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Two Efficient Implementation Forms of Unscented Kalman Filter

Two efficient implementation forms of unscented Kalman filter (UKF) are proposed. They respectively utilize Cholesky factors and modified Cholesky factors to update state covariance. In these new forms, sequential measurement processing will be used. Van der Merwe's square root form of UKF is elaborated further. The computational complexity of all the forms for UKF are analysed. It is also shown that in some cases the UD U T form is faster than the standard UKF. Simulation examples are used to test all the forms' numerical robustness of covariance update and gain computation. It will be shown that the square root forms and the UDUT form have better numerical robustness than the standard form. Also it is demonstrated that for some problems the weight values of sigma points can influence the numerical robustness of UKF.