    R.E. Kalman, “A new approach to linear filter and prediction problem”, IEEE Transactions of the ASME Journal of Basic Engineering, Vol.82, pp.35–45, 1960.
    Y. Sunahara and K. Yamashita, “An approximate method of state estimation for nonlinear dynamical systems with state-dependent noise”, International Journal of Control, Vol.11, No.4, pp.957–972, 1970.
    R.J. Meinhold and N.D. Singpurwalla, “Robustification of Kalman filter models”, Journal of the American Statistical Association, Vol.84, No.406, pp.479–486, 1989.
    S.J. Julier and J.K. Uhlmann, “Unscented filtering and nonlinear estimation”, Proceedings of the IEEE, Vol.92, No.3, pp.401–422, 2004.
    L. Wang, X.H. Cheng and S.X. Li, “Gaussian sum high order unscented kalman filtering algorithm”, Acta Electronica Sinica, Vol.45, No.2, pp.424–430, 2017. (in Chinese)
    I. Arasaratnam and S. Haykin, “Cubature Kalman filters”, IEEE Transactions on Automatic Control, Vol.54, No.6, pp.1254–1269, 2009.
    I. Arasaratnam and S. Haykin, “Square-root quadrature Kalman filtering”, IEEE Transactions on Signal Processing, Vol.56, No.6, pp.2589–2593, 2008.
    K. Kowalski and W.H. Steeb, Nonlinear Dynamical Systems and Carleman Linearization, World Scientific, Singapore, 1991.
    A.Germani, C.Manes and P.Palumbo, “Polynomial extended Kalman filter”, IEEE Transactions on Automatic Control, Vol.50, No.12, pp.2059–2064, 2005.
    Y. Liu, Z.D. Wang, X. He, et al., “Filtering and fault detection for nonlinear systems with polynomial approximation”, Automatica, Vol.54, pp.348–359, 2015.
    A. Germani, C. Manes and P.Palumbo, “Polynomial extended Kalman filtering for discrete-time nonlinear stochastic systems”, In Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii USA, pp.886–891, 2003.
    A. Germani, C. Manes and P.Palumbo, “Filtering of stochastic nonlinear differential systems via a Carleman approximation approach”, IEEE Transactions on Automatic Control, Vol.52, No.11, pp.2166–2172, 2007.
    A. Germani, C. Manes and P.Palumbo, “State estimation of stochastic systems with switching measurements: A polynomial approach”, International Journal of Robust and Nonlinear Control, Vol.19, No.14, pp.1632–1655, 2009.
    G.Mavelli and P. Palumbo, “The Carleman approximation approach to solve a stochastic nonlinear control problem”, IEEE Transactions on Automatic Control, Vol.55, No.4, pp.976–982, 2010.
    C.Zhang and H.S. Yan, “Identification of nonlinear time-varying system with noise based on multi-dimensional Taylor network with optimal structure”, Journal of Southeast University, Vol.47, No.6, pp.1086–1093, 2017. (in Chinese)
  • 加载中

Catalog

    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

    Article Metrics

    Article views (684) PDF downloads(47) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return