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.

thanks