Kalman Filtering the Vasicek Model, are there different Kalman Filters for the same application?

Question

While studying parameter estimation in affine term structure models, I stumbeled across two papers.

1. Affine Term-Structure Models: Theory and Implementation by David Bolder (2001) https://www.researchgate.net/publication/4744752_Affine_Term-Structure_Models_Theory_and_Implementation
2. Calibration of the Vasicek Model of Interest rates Using Bicriteria Optimization by Jasurkova and Stehlikova (2020) http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1585

In both papers, a Kalman filter is implemented for the Vasicek model. In Bolder's work, for a 3-factor Vasicek model, and in Jasurkova and Stehlikova's work, a 1-factor Vasicek model. However, in my opinion, both methods should be independent of the number of factors. But upon closer inspection, there are a few differences, in addition to some different writing styles. When both present the necessary steps for implementing the Kalman filter, there are some discrepancies:

-In the first and second step, everythink agrees in both papers. When moving to the third step, however, things differ: Bolder writes in equation (74) the following:

$var[y_{t_i} \vert \mathcal{F}_{t_{i}}] = (I-K_{t_i}H)var[y_{t_i} \vert \mathcal{F}_{t_{i-1}}]$

whereas Jasurkova and Stehlikova state that: (page 214)

$Var[r_{t_i} \vert \mathcal{F}_{t_{i}}] = (I-K_{t_i}H)Var[R_{t_i} \vert \mathcal{F}_{t_{i-1}}]$

the small $y$ in Bolder's work corresponds to the small $r$, which are in both cases the short rates. And for the bond rates Bolder writes $z_{t_i}$ corresponding to $R_{t_i}$ in the work from Jasurkova and Stehlikova.

Proceeding to step 4, when the state vector/variable is updated things continue to differ:

Bolder writes:

$\mathbb{E}[y_{t_{i+1}} \vert \mathcal{F}_{t_{i}}] = C + F\mathbb{E}[y_{t_{i}} \vert \mathcal{F}_{t_{i}}]$

In the other paper it is written that:

$\mathbb{E}[r_{t_{i+1}} \vert \mathcal{F}_{t_{i+1}}] = C + F\mathbb{E}[r_{t_{i}} \vert \mathcal{F}_{t_{i}}]$

and for the conditional variance:

$var[y_{t_{i+1}} \vert \mathcal{F}_{t_{i}}] = var[y_{t_{i}} \vert \mathcal{F}_{t_{i-1}}]-Fvar[y_{t_{i}} \vert \mathcal{F}_{t_{i}}]F^T + Q$

$Var[r_{t_{i+1}} \vert \mathcal{F}_{t_{i}}] = FVar[r_{t_{i}} \vert \mathcal{F}_{t_{i}}]F^T + Q$

Additionally, the construction of the Likelihood function differs, beside the fact that Bolder uses the log-likelihood function:

Log-likelihood function by Bolder (equation (77)):

$l(\theta) = - \frac{nNln(2\pi)}{2}-\frac{1}{2} \sum_{i=1}^N [ln(det(var[y_{t_{i}} \vert \mathcal{F}_{t_{i-1}}])) + \zeta_{t_i}^{T}(var[y_{t_{i}} \vert \mathcal{F}_{t_{i-1}}]^{-1}\zeta_{t_i}]$

The Likelihood function by Jasurkova and Stehlikova:

$\mathcal{L}(\kappa,\theta,\sigma,\lambda) = \prod_{i=1}^n \frac{1}{(2 \pi )^{\frac{m}{2}} \vert Var[R_{t_i} \vert \mathcal{F}_{t_{i-1}}] \vert ^{\frac{1}{2}} } e^{-\frac{1}{2} \zeta_{t_i}^{T}Var[R_{t_i} \vert \mathcal{F}_{t_{i-1}}]^{-1}\zeta_{t_i}}$

In total, these differences should result in a completely different likelihood function (beside the log) and therefore also in a different output of the Kalman filter. My question now is whether there is a mistake in one of the papers? Or are there different Kalman filters that can explain these differences?