Algorithm 3 . UKF prediction step with FMU evaluations

1. ${\mathit{X}}_{k-1}=\left[{\widehat{\mathit{x}}}_{k-1},{\widehat{\mathit{X}}}_{k-1}+\gamma \sqrt{{\mathit{P}}_{k-1}^{+}},{\widehat{\mathit{X}}}_{k-1}-\gamma \sqrt{{\mathit{P}}_{k-1}^{+}}\right]$ for$i=1\mathrm{to}2\cdot n_{\mathit{x}}+1$do ${\left({\mathit{X}}_{k|k-1}\right)}_{:,i}={\mathit{f}}_{k|k-1}({({\mathit{X}}_{k-1})}_{:,i},{\mathit{u}}_{k-1})$ end for $${\widehat{\mathit{x}}}_k^{-}={\displaystyle \sum }_{i=0}^{2\cdot n}{\mathit{w}}_i^{\mathrm{m}}\cdot {\mathit{X}}_{k|k-1,i}$$ $${\mathit{P}}_k^{-}={\displaystyle \sum }_{i=0}^{2\cdot n}{\mathit{w}}_i^{\mathrm{c}}\cdot \left({\mathit{X}}_{k|k-1,i}-{\widehat{\mathit{x}}}_k^{-}\right){\left({\mathit{X}}_{k|k-1,i}-{\widehat{\mathit{x}}}_k^{-}\right)}^T+\mathit{Q}$$ $${\mathit{X}}_k^{’}=\left[{\widehat{\mathit{x}}}_k^{-},{\widehat{\mathit{X}}}_k^{-}+\gamma \sqrt{{\mathit{P}}_k^{-}},{\widehat{\mathit{X}}}_k^{-}-\gamma \sqrt{{\mathit{P}}_k^{-}}\right]$$ for$i=1\mathrm{to}2\cdot n_{\mathit{x}}+1$do  ${\left({\mathit{Y}}_k\right)}_{:,i}=\mathit{h}\left({\left({\mathit{X}}_k^{’}\right)}_{:,i}\right)$ end for $${\widehat{\mathit{y}}}_k^{-}={\displaystyle \sum }_{i=0}^{2\cdot n}{\mathit{w}}_i^{\mathrm{m}}\cdot {\mathit{Y}}_{k,i}$$