Filters relying on the Gaussian approximation typically incorporate the measurement linearly, i.e., the value of the measurement is premultiplied by a matrix-valued gain in the state update. Nonlinear filters that relax the Gaussian assumption, on the other hand, typically approximate the distribution of the state with a finite sum of point masses or Gaussian distributions. In this work, the distribution of the state is approximated by a polynomial transformation of a Gaussian distribution, allowing for all moments, central and raw, to be rapidly computed in a closed form. Knowledge of the higher order moments is then employed to perform a polynomial measurement update, i.e., the value of the measurement enters the update function as a polynomial of arbitrary order. A filter employing a Gaussian approximation with linear update is, therefore, a special case of the proposed algorithm when both the order of the series and the order of the update are set to one: it reduces to the extended Kalman filter. At the cost of more computations, the new methodology guarantees performance better than the linear/Gaussian approach for nonlinear systems. This work employs monomial basis functions and Taylor series, developed in the differential algebra framework, but it is readily extendable to an orthogonal polynomial basis.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Nonlinear Filtering With a Polynomial Series of Gaussian Random Variables


    Contributors:


    Publication date :

    2021-02-01


    Size :

    2439638 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Nonlinear Gaussian Mixture Filtering with Intrinsic Fault Resistance

    Fritsch, Gunner S. / DeMars, Kyle J. | AIAA | 2021


    Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models

    Jianjun, Y. / Jianqiu, Z. / Zesen, Z. | British Library Online Contents | 2008


    A Gaussian Filtering Method for Multitarget Tracking With Nonlinear/Non-Gaussian Measurements

    F. Garcia-Fernandez, Angel / Ralph, Jason / Horridge, Paul et al. | IEEE | 2021


    Nonlinear Gaussian Filtering With Network-Induced Delay in Measurements

    Kumar, Guddu / Nanda, Sumanta Kumar / Verma, Alok Kumar et al. | IEEE | 2022


    FORM-Based Filtering of Limit States for Gaussian Random Fields

    Sparkman, D. / Domyancic, L. / Millwater, H. et al. | British Library Conference Proceedings | 2010