Algorithm 1: Compute state and error covariance time update

$for i=1 to N_s$ $\left\{x_{ekf}\left[i\right]=A\left[i\right]\ast x_{ekf}\left[i\right]+u_{k-1}\right\}$ $for i=1 to N_s$ $\{for j=1 to N_s$ $\{{\sigma }_x\left[i\right]\left[j\right]=A\left[i\right]\ast A\left[j\right]\ast {\sigma }_x\left[i\right]\left[j\right]+{\sigma }_w\left[i\right]\left[j\right]\}\}$