Latent AR processes and observed linear combinations

I have a model where there several latent unbserved AR processes with normal errors:

x1[t] = mu1 + \theta_1 * x1[t-1] + error_x1
x2[t] = mu2 + \theta_2 * x2[t-1] + error_x2
x3[t] = mu3 + \theta_3 * x3[t-1] + error_x3

and observations where each is a linear combination of two of them (it depend on what data we have) plus normal error:

y1[t] = \beta_1 * x1[t] + \gamma_1 * x2[t] + error_y1
y2[t] = \beta_2 * x2[t] + \gamma_2 * x3[t] + error_y2
y3[t] = \beta_3 * x3[t] + \gamma_3 * x1[t] + error_y3

I want to infer the latent processes.
Is there a way to model this? I have tried some option but never able to fit it.


It looks like there is some nice, intuitive documentation for this in the Stan User’s Guide

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