A Novel Fifth-Degree Cubature Kalman Filter Approaching the Lower Bound on the Number of Cubature Points

Abstract

In this paper, a novel fifth-degree cubature Kalman filter, which approaches the lower bound on the number of cubature points, is proposed to reduce the computational complexity while maintaining the fifth-degree filtering accuracy. The Gaussian weighted integral of a nonlinear function is approximated using a numerical cubature rule, whose number of cubature points needed is only one more than the theoretical lower bound, and the filter is deduced under the Bayesian filtering framework by this rule. Furthermore, a square-root version of the proposed fifth-degree cubature Kalman filter is given, and it acquires higher computational efficiency and ensures the numerical stability of the filter. Three numerical simulations are taken, and the results show that the proposed filters maintain the fifth-degree filtering accuracy, while needing the least amount of computation and achieving the best real-time performance.