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.

最近，针对无味卡尔曼滤波器（UKF）和五度容积卡尔曼滤波器（5D-CKF）以及由扩展卡尔曼滤波器（EKF）时间更新组成的混合类型方法，提出了一种稳定的平方根方法。以及UKF / 5D-CKF测量更新步骤。由于涉及到EKF矩微分方程，因此混合类型的估计器在估计精度和计算需求之间提供了一个很好的平衡。关键优势在于，通过使用精细的离散化误差控制，同时解决EKF矩微分方程，并根据先进的UKF和/或5D-CKF滤波策略进行准确的测量更新，可以巩固可靠的状态均值和误差协方差传播。同时，先前提出的估计器的缺点是利用具有内置离散误差控制的复杂的数值积分方案，这实际上是一种复杂且计算上昂贵的工具。相反，我们在这里设计了混合类型的方法，这些方法可以保持相同的估计质量，但可以显着减少计算时间。新颖的估算器可以优雅地利用为解决常微分方程（ODE）而开发的任何基于MATLAB的数值积分方案，并具有用户预先定义的所需精度公差。总而言之，建议的估算器非常简单，由于使用了平方根形式，因此它们对于舍入的数值鲁棒性以及由于具有离散化误差控制的MATLAB ODE解算器而产生的估计精度是新颖估计器的吸引人的特征。数值实验用于说明所建议方法与现有方法相比的性能。