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.


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    Titel :

    Nonlinear Filtering With a Polynomial Series of Gaussian Random Variables


    Beteiligte:


    Erscheinungsdatum :

    2021-02-01


    Format / Umfang :

    2439638 byte




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



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