  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.
