Exponentially Fitted Cubature Kalman Filter With Application to Oscillatory Dynamical Systems

This paper proposes a new nonlinear filtering technique under the Gaussian filtering approach, which is based on the numerical approximation of intractable integrals. The proposition is in the category of spherical-radial rule based Gaussian filtering (dominated by cubature Kalman filter), which is most commonly used in practical applications. The existing Gaussian filters with spherical-radial rule are accurate only for the systems modelled with polynomials of a certain order and suffer from poor estimation accuracy for the oscillatory systems. The proposed method, however, provides an efficient approach for estimation and filtering in oscillatory environment. It introduces an exponentially-fitted spherical-radial rule of numerical approximation, which is accurate for oscillatory functions. The exponentially-fitted spherical-radial rule is composed of a third-degree spherical-cubature rule and an exponentially-fitted Gauss-Laguerre quadrature rule. The proposed filter is named as exponentially-fitted cubature Kalman filter (ECKF). The estimation accuracy of the ECKF is analyzed for nonlinear filtering problems related to the Duffing and Coulomb oscillators in terms of root mean square error (RMSE). The RMSE analysis concludes an improved estimation accuracy for the proposed ECKF compared to the existing Gaussian filters.