Can dynare solve the latent gaussian process

Hello, I’m a newbie in Dynare. Except for DSGE model, I want to know whether Dynare can solve the latent Gaussian model. I have the model about this:
And x_{1t},x_{2t},x_{3t} are latent variables, they have the distribution:
x_{1t} \sim Normal(\mu_1,\sigma_1)
x_{2t} \sim Normal(\mu_2,\sigma_2)
x_{3t} \sim Normal(\mu_3,\sigma_3)
I only have observations y_t,
can I estimate the parameters \mu_1,\mu_2,\mu_3,\sigma_1,\sigma_2,\sigma_3,cr?
The model can estimate using Kalman filter. Can I use Dynare to make it come true?
Some suggestions?

Or I want to complete the model like this:

y_{t} = a+ Bs_t+u_t
s_t =Gs_{t-1}+ e_t
y_t is a 10 \times 1 vector of observables at time t. s_t is a 5 \times 1 vector of time-t unobserved (latent) states

I need the Tarb_MH algorithm in Dynare to calculate latent Gaussian process model (State space model)(Siddhartha Chib, Srikanth Ramamurthy,2010)
Tailored randomized block MCMC methods with application to DSGE models - ScienceDirect

What do you mean with

? I guess you want to estimate the model. Why are you thinking about the TaRB-MH? Because the model will be multi-modal?

Thanks for your reply~
Kalman filter can solve this problem. So I want to estimate it using the Bayesian method. I have used the NUTS algorithm, and I found that the posterior has lots of divergences. And I find the TaRB-MH algorithm can estimate this latent gaussian model.
I don’t understand the multi-modal means. Actually, I have two different observations(y_1 is 5 \times 293 matrix, y2 is 5 \times 293 matrix, I combine two observations to a y is 10 \times 293 matrix). I think these two observations have common factors (use the latent variables). at the same time, they have a special factor for themselves (use the latent variables). matrix B with parameters to describe this relationship.

You can definitely give it a try. The Slice sampler in Dynare may also be an option.

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Very Thanks~