# A Square-Root Kalman Filter Using Only QR Decompositions

arXiv: https://arxiv.org/abs/2208.06452 · HTML: https://mlsanity.com/paper/2208.06452/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2022.

## Built on by (most cited first, 1 of 1)

- [Martingale Posterior Neural Networks for Fast Sequential Decision Making](https://mlsanity.com/paper/2506.11898/) (2025)

## Abstract (arXiv)

The Kalman filter operates by storing a Gaussian description of the state estimate in the form of a mean and covariance. Instead of storing and manipulating the covariance matrix directly, a square-root Kalman filter only forms and updates a triangular matrix square root of the covariance matrix. The resulting algorithm is more numerically stable than a traditional Kalman filter, benefiting from double the working precision. This paper presents a formulation of the square root Kalman filter that leverages the QR decomposition to dramatically simplify the resulting algorithm.