Step No.	Filtering Steps	The Equations Corresponding to the Filtering Steps
a	Set initial value based on the training data	${\mathit{L}}_1,{\mathit{P}}_1,{\mathit{r}}_1,{\mathit{R}}_1,{\mathit{q}}_1,{\mathit{Q}}_1,{\mathbf{\Gamma }}_1$
b	Calculation of weighting factors	$d_k=(1-b)/(1-b^{k+1})$
c	One-step forecast	${\hat{\mathit{L}}}_{k,k-1}={\mathbf{\Phi }}_{k,k-1}{\hat{\mathit{L}}}_{k-1}+{\hat{\mathit{q}}}_{k-1}$
d	One-step mean square error estimation	${\mathit{P}}_{k,k-1}={\mathbf{\Phi }}_{k,k-1}{\mathit{P}}_{k-1}{\mathbf{\Phi }}_{k,k-1}^T+{\hat{\mathit{Q}}}_{k-1}$
e	Filter residual variance estimation	${\hat{\mathit{r}}}_k=(1-d_k){\hat{\mathit{r}}}_{k-1}+d_k({\mathit{Z}}_k-{\mathbf{H}}_k{\hat{\mathit{L}}}_{k,k-1})$ ${\mathit{\nu }}_k={\mathit{Z}}_k-{\mathbf{H}}_k{\hat{\mathit{L}}}_{k,k-1}-{\hat{\mathit{r}}}_k$
f	Measurement noise estimation	${\hat{\mathit{R}}}_k=(1-{\displaystyle \frac{1}{k-1}}){\hat{\mathit{R}}}_{k-1}+{\displaystyle \frac{1}{2(k-1)}}{({\mathit{Z}}_k-{\mathit{Z}}_{k-1})}^2$
g	Calculating filter gain	${\mathit{K}}_k={\mathit{P}}_{k,k-1}{{\mathbf{H}}_k}^T{[{\mathbf{H}}_k{\mathit{P}}_{k,k-1}{{\mathbf{H}}_k}^T+{\hat{\mathit{R}}}_k]}^{-1}$
h	State estimation	${\hat{\mathit{L}}}_k={\hat{\mathit{L}}}_{k,k-1}+{\mathit{K}}_k[{\mathit{Z}}_k-{\mathbf{H}}_k{\hat{\mathit{L}}}_{k,k-1}]$
i	Mean square error estimation	${\mathit{P}}_k=[\mathit{I}-{\mathit{K}}_k{\mathbf{H}}_k]{\mathit{P}}_{k,k-1}$
j	Model accuracy discrimination	${\hat{\mathit{R}}}_k\le \eta [{\mathbf{H}}_k{\mathit{P}}_{k,k-1}{\mathbf{H}}_k^T+{\hat{\mathit{R}}}_k]$
k	Variance matching	${\mathit{\nu }}_k{\mathit{v}}_k^T>{\mathbf{H}}_k{\mathit{P}}_{k,k-1}{\mathbf{H}}_k^T+{\hat{\mathit{R}}}_k$
l	System noise estimate	${\hat{\mathit{q}}}_k=(1-d_k){\hat{\mathit{q}}}_{k-1}+d_k\left({\hat{\mathit{X}}}_k-{\mathbf{\Phi }}_{k,k-1}{\hat{\mathit{X}}}_{k-1}\right)$ ${\hat{\mathit{Q}}}_k=(1-d_k){\hat{\mathit{Q}}}_{k-1}+d_k({\mathit{K}}_k{\mathit{\nu }}_k{\mathit{\nu }}_k^T{\mathit{K}}_k^T+{\mathit{P}}_k-{\mathbf{\Phi }}_{k,k-1}{\mathit{P}}_{k-1}{\mathbf{\Phi }}_{k,k-1}^T)$