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arXiv · 2208.06452

A Square-Root Kalman Filter Using Only QR Decompositions

Kevin Tracy
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Abstract

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.

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Kevin Tracy. 2022-08-12. A Square-Root Kalman Filter Using Only QR Decompositions. https://arxiv.org/abs/2208.06452

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