Algorithm 2 uKF algorithm description.

Require: ${\mathit{z}}_t$, for $t=0,\dots ,T-1$, $\mathit{Q}$, $\mathit{C}$, $\mathit{S}$

1: Initialization: ${\widehat{\mathit{x}}}_{0|0}\leftarrow \left(15\right)$, ${\widehat{P}}_0\leftarrow \left(16\right)$, ${\widehat{\mathbf{\theta }}}_{0|0}\leftarrow {[{\widehat{\mathit{x}}}_{0|0}^T,0,0]}^T$, ${\widehat{\mathbf{\Sigma }}}_{0|0}\leftarrow {\mathit{I}}_4$

2: for $t=1,\dots ,T-1$ do

3:  Prediction:

4:    $\begin{array}{c}•{\widehat{\mathbf{\theta }}}_{t|t-1}\leftarrow (22\mathrm{a})\hfill \\ •{\widehat{\mathbf{\Sigma }}}_{t|t-1}\leftarrow (22\mathrm{b})\end{array}$

5:  ${\mathit{K}}_t\leftarrow {\widehat{\mathbf{\Sigma }}}_{t|t-1}{\mathit{G}}_t^T{({\mathit{G}}_t{\widehat{\mathbf{\Sigma }}}_{t|t-1}{\mathit{G}}_t^T+\mathit{C})}^{-1}$

6:  Update:

7:    $\begin{array}{l}•{\widehat{\mathbf{\theta }}}_{t|t}\leftarrow \left(26\mathrm{a}\right)\\ •{\widehat{\mathbf{\Sigma }}}_{t|t}\leftarrow \left(26\mathrm{b}\right)\\ •{\widehat{P}}_0\leftarrow \left(16\right)\end{array}$

8: end for