This work develops a factorized version of the partial-update Schmidt–Kalman filter: a partial-update filter that operates on the covariance matrix modified Cholesky factors $U$ (the upper triangular factor) and $D$ (a diagonal factor) rather than on the error covariance matrix $\mathit{P}$. Effectively, this new formulation combines the well-known numerical stability properties of the UD factorized Kalman filter with the enhanced tolerance to high nonlinearities and uncertainties of the partial-update filter. Two versions of the UD partial-update filter are presented: one for sequential measurement processing, delivering the most computationally efficient update, and another for the more convenient but slightly more expensive batch measurement update. Additionally, an implementation of the partial update for the multiplicative extended Kalman filter and the associated quaternion attitude representation is provided. The efficacy of the UD partial-update filter is demonstrated via numerical simulations and hardware experiments; the results show that the combined UD partial-update filter provides a more robust filtering capability than when either component is used individually.

这项工作开发了部分更新 Schmidt-Kalman 滤波器的分解版本：一种对协方差矩阵修改的 Cholesky 因子进行操作的部分更新滤波器$ü$（上三角因子）和$D$（对角线因子）而不是误差协方差矩阵$\mathit{磷}$. 有效地，这个新公式结合了 UD 分解卡尔曼滤波器众所周知的数值稳定性特性与部分更新滤波器对高非线性和不确定性的增强容忍度。提供了两个版本的 UD 部分更新过滤器：一个用于顺序测量处理，提供计算效率最高的更新，另一个用于更方便但稍微昂贵的批量测量更新。此外，还提供了乘法扩展卡尔曼滤波器和相关四元数姿态表示的部分更新的实现。通过数值模拟和硬件实验证明了UD部分更新滤波器的功效；