In this article, square-root formulations of the statistical linear regression filter and smoother are developed. Crucially, the method uses QR decompositions rather than Cholesky downdates. This makes the method inherently more numerically robust than the downdate based methods, which may fail in the face of rounding errors. This increased robustness is demonstrated in an ill-conditioned problem, where it is compared against a reference implementation in both double and single precision arithmetic. The new implementation is found to be more robust, when implemented in lower precision arithmetic as compared to the alternative.

翻译：本文提出了统计线性回归滤波器与平滑器的平方根形式。该方法的关键在于使用QR分解而非Cholesky降阶更新，从而在数值上固有地比基于降阶更新的方法更为鲁棒——后者在舍入误差面前可能失效。通过一个病态问题的实验，在双精度与单精度算术下与参考实现进行对比，验证了这种增强的鲁棒性。结果表明，在较低精度算术实现时，新方法相比替代方案具有更好的鲁棒性。