Iterative Sigmapoint (Unscented) Kalman Filter

Its the Sigmapoint (Unscented) Kalman Filter except instead of getting your posterior and moving onto the next timestep, take that posterior and turn it into your predicted prior and keep doing this until some threshold

In the Update Step ONLY

First iteration

$${\mathbf{\mu }}_z=\left[\begin{array}{c}{\check{\mathbf{x}}}_k\\ 0\end{array}\right]{\mathbf{\Sigma }}_{zz}=\left[\begin{array}{cc}{\check{\mathbf{P}}}_k& 0\\ 0& {\mathbf{R}}_k\end{array}\right]$$ $${\mathbf{x}}_{op,k}\leftarrow {\hat{\mathbf{x}}}_k$$

Second iteration

$${\mathbf{\mu }}_z=\left[\begin{array}{c}{\mathbf{x}}_{op,k}\\ 0\end{array}\right]{\mathbf{\Sigma }}_{zz}=\left[\begin{array}{cc}{\check{\mathbf{P}}}_k& 0\\ 0& {\mathbf{R}}_k\end{array}\right]$$ $${\mathbf{x}}_{op,k}\leftarrow {\hat{\mathbf{x}}}_k$$

Third iteration

$${\mathbf{\mu }}_z=\left[\begin{array}{c}{\mathbf{x}}_{op,k}\\ 0\end{array}\right]{\mathbf{\Sigma }}_{zz}=\left[\begin{array}{cc}{\check{\mathbf{P}}}_k& 0\\ 0& {\mathbf{R}}_k\end{array}\right]$$ $${\mathbf{x}}_{op,k}\leftarrow {\hat{\mathbf{x}}}_k$$

… Stop once $\Delta {\mathbf{x}}_{op,k}<threshold$