  We obtain a class of higher-degree stochastic integration filters (SIF) for
nonlinear filtering applications. SIF are based on stochastic spherical-radial
integration rules that achieve asymptotically exact evaluations of Gaussian
weighted multivariate integrals found in nonlinear Bayesian filtering. The
superiority of the proposed scheme is demonstrated by comparing the performance
of the proposed fifth-degree SIF against a number of existing stochastic,
quasi-stochastic and cubature (Kalman) filters. The proposed filter is
demonstrated to outperform existing filters in all cases.
