Higher-Degree Stochastic Integration Filtering
This work addresses nonlinear filtering applications, but it appears incremental as it builds on existing stochastic integration methods with a higher-degree approach.
The authors tackled the problem of nonlinear Bayesian filtering by developing a class of higher-degree stochastic integration filters (SIF) that use stochastic spherical-radial integration rules to achieve asymptotically exact evaluations of Gaussian weighted multivariate integrals. The result showed that the proposed fifth-degree SIF outperformed existing stochastic, quasi-stochastic, and cubature filters in all cases.
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.