Table 2 UKF algorithm.

2:

\({X}_{t-1}=({\mu }_{t-1} {\mu }_{t-1}+\gamma \sqrt{{\sum }_{t-1} } {\mu }_{t-1}-\gamma \sqrt{{\sum }_{t-1}}\)

3:

\(\overline{{X }_{t}^{*}}=g({u}_{t},{X}_{t-1})\)

4:

\(\overline{{\mu }_{t}}=\sum_{i=0}^{2n}{w}_{m}^{[i]}{\overline{{X }_{t}^{*}}}^{[i]}\)

5:

\(\overline{{\sum }_{t} }=\sum_{i=0}^{2n}{w}_{c}^{\left[i\right]}\left({\overline{{X }_{t}^{*}}}^{\left[i\right]}-\overline{{\mu }_{t}}\right){\left({\overline{{X }_{t}^{*}}}^{\left[i\right]}-\overline{{\mu }_{t}}\right)}^{T}+{R}_{t}\)

6:

\(\overline{{X }_{t}}=(\overline{{\mu }_{t}} \overline{{\mu }_{t}}+\gamma \sqrt{\overline{{\sum }_{t} }} \overline{{\mu }_{t}}-\gamma \sqrt{\overline{{\sum }_{t} }})\)

7:

\(\overline{{Z }_{t}}=h(\overline{{X }_{t}})\)

8:

\(\widehat{{z}_{t}}=\sum_{i=0}^{2n}{w}_{m}^{[i]}{\overline{{Z }_{t}}}^{[i]}\)

9:

\({S}_{t}=\sum_{i=0}^{2n}{w}_{c}^{\left[i\right]}\left({\overline{{Z }_{t}}}^{\left[i\right]}-\widehat{{z}_{t}}\right){\left({\overline{{Z }_{t}}}^{\left[i\right]}-\widehat{{z}_{t}}\right)}^{T}+{Q}_{t}\)

10:

\({\overline{{\sum }_{t} }}^{x,z}=\sum_{i=0}^{2n}{w}_{c}^{\left[i\right]}\left({\overline{{X }_{t}^{*}}}^{\left[i\right]}-\overline{{\mu }_{t}}\right){\left({\overline{{Z }_{t}}}^{\left[i\right]}-\widehat{{z}_{t}}\right)}^{T}\)

11:

\({K}_{t}={\overline{{\sum }_{t} }}^{x,z}{S}_{t}^{-1}\)

12:

return SER \({\mu }_{t}=\overline{{\mu }_{t}}+{K}_{t}({z}_{t}-\widehat{{z}_{t}})\)

13:

\({\sum }_{t} =\overline{{\sum }_{t} }-{K}_{t}{S}_{t}{K}_{t}^{T}\)

14:

Return \({\mu }_{t},{\sum }_{t}\)