Numerically robust square root implementations of statistical linear regression filters and smoothers

TL;DR

This paper introduces a numerically robust square-root implementation of statistical linear regression filters and smoothers using QR decompositions, enhancing stability especially in low-precision computations.

Contribution

The authors develop a new square-root formulation that replaces Cholesky downdates with QR decompositions, improving numerical robustness over existing methods.

Findings

The QR-based method is more stable in ill-conditioned problems.

It outperforms traditional methods in both double and single precision.

The approach is particularly effective in low-precision arithmetic.

Abstract

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.