A robust Student's t based cubature filter

In the paper, a novel third-degree Student's t spherical-radial cubature rule (SRCR) is proposed, from which a new robust Student's t based cubature filter is developed. The standard third-degree SRCR is a special case of the proposed Student's t SRCR when the degrees of freedom parameter tends to infinity. Moreover, the proposed Student's t SRCR is identical to the unscented transform (UT) when the free parameter of the UT equals to zero, which provides a reasonable choice of the free parameter of the UT for the calculation of the Student's t weighted integral. Finally, the effectiveness and superiority of the proposed filter is illustrated in two representative examples concerning univariate non-stationary growth model and target tracking.