Square-Root Unscented Filtering and Smoothing

A square-root Kalman filter propagates the square-root (often the Cholesky factor) of the state covariance, rather than the full covariance matrix. Propagating these factors offers both computational efficiencies and greatly improved numerical properties. This paper introduces a new method of implementing the square-root unscented filter and the square-root unscented Rauch-Tung-Striebel smoother, which provide similar computational and numerical advantages over their traditional implementations. The new algorithms rely on the QR factorisation for calculating the covariance square-roots. A comparison with the previous development of the square-root unscented filter shows similar computational cost, while dramatically simplifying the implementation and improving numerical stability.