Factorized Partial-Update Schmidt–Kalman Filter

Abstract

This work develops a factorized version of the partial-update Schmidt–Kalman filter: a partial-update filter that operates on the covariance matrix modified Cholesky factors $U$ (the upper triangular factor) and $D$ (a diagonal factor) rather than on the error covariance matrix $\mathit{P}$ . Effectively, this new formulation combines the well-known numerical stability properties of the UD factorized Kalman filter with the enhanced tolerance to high nonlinearities and uncertainties of the partial-update filter. Two versions of the UD partial-update filter are presented: one for sequential measurement processing, delivering the most computationally efficient update, and another for the more convenient but slightly more expensive batch measurement update. Additionally, an implementation of the partial update for the multiplicative extended Kalman filter and the associated quaternion attitude representation is provided. The efficacy of the UD partial-update filter is demonstrated via numerical simulations and hardware experiments; the results show that the combined UD partial-update filter provides a more robust filtering capability than when either component is used individually.