  This paper proposes a symbolic-numeric Bayesian filtering method for a class
of discrete-time nonlinear stochastic systems to achieve high accuracy with a
relatively small online computational cost. The proposed method is based on the
holonomic gradient method (HGM), which is a symbolic-numeric method to evaluate
integrals efficiently depending on several parameters. By approximating the
posterior probability density function (PDF) of the state as a Gaussian PDF,
the update process of its mean and variance can be formulated as evaluations of
several integrals that exactly take into account the nonlinearity of the system
dynamics. An integral transform is used to evaluate these integrals more
efficiently using the HGM than our previous method. Further, a numerical
example is provided to demonstrate the efficiency of the proposed method
compared to other existing methods.
