  A stable square-root approach has been recently proposed for the unscented
Kalman filter (UKF) and fifth-degree cubature Kalman filter (5D-CKF) as well as
for the mixed-type methods consisting of the extended Kalman filter (EKF) time
update and the UKF/5D-CKF measurement update steps. The mixed-type estimators
provide a good balance in trading between estimation accuracy and computational
demand because of the EKF moment differential equations involved. The key
benefit is a consolidation of reliable state mean and error covariance
propagation by using delicate discretization error control while solving the
EKF moment differential equations and an accurate measurement update according
to the advanced UKF and/or 5D-CKF filtering strategies. Meanwhile the drawback
of the previously proposed estimators is an utilization of sophisticated
numerical integration scheme with the built-in discretization error control
that is, in fact, a complicated and computationally costly tool. In contrast,
we design here the mixed-type methods that keep the same estimation quality but
reduce a computational time significantly. The novel estimators elegantly
utilize any MATLAB-based numerical integration scheme developed for solving
ordinary differential equations (ODEs) with the required accuracy tolerance
pre-defined by users. In summary, a simplicity of the suggested estimators,
their numerical robustness with respect to roundoff due to the square-root form
utilized as well as their estimation accuracy due to the MATLAB ODEs solvers
with discretization error control involved are the attractive features of the
novel estimators. The numerical experiments are provided for illustrating a
performance of the suggested methods in comparison with the existing ones.
