The J-Orthogonal Square-Root Fifth-Degree Cubature Kalman Filtering Method for Nonlinear Stochastic Systems
Gennady Yu. Kulikov, Maria Vyacheslavovna Kulikova · IFAC-PapersOnLine · 2020
This paper addresses the issue of square-rooting in the Fifth-Degree Cubature Kalman Filtering (5D-CKF) method grounded in the Itô-Taylor approximation of order 1.5 and designed by Santos-Diaz, Haykin and Hurd in 2018. That filter is rather accurate and efficient in treating nonlinear continuous-discrete stochastic systems of practical value and shown to outperform many other algorithms in a radar tacking scenario. However, the cited authors mention “the lack of a square-root implementation” of the filter under consideration as a principle shortcoming reducing its applied potential. Here, we address the reported lack and resolve it with a hyperbolic QR factorization used for devising the filter’s J-orthogonal square-root version, which possesses an exceptional robustness to round-off and other disturbances. Our square-root implementation of the 5D-CKF technique is justified theoretically and examined and compared numerically to its non-square-root predecessor in a flight control scenario with ill-conditioned measurements.